WorldWideScience

Sample records for superspaces exact solutions

  1. Exact propagators in harmonic superspace

    Science.gov (United States)

    Kuzenko, Sergei M.

    2004-10-01

    Within the background field formulation in harmonic superspace for quantum N = 2 super-Yang-Mills theories, the propagators of the matter, gauge and ghost superfields possess a complicated dependence on the SU(2) harmonic variables via the background vector multiplet. This dependence is shown to simplify drastically in the case of an on-shell vector multiplet. For a covariantly constant background vector multiplet, we exactly compute all the propagators. In conjunction with the covariant multi-loop scheme developed in arxiv:hep-th/0302205, these results provide an efficient (manifestly N = 2 supersymmetric) technical setup for computing multi-loop quantum corrections to effective actions in N = 2 supersymmetric gauge theories, including the N = 4 super-Yang-Mills theory.

  2. Exact propagators in harmonic superspace

    CERN Document Server

    Kuzenko, S M

    2004-01-01

    Within the background field formulation in harmonic superspace for quantum N = 2 super Yang-Mills theories, the propagators of the matter, gauge and ghost superfields possess a complicated dependence on the SU(2) harmonic variables via the background vector multiplet. This dependence is shown to simplify drastically in the case of an on-shell vector multiplet. For a covariantly constant background vector multiplet, we exactly compute all the propagators. In conjunction with the covariant multi-loop scheme developed in hep-th/0302205, these results provide an efficient (manifestly N = 2 supersymmetric) technical setup for computing multi-loop quantum corrections to effective actions in N = 2 supersymmetric gauge theories, including the N = 4 super Yang-Mills theory.

  3. Superspace

    CERN Document Server

    Zumino, B

    1980-01-01

    Superspace is an extension of ordinary space-time. Its points are labelled not only by commuting bosonic (vectorial) co-ordinates but also in addition by anticommuting fermionic (spinorial) co-ordinates. Superspace gives a geometric picture of supersymmetry and provides a technique for finding representations of the supersymmetry algebra by fields. The author gives first a brief discussion of rigid (flat) superspace which has rigid supersymmetry as a group of motions. Then curved flexible superspace is discussed. The latter is relevant to a geometric description of supergravity. (17 refs).

  4. Exact Solutions to Maccari's System

    Institute of Scientific and Technical Information of China (English)

    PAN Jun-Ting; GONG Lun-Xun

    2007-01-01

    Based on the generalized Riccati relation, an algebraic method to construct a series of exact solutions to nonlinear evolution equations is proposed. Being concise and straightforward, the method is applied to Maccari's system, and some exact solutions of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations.

  5. Black holes and Rindler superspace: classical singularity and quantum unitarity

    CERN Document Server

    Chou, C H; Yu, H L; Chou, Chung-Hsien; Soo, Chopin; Yu, Hoi-Lai

    2007-01-01

    Canonical quantization of spherically symmetric initial data which is appropriate to classical interior black hole solutions in four dimensions is carried out and solved exactly without gauge fixing. The resultant mini-superspace manifold and arena for quantum geometrodynamics is two-dimensional, of signature (+, -), non-singular, and can in fact be identified precisely with the first Rindler wedge. The associated Wheeler-DeWitt equation with evolution in intrinsic superspace time can be formulated as a free massive Klein-Gordon equation; and the Hamilton-Jacobi semiclassical limit of plane wave solutions can be matched precisely to the interiors of Schwarzschild black holes. Furthermore, classical black hole horizons and singularities correspond to the boundaries of the Rindler wedge. Exact wavefunctions of the first-order-in-superspace intrinsic time Dirac equation are also considered. Precise correspondence between Schwarzschild black holes and free particle mechanics in superspace is noted. Another intrig...

  6. Exact solution for generalized pairing

    OpenAIRE

    Pan, Feng; J.P. Draayer

    1997-01-01

    An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with some numerical examples.

  7. Exact cosmological solutions for MOG

    Energy Technology Data Exchange (ETDEWEB)

    Roshan, Mahmood [Ferdowsi University of Mashhad, Department of Physics, P.O. Box 1436, Mashhad (Iran, Islamic Republic of)

    2015-09-15

    We find some new exact cosmological solutions for the covariant scalar-tensor-vector gravity theory, the so-called modified gravity (MOG). The exact solution of the vacuum field equations has been derived. Also, for non-vacuum cases we have found some exact solutions with the aid of the Noether symmetry approach. More specifically, the symmetry vector and also the Noether conserved quantity associated to the point-like Lagrangian of the theory have been found. Also we find the exact form of the generic vector field potential of this theory by considering the behavior of the relevant point-like Lagrangian under the infinitesimal generator of the Noether symmetry. Finally, we discuss the cosmological implications of the solutions. (orig.)

  8. Exact analytical solutions for ADAFs

    CERN Document Server

    Habibi, Asiyeh; Shadmehri, Mohsen

    2016-01-01

    We obtain two-dimensional exact analytic solutions for the structure of the hot accretion flows without wind. We assume that the only non-zero component of the stress tensor is $T_{r\\varphi}$. Furthermore we assume that the value of viscosity coefficient $\\alpha$ varies with $\\theta$. We find radially self-similar solutions and compare them with the numerical and the analytical solutions already studied in the literature. The no-wind solution obtained in this paper may be applied to the nuclei of some cool-core clusters.

  9. Superspace version of BF theories

    Energy Technology Data Exchange (ETDEWEB)

    Aidaoui, A.; Tahiri, M. [Laboratoire de Physique Theorique, Universite d' Oran Es-senia, 31100 Oran (Algeria)

    2012-06-27

    The BF theory is presented in a superspace formalism. This permits us to see that the necessary fields of the quantized theory enlarged with auxiliary fields naturally occur and lead to a BRST-VSUY exact quantum action.

  10. Collinear Superspace

    CERN Document Server

    Cohen, Timothy; Larkoski, Andrew J

    2016-01-01

    This letter provides a superfield based approach to constructing a collinear slice of $\\mathcal{N}$ = 1 superspace. The strategy is analogous to integrating out anti-collinear fermionic degrees-of-freedom as was developed in the context of soft-collinear effective theory. The resulting Lagrangian can be understood as an integral over collinear superspace, where half the supercoordinates have been integrated out. The application to $\\mathcal{N}$ = 1 super Yang-Mills is presented. Collinear superspace provides the foundation for future explorations of supersymmetric soft-collinear effective theory.

  11. Multi-dimensional classical and quantum cosmology: Exact solutions, signature transition and stabilization

    CERN Document Server

    Jalalzadeh, S; Sepangi, H R

    2003-01-01

    We study the classical and quantum cosmology of a $(4+d)$-dimensional spacetime minimally coupled to a scalar field and present exact solutions for the resulting field equations for the case where the universe is spatially flat. These solutions exhibit signature transition from a Euclidean to a Lorentzian domain and lead to stabilization of the internal space, in contrast to the solutions which do not undergo signature transition. The corresponding quantum cosmology is described by the Wheeler-DeWitt equation which has exact solutions in the mini-superspace, resulting in wavefunctions peaking around the classical paths. Such solutions admit parametrizations corresponding to metric solutions of the field equations that admit signature transition.

  12. Exact Solutions in Modified Gravity Models

    Directory of Open Access Journals (Sweden)

    Valery V. Obukhov

    2012-06-01

    Full Text Available We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations. In this paper we consider a number of exact solutions obtained by the method of separation of variables. Some applications to Cosmology and BH entropy are briefly mentioned.

  13. Exact Solutions in Modified Gravity Models

    CERN Document Server

    Makarenko, Andrey N

    2012-01-01

    We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations. In this paper we consider a number of exact solutions obtained by the method of separation of variables. Some applications to Cosmology and BH entropy are briefly mentioned.

  14. Weyl Superspace

    CERN Document Server

    Howe, Paul S

    1997-01-01

    It is shown that the equations of motion of eleven-dimensional supergravity follow from setting the dimension zero components of the superspace torsion tensor equal to the Dirac matrices. The proof of this assertion is facilitated by the introduction of a connection taking its values in the Lie algebra of $Spin(1,10)\\times R^+$.

  15. Exact Solutions for Einstein's Hyperbolic Geometric Flow

    Institute of Scientific and Technical Information of China (English)

    HE Chun-Lei

    2008-01-01

    In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow.

  16. New exact solutions in standard inflationary models

    CERN Document Server

    Chervon, S V; Shchigolev, V K

    1997-01-01

    The exact solutions in the standard inflationary model based on the self-interacting scalar field minimally coupled to gravity are considered. The shape's freedom of the self-interacting potential $V(\\phi)$ is postulated to obtain a new set of the exact solutions in the framework of Friedmann-Robertson-Walker Universes. The general solution was found in the case of power law inflation. We obtained new solutions and compared them with obtained ones earlir for the exponential type inflation.

  17. Howe duality in Dunkl superspace

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    In the framework of superspace in Clifford analysis for the Dunkl version, the Fischer decomposition is established for solutions of the Dunkl super Dirac operators. The result is general without restrictions on multiplicity functions or on super dimensions. The Fischer decomposition provides a module for the Howe dual pair G × osp(1|2) on the space of spinor valued polynomials with G the Coxeter group, while the generators of the Lie superspace reveal the naturality of the Fischer decomposition.

  18. Exact solutions in three-dimensional gravity

    CERN Document Server

    Garcia-Diaz, Alberto A

    2017-01-01

    A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...

  19. New exact wave solutions for Hirota equation

    Indian Academy of Sciences (India)

    M Eslami; M A Mirzazadeh; A Neirameh

    2015-01-01

    In this paper, we construct the topological or dark solitons of Hirota equation by using the first integral method. This approach provides first integrals in polynomial form with a high accuracy for two-dimensional plane autonomous systems. Exact soliton solution is constructed through the established first integrals. This method is a powerful tool for searching exact travelling solutions of nonlinear partial differential equations (NPDEs) in mathematical physics.

  20. On exact solutions of the Bogoyavlenskii equation

    Indian Academy of Sciences (India)

    Yan-Ze Peng; Ming Shen

    2006-09-01

    Exact solutions for the Bogoyavlenskii equation are studied by the travelling wave method and the singular manifold method. It is found that the linear superposition of the shock wave solution and the complex solitary wave solution for the physical field is still a solution of the equation of interest, except for a phase-shift. The dromion-like structures with elastic and nonelastic interactions are found.

  1. Exact Solutions in Nonlocal Linear Models

    OpenAIRE

    Vernov, S. Yu.

    2008-01-01

    A general class of cosmological models driven by a nonlocal scalar field inspired by the string field theory is studied. Using the fact that the considering linear nonlocal model is equivalent to an infinite number of local models we have found an exact special solution of the nonlocal Friedmann equations. This solution describes a monotonically increasing Universe with the phantom dark energy.

  2. Classes of exact Einstein Maxwell solutions

    Science.gov (United States)

    Komathiraj, K.; Maharaj, S. D.

    2007-12-01

    We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

  3. Exact solution to fractional logistic equation

    Science.gov (United States)

    West, Bruce J.

    2015-07-01

    The logistic equation is one of the most familiar nonlinear differential equations in the biological and social sciences. Herein we provide an exact solution to an extension of this equation to incorporate memory through the use of fractional derivatives in time. The solution to the fractional logistic equation (FLE) is obtained using the Carleman embedding technique that allows the nonlinear equation to be replaced by an infinite-order set of linear equations, which we then solve exactly. The formal series expansion for the initial value solution of the FLE is shown to be expressed in terms of a series of weighted Mittag-Leffler functions that reduces to the well known analytic solution in the limit where the fractional index for the derivative approaches unity. The numerical integration to the FLE provides an excellent fit to the analytic solution. We propose this approach as a general technique for solving a class of nonlinear fractional differential equations.

  4. Exact solutions for nonlinear foam drainage equation

    Science.gov (United States)

    Zayed, E. M. E.; Al-Nowehy, Abdul-Ghani

    2016-09-01

    In this paper, the modified simple equation method, the exp-function method, the soliton ansatz method, the Riccati equation expansion method and the ( G^' }/G) -expansion method are used to construct exact solutions with parameters of the nonlinear foam drainage equation. When these parameters are taken to be special values, the solitary wave solutions and the trigonometric function solutions are derived from the exact solutions. The obtained results confirm that the proposed methods are efficient techniques for analytic treatments of a wide variety of nonlinear partial differential equations in mathematical physics. We compare our results together with each other yielding from these integration tools. Also, our results have been compared with the well-known results of others.

  5. Exact solutions for nonlinear foam drainage equation

    Science.gov (United States)

    Zayed, E. M. E.; Al-Nowehy, Abdul-Ghani

    2017-02-01

    In this paper, the modified simple equation method, the exp-function method, the soliton ansatz method, the Riccati equation expansion method and the ( G^' }/G)-expansion method are used to construct exact solutions with parameters of the nonlinear foam drainage equation. When these parameters are taken to be special values, the solitary wave solutions and the trigonometric function solutions are derived from the exact solutions. The obtained results confirm that the proposed methods are efficient techniques for analytic treatments of a wide variety of nonlinear partial differential equations in mathematical physics. We compare our results together with each other yielding from these integration tools. Also, our results have been compared with the well-known results of others.

  6. EXACT SOLUTIONS TO NONLINEAR WAVE EQUATION

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    In this paper,we use an invariant set to construct exact solutions to a nonlinear wave equation with a variable wave speed. Moreover,we obtain conditions under which the equation admits a nonclassical symmetry. Several different nonclassical symmetries for equations with different diffusion terms are presented.

  7. Exact Vacuum Solutions to the Einstein Equation

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    In this paper, the author presents a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations,which are much convenient for the resolution.

  8. Solitons in nonlocal nonlinear media: Exact solutions

    DEFF Research Database (Denmark)

    Krolikowski, Wieslaw; Bang, Ole

    2001-01-01

    We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties...

  9. EXACT SOLUTIONS OF A DIPOLAR FLUID FLOW

    Institute of Scientific and Technical Information of China (English)

    T. HAYAT

    2003-01-01

    Exact solutions for three canonical flow problems of a dipolar fluid are obtained: (i)The flow of a dipolar fluid due to a suddenly accelerated plate, (ii) The flow generated by periodic oscillation of a plate, (iii) The flow due to plate oscillation in the presence of a transverse magnetic field. The solutions of some interesting flows caused by an arbitrary velocity of the plate and of certain special oscillations are also obtained.

  10. Exact cosmological solutions from Hojman conservation quantities

    Energy Technology Data Exchange (ETDEWEB)

    Capozziello, Salvatore, E-mail: capozzie@na.infn.it [Dipartimento di Fisica, Università di Napoli “Federico II”, Napoli (Italy); INFN Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli (Italy); Roshan, Mahmood, E-mail: rowshan@alumni.ut.ac.ir [Department of Physics, Ferdowsi University of Mashhad, P.O. Box 1436, Mashhad (Iran, Islamic Republic of)

    2013-10-07

    We present a new approach to find exact solutions for cosmological models. By requiring the existence of a symmetry transformation vector for the equations of motion of the given cosmological model (without using either Lagrangian or Hamiltonian), one can find corresponding Hojman conserved quantities. With the help of these conserved quantities, the analysis of the cosmological model can be simplified. In the case of quintessence scalar–tensor models, we show that the Hojman conserved quantities exist for a wide range of V(ϕ)-potentials and allow to find exact solutions for the cosmic scale factor and the scalar field. Finally, we investigate the general cosmological behavior of solutions by adopting a phase-space view.

  11. Exact cosmological solutions from Hojman conservation quantities

    CERN Document Server

    Capozziello, Salvatore

    2013-01-01

    We present a new approach to find exact solutions for cosmological models. By requiring the existence of a symmetry transformation vector for the equations of motion of the given cosmological model (without using either Lagrangian or Hamiltonian), one can find corresponding Hojman conserved quantities. With the help of these conserved quantities, the analysis of the cosmological model can be simplified. In the case of quintessence scalar-tensor models, we show that the Hojman conserved quantities exist for a wide range of V(\\phi)-potentials and allow to find exact solutions for the cosmic scale factor and the scalar field. Finally, we investigate the general cosmological behavior of solutions by adopting a phase-space view.

  12. Exact solution of phantom dark energy model

    Institute of Scientific and Technical Information of China (English)

    Wang Wen-Fu; Shui Zheng-Wei; Tang Bin

    2010-01-01

    We investigate the phantom dark energy model derived from the scalar field with a negative kinetic term. By assuming a particular relation between the time derivative of the phantom field and the Hubble function, an exact solution of the model is constructed. Absence of the 'big rip' singularity is shown explicitly. We then derive special features of phantom dark energy model and show that its predictions are consistent with all astrophysical observations.

  13. Exact solutions for Weyl fermions with gravity

    Energy Technology Data Exchange (ETDEWEB)

    Cianci, Roberto; Fabbri, Luca; Vignolo, Stefano [Universita di Genova, DIME Sez. Metodi e Modelli Matematici, Genoa (Italy)

    2015-10-15

    We consider the single-handed spinor field in interaction with its own gravitational field described by the set of field equations given by the Weyl field equations written in terms of derivatives that are covariant with respect to the gravitational connection plus Einstein field equations soured with the energy tensor of the spinor: for the Weyl spinor and the ensuing spacetime of Weyl-Lewis-Papapetrou structure, we find all exact solutions. The obtained solution for the metric tensor is that of a PP-wave spacetime, while the spinor field is a flag-dipole. (orig.)

  14. Nonuniform Braneworld Stars: AN Exact Solution

    Science.gov (United States)

    Ovalle, J.

    In this paper the first exact interior solution to Einstein's field equations for a static and nonuniform braneworld star with local and nonlocal bulk terms is presented. It is shown that the bulk Weyl scalar U(r) is always negative inside the stellar distribution, and in consequence it reduces both the effective density and the effective pressure. It is found that the anisotropy generated by bulk gravity effect has an acceptable physical behavior inside the distribution. Using a Reissner-Nördstrom-like exterior solution, the effects of bulk gravity on pressure and density are found through matching conditions.

  15. Submerged Landau jet: exact solutions, their meaning and application

    Energy Technology Data Exchange (ETDEWEB)

    Broman, Goran I [Blekinge Institute of Technology, Karlskrona (Sweden); Rudenko, Oleg V [M. V. Lomonosov Moscow State University, Faculty of Physics, Moscow (Russian Federation)

    2010-01-31

    Exact hydrodynamic solutions generalizing the Landau submerged jet solution are reviewed. It is shown how exact inviscid solutions can be obtained and how boundary layer viscosity can be included by introducing parabolic coordinates. The use of exact solutions in applied hydrodynamics and acoustics is discussed. A historical perspective on the discovery of a class of exact solutions and on the analysis of their physical meaning is presented. (methodological notes)

  16. On exact solutions of modified KdV-ZK equation

    Directory of Open Access Journals (Sweden)

    Syed Tauseef Mohyud-Din

    2016-12-01

    Full Text Available In this work, we established some exact particular solutions with parameters for Modified KdV-ZK Equation. The improved tanϕ(ξ2-expansion method is introduced to construct exact particular solutions of nonlinear evolution equations. The exact particular solutions contain four types: hyperbolic function solution, trigonometric function solution, exponential solution, and rational solution. The method appears to be effective mathematical tool for solving nonlinear evolution equations (NLEEs in applied mathematics and engineering.

  17. Exact Solution and Exotic Fluid in Cosmology

    Directory of Open Access Journals (Sweden)

    Phillial Oh

    2012-09-01

    Full Text Available We investigate cosmological consequences of nonlinear sigma model coupled with a cosmological fluid which satisfies the continuity equation. The target space action is of the de Sitter type and is composed of four scalar fields. The potential which is a function of only one of the scalar fields is also introduced. We perform a general analysis of the ensuing cosmological equations and give various critical points and their properties. Then, we show that the model exhibits an exact cosmological solution which yields a transition from matter domination into dark energy epoch and compare it with the Λ-CDM behavior. Especially, we calculate the age of the Universe and show that it is consistent with the observational value if the equation of the state ωf of the cosmological fluid is within the range of 0.13 < ωf < 0.22. Some implication of this result is also discussed.

  18. Exact Spherically Symmetric Solutions in Massive Gravity

    CERN Document Server

    Berezhiani, Z; Nesti, F; Pilo, L

    2008-01-01

    A phase of massive gravity free from pathologies can be obtained by coupling the metric to an additional spin-two field. We study the gravitational field produced by a static spherically symmetric body, by finding the exact solution that generalizes the Schwarzschild metric to the case of massive gravity. Besides the usual 1/r term, the main effects of the new spin-two field are a shift of the total mass of the body and the presence of a new power-like term, with sizes determined by the mass and the shape (the radius) of the source. These modifications, being source dependent, give rise to a dynamical violation of the Strong Equivalence Principle. Depending on the details of the coupling of the new field, the power-like term may dominate at large distances or even in the ultraviolet. The effect persists also when the dynamics of the extra field is decoupled.

  19. A Family of Exact Solutions for the Nonlinear Schrodinger Equation

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    In this paper, the nonlinear Schrodinger (NLS) equation was analytically solved. Firstly, the stationary solutions of NLSequation were explicitly given by the elliptic functions. Then a family of exact solutions of NLS equation were obtained from these sta-tionary solutions by a method for finding new exact solutions from the stationary solutions of integrable evolution equations.

  20. New Approach to Find Exact Solutions to Classical Boussinesq System

    Institute of Scientific and Technical Information of China (English)

    ZHI Hong-Yan; ZHAO Xue-Qin; ZHANG Hong-Qing

    2005-01-01

    In this paper, based on a new system of three Riccati equations, we give a new method to construct more new exact solutions of nonlinear differential equations in mathematical physics. The classical Boussinesq system is chosen to illustrate our method. As a consequence, more families of new exact solutions are obtained, which include solitary wave solutions and periodic solutions.

  1. Time-dependent exact solutions of the nonlinear Kompaneets equation

    Energy Technology Data Exchange (ETDEWEB)

    Ibragimov, N H, E-mail: nib@bth.s [Department of Mathematics and Science, Blekinge Institute of Technology, 371 79 Karlskrona (Sweden)

    2010-12-17

    Time-dependent exact solutions of the Kompaneets photon diffusion equation are obtained for several approximations of this equation. One of the approximations describes the case when the induced scattering is dominant. In this case, the Kompaneets equation has an additional symmetry which is used for constructing some exact solutions as group invariant solutions. (fast track communication)

  2. Comments on Noncommutative Superspace

    CERN Document Server

    Terashima, S; Terashima, Seiji; Yee, Jung-Tay

    2003-01-01

    We study the N=1/2 supersymmetric theory on noncommutative superspace found by Seiberg which is a deformation of usual superspace. We consider deformed Wess-Zumino model as an example and shows vanishing of vacuum energy, renormalization of superpotential and nonvanishing of tadpole. We find that the perturbative effective action has terms which are not written in the star deformation. Also we consider gauge theory on noncommutative superspace and observe that gauge group is restricted. We generalize the star deformation to include noncommutativity between bosonic coordinates and fermionic coordinates.

  3. Exact Periodic Solitary Solutions to the Shallow Water Wave Equation

    Institute of Scientific and Technical Information of China (English)

    LI Dong-Long; ZHAO Jun-Xiao

    2009-01-01

    Exact solutions to the shallow wave equation are studied based on the idea of the extended homoclinic test and bilinear method. Some explicit solutions, such as the one soliton solution, the doubly-periodic wave solution and the periodic solitary wave solutions, are obtained. In addition, the properties of the solutions are investigated.

  4. Exact solutions to the generalized Lienard equation and its applications

    Indian Academy of Sciences (India)

    Yang Xian-Lin; Tang Jia-Shi

    2008-12-01

    Some new exact solutions of the generalized Lienard equation are obtained, and the solutions of the equation are applied to solve nonlinear wave equations with nonlinear terms of any order directly. The generalized one-dimensional Klein–Gordon equation, the generalized Ablowitz (A) equation and the generalized Gerdjikov–Ivanov (GI) equation are investigated and abundant new exact travelling wave solutions are obtained that include solitary wave solutions and triangular periodic wave solutions.

  5. Exact solution of the robust knapsack problem☆

    Science.gov (United States)

    Monaci, Michele; Pferschy, Ulrich; Serafini, Paolo

    2013-01-01

    We consider an uncertain variant of the knapsack problem in which the weight of the items is not exactly known in advance, but belongs to a given interval, and an upper bound is imposed on the number of items whose weight differs from the expected one. For this problem, we provide a dynamic programming algorithm and present techniques aimed at reducing its space and time complexities. Finally, we computationally compare the performances of the proposed algorithm with those of different exact algorithms presented so far in the literature for robust optimization problems. PMID:24187428

  6. Exact periodic wave solutions for some nonlinear partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    El-Wakil, S.A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt); Elgarayhi, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: elgarayhi@yahoo.com; Elhanbaly, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)

    2006-08-15

    The periodic wave solutions for some nonlinear partial differential equations, including generalized Klein-Gordon equation, Kadomtsev-Petviashvili (KP) equation and Boussinesq equations, are obtained by using the solutions of Jacobi elliptic equation. Under limit conditions, exact solitary wave solutions, shock wave solutions and triangular periodic wave solutions have been recovered.

  7. Exact solutions for a class of quasi-exactly solvable models: A unified treatment

    Science.gov (United States)

    Hatami, N.; Setare, M. R.

    2017-07-01

    The exact solution of the Schrödinger equation for the four quasi-exactly solvable potentials is presented using the functional Bethe ansatz method. It is shown that all models give rise to the same basic differential equation which is quasi-exactly solvable. The eigenvalues, eigenfunctions and the allowed potential parameters are given for each of the four models in terms of the roots of a set of algebraic Bethe ansatz equations.

  8. Exact solutions of (3 + 1)-dimensional stochastic Burgers equation

    Energy Technology Data Exchange (ETDEWEB)

    Wang Tieying [Department of Applied Mathematics and Physics, Dalian Nationalities for University, Dalian 116600 (China)]. E-mail: wangty@dlnu.edu.cn; Ren Yonghong [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China); Zhao Yali [Department of Mathematics, Chaoyang Teachers College, Chaoyang 122000 (China)

    2006-08-15

    A generalized tan h function method is used for constructing exact travelling wave solutions of nonlinear stochastic partial differential equations. The main idea of this method is to take full advantage of the Riccati equation, which has more exact solutions. More Wick-type stochastic multiple soliton-like solutions and triangular periodic solutions are obtained for the (3 + 1)-dimensional Wick-type stochastic Burgers equation via Hermite transformation.

  9. Differential equations extended to superspace

    Energy Technology Data Exchange (ETDEWEB)

    Torres, J. [Instituto de Fisica, Universidad de Guanajuato, A.P. E-143, Leon, Guanajuato (Mexico); Rosu, H.C. [Instituto Potosino de Investigacion Cientifica y Tecnologica, A.P. 3-74, Tangamanga, San Luis Potosi (Mexico)

    2003-07-01

    We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)

  10. Exact solutions for the cubic-quintic nonlinear Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Zhu Jiamin [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China)]. E-mail: zjm64@163.com; Ma Zhengyi [Department of Physics, Zhejiang Lishui University, Lishui 323000 (China); Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072 (China)

    2007-08-15

    In this paper, the cubic-quintic nonlinear Schroedinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which including bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions.

  11. Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[

    Institute of Scientific and Technical Information of China (English)

    HUANGDing-Jiang; ZHANGHong-Qing

    2004-01-01

    By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.

  12. Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation

    Institute of Scientific and Technical Information of China (English)

    HUANG Ding-Jiang; ZHANG Hong-Qing

    2004-01-01

    By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.

  13. Exact Solutions of the Generalized Benjamin-Bona-Mahony Equation

    Directory of Open Access Journals (Sweden)

    Xun Liu

    2010-01-01

    Full Text Available We apply the theory of Weierstrass elliptic function to study exact solutions of the generalized Benjamin-Bona-Mahony equation. By using the theory of Weierstrass elliptic integration, we get some traveling wave solutions, which are expressed by the hyperbolic functions and trigonometric functions. This method is effective to find exact solutions of many other similar equations which have arbitrary-order nonlinearity.

  14. Exact solutions for steady flows of second-grade fluids

    Institute of Scientific and Technical Information of China (English)

    ZHANG Dao-xiang; FENG Su-xiao; LU Zhi-ming; LIU Yu-lu

    2009-01-01

    This paper aims to investigate exact solutions for a second-grade fluid flow with the inverse method.By assuming the relation between the vorticity field and the streamfunction,the exact solutions of the motion of plane second-grade fluids are investigated and obtained.The solutions obtained include simple Couette flows,slit jet flows and uniform flows over a series of distributed obstacles.

  15. A procedure to construct exact solutions of nonlinear evolution equations

    Indian Academy of Sciences (India)

    Adem Cengiz Çevikel; Ahmet Bekir; Mutlu Akar; Sait San

    2012-09-01

    In this paper, we implemented the functional variable method for the exact solutions of the Zakharov-Kuznetsov-modified equal-width (ZK-MEW), the modified Benjamin-Bona-Mohany (mBBM) and the modified kdV-Kadomtsev-Petviashvili (kdV-KP) equation. By using this scheme, we found some exact solutions of the above-mentioned equation. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. The functional variable method presents a wider-applicability for handling nonlinear wave equations.

  16. EXACT TRAVELLING WAVE SOLUTIONS TO BBM EQUATION

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    Abundant new travelling wave solutions to the BBM (Benjamin-Bona-Mahoni) equation are obtained by the generalized Jacobian elliptic function method. This method can be applied to other nonlinear evolution equations.

  17. Exact Solutions to Short Pulse Equation

    Institute of Scientific and Technical Information of China (English)

    FU Zun-Tao; ZHENG Ming-Hua; LIU Shi-Kuo

    2009-01-01

    In this paper, dependent and independent variable transformations are introduced to solve the short pulse equation. It is shown that different kinds of solutions can be obtained to the short pulse equation.

  18. Three dimensional dilatonic gravity's rainbow: exact solutions

    CERN Document Server

    Hendi, Seyed Hossein; Panahiyan, Shahram

    2016-01-01

    Deep relations of dark energy scenario and string theory results with dilaton gravity, on one hand, and the connection between quantum gravity with gravity's rainbow, on the other hand, motivate us to consider three dimensional dilatonic black hole solutions in gravity's rainbow. We obtain two classes of the solutions which are polynomial and logarithmic forms. We also calculate conserved and thermodynamic quantities, and examine the first law of thermodynamics for both classes. In addition, we study thermal stability and show that one of the classes is thermally stable while the other one is unstable.

  19. Searching Exact Solutions for Compact Stars in Braneworld: a conjecture

    CERN Document Server

    Ovalle, J

    2007-01-01

    In the context of the braneworld, a spherically symmetric, static and nonhomogeneous stellar distribution with local and non-local bulk terms is studied. Using a toy solution, it is shown how the general relativistic limit could be lost while a solution is being generated on the brane. The source of this problem is clearly identified and solved by a general solution where a constraint can be identified. This constraint is physically interpreted as a necessary condition to regain general relativity, and a particular solution for it is used to find an exact analytical internal solution to no-uniform stellar distributions on the brane. It is shown that such an exact solution is possible due to the fact that bulk corrections to pressure, density and a metric component are a null source of anisotropic effects on the brane. A conjecture is proposed about the possibility of finding physically relevant exact solutions to non-uniform stellar distributions on the brane.

  20. On exact solutions in multidimensional gravity with antisymmetric forms

    CERN Document Server

    Ivashchuk, V D

    2001-01-01

    This short review deals with a multidimensional gravitational model containing dilatonic scalar fields and antisymmetric forms. The manifold is chosen in the product form. The sigma-model approach and exact solutions are reviewed.

  1. The exact solutions for a nonisospectral nonlinear Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Ning Tongke [Finance College, Shanghai Normal University, Shanghai 200234 (China)], E-mail: tkning@shnu.edu.cn; Zhang Weiguo; Jia Gao [Science College, University of Shanghai for Science and Technology, Shanghai 200093 (China)

    2009-10-30

    In this paper, lax pair for the nonisospectral nonlinear Schroedinger hierarchy is given, the time dependence of nonisospectral scattering data is derived and exact solutions for the nonisospectral nonlinear Schroedinger hierarchy are obtained through the inverse scattering transform.

  2. New Exact Solutions to Long-Short Wave Interaction Equations

    Institute of Scientific and Technical Information of China (English)

    TIAN Ying-Hui; CHEN Han-Lin; LIU Xi-Qiang

    2006-01-01

    New exact solutions expressed by the Jacobi elliptic functions are obtained to the long-short wave interaction equations by using the modified F-expansion method. In the limit case, solitary wave solutions and triangular periodic wave solutions are obtained as well.

  3. Exact solution of the neutron transport equation in spherical geometry

    Energy Technology Data Exchange (ETDEWEB)

    Anli, Fikret; Akkurt, Abdullah; Yildirim, Hueseyin; Ates, Kemal [Kahramanmaras Suetcue Imam Univ. (Turkey). Faculty of Sciences and Letters

    2017-03-15

    Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using P{sub N} approximation which is widely used in neutron transport theory.

  4. Some exact solutions in K-essence theory isotropic cosmology

    CERN Document Server

    Pimentel, Luis O

    2016-01-01

    We use a simple form of the K-essence theory and apply it to the classic isotropic cosmological model and seek exact solutions. The particular form of the kinetic term that we choose is $K \\left(\\phi, X \\right)= K_0(\\phi)X^m +K_1$. The resulting field equations in the homogeneous and isotropic cosmology (FRW)is considered. Several exact solutions are obtained.

  5. Generating exact solutions to Einstein's equation using linearized approximations

    Science.gov (United States)

    Harte, Abraham I.; Vines, Justin

    2016-10-01

    We show that certain solutions to the linearized Einstein equation can—by the application of a particular type of linearized gauge transformation—be straightforwardly transformed into solutions of the exact Einstein equation. In cases with nontrivial matter content, the exact stress-energy tensor of the transformed metric has the same eigenvalues and eigenvectors as the linearized stress-energy tensor of the initial approximation. When our gauge exists, the tensorial structure of transformed metric perturbations identically eliminates all nonlinearities in Einstein's equation. As examples, we derive the exact Kerr and gravitational plane wave metrics from standard harmonic-gauge approximations.

  6. Generating exact solutions to Einstein's equation using linearized approximations

    CERN Document Server

    Harte, Abraham I

    2016-01-01

    We show that certain solutions to the linearized Einstein equation can---by the application of a particular type of linearized gauge transformation---be straightforwardly transformed into solutions of the exact Einstein equation. In cases with nontrivial matter content, the exact stress-energy tensor of the transformed metric has the same eigenvalues and eigenvectors as the linearized stress-energy tensor of the initial approximation. When our gauge exists, the tensorial structure of transformed metric perturbations identically eliminates all nonlinearities in Einstein's equation. As examples, we derive the exact Kerr and gravitational plane wave metrics from standard harmonic-gauge approximations.

  7. New Exact Solutions for Isothermal Magnetostatic Atmosphere Equations

    Directory of Open Access Journals (Sweden)

    Mohamed Tawfik ATTIA

    2014-12-01

    Full Text Available Here, an extended, (G'/G-expansion method with a computerized symbolic computation is used for constructing the exact travelling wave solutions for isothermal magnetostatic atmospheres equations. These equations depend on arbitrary functions that must be specified with choices of the different choice of the different arbitrary functions. The proposed method has been successfully used to obtain some exact travelling wave solutions for the Liouville and sinh-Poisson equations. The obtained travelling wave solutions are expressed by hyperbolic, triangular and exponential function. The solutions obtained via the propose method have many potential applications in physics.

  8. Anisotropic exact solutions in scalar-tensor-vector gravity

    Science.gov (United States)

    Sharif, M.; Yousaf, Aasma

    2016-09-01

    The aim of this paper is to explore exact solutions in the scalar-tensor-vector theory of gravity with two scalar fields and one vector field. We consider a locally rotationally symmetric Bianchi type-I universe filled with perfect fluid. The first exact solution is found through certain assumptions while the second solution is obtained through Noether symmetry approach. We discuss the behavior of the resulting solutions numerically and also explore the corresponding energy conditions. It is found that the strong energy condition is violated in both cases indicating the accelerated expansion of the universe.

  9. Instantaneous Bethe-Salpeter Equation and Its Exact Solution

    Institute of Scientific and Technical Information of China (English)

    CHANG Chao-Hsi; CHEN Jiao-Kai; LI Xue-Qian; WANG Guo-Li

    2005-01-01

    We present an approach to solve Bethe-Salpeter (BS) equations exactly without any approximation if the kernel of the BS equations exactly is instantaneous, and take positronium as an example to illustrate the general features of the exact solutions. The key step for the approach is from the BS equations to derive a set of coupled and welldetermined integration equations in linear eigenvalue for the components of the BS wave functions equivalently, which may be solvable numerically under a controlled accuracy, even though there is no analytic solution. For positronium,the exact solutions precisely present corrections to those of the corresponding Schrodinger equation in order v1 (v is the relative velocity) for eigenfunctions, in order v2 for eigenvalues, and the mixing between S and D components in JPC = 1- states etc., quantitatively. Moreover, we also point out that there is a questionable step in some existent derivations for the instantaneous BS equations if one is pursuing the exact solutions. Finally, we emphasize that one should take the O(v) corrections emerging in the exact solutions into account accordingly if one is interested in the relativistic corrections for relevant problems to the bound states.

  10. Exact solitary wave solutions of nonlinear wave equations

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    The hyperbolic function method for nonlinear wave equations ispresented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Grbner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions.

  11. New Exact Travelling Wave Solutions to Kundu Equation

    Institute of Scientific and Technical Information of China (English)

    HUANG Ding-Jiang; LI De-Sheng; ZHANG Hong-Qing

    2005-01-01

    Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics.

  12. New exact solutions to some difference differential equations

    Institute of Scientific and Technical Information of China (English)

    Wang Zhen; Zhang Hong-Qing

    2006-01-01

    In this paper, we use our method to solve the extended Lotka-Volterra equation and discrete KdV equation. With the help of Maple, we obtain a number of exact solutions to the two equations including soliton solutions presented by hyperbolic functions of sinh and cosh, periodic solutions presented by trigonometric functions of sin and cos, and rational solutions. This method can be used to solve some other nonlinear difference-differential equations.

  13. Superspace conformal field theory

    Energy Technology Data Exchange (ETDEWEB)

    Quella, Thomas [Koeln Univ. (Germany). Inst. fuer Theoretische Physik; Schomerus, Volker [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2013-07-15

    Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and developments, including the general construction of WZW models on type I supergroups, the classification of conformal sigma models and their embedding into string theory.

  14. Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

    Directory of Open Access Journals (Sweden)

    Khaled A. Gepreel

    2013-01-01

    Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.

  15. Exact travelling wave solutions for some important nonlinear physical models

    Indian Academy of Sciences (India)

    Jonu Lee; Rathinasamy Sakthivel

    2013-05-01

    The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.

  16. Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer

    DEFF Research Database (Denmark)

    Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.

    1998-01-01

    We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...... differential equation....

  17. REDUCTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATION AND EXACT SOLUTIONS

    Institute of Scientific and Technical Information of China (English)

    YeCaier; PanZuliang

    2003-01-01

    Nonlinear partial differetial equation(NLPDE)is converted into ordinary differential equation(ODE)via a new ansatz.Using undetermined function method,the ODE obtained above is replaced by a set of algebraic equations which are solved out with the aid of Mathematica.The exact solutions and solitary solutions of NLPDE are obtained.

  18. NEW EXACT TRAVELLING WAVE SOLUTIONS TO THREE NONLINEAR EVOLUTION EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Sirendaoreji

    2004-01-01

    Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solutions of a new auxiliary ordinary differential equation.

  19. General Exact Solutions of the Harry—Dym Equation

    Science.gov (United States)

    Reza, Mokhtari

    2011-02-01

    The aim of this paper is to generate exact travelling wave solutions of the Harry—Dym equation through the methods of Adomian decomposition, He's variational iteration, direct integration, and power series. We show that the two later methods are more successful than the two former to obtain more solutions of the equation.

  20. AdS Waves as Exact Solutions to Quadratic Gravity

    CERN Document Server

    Gullu, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram

    2011-01-01

    We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity.

  1. Exact solutions, energy, and charge of stable Q-balls

    Energy Technology Data Exchange (ETDEWEB)

    Bazeia, D.; Marques, M.A. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Menezes, R. [Universidade Federal da Paraiba, Departamento de Ciencias Exatas, Rio Tinto, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil)

    2016-05-15

    In this work we deal with nontopological solutions of the Q-ball type in two spacetime dimensions. We study models of current interest, described by a Higgs-like and other, similar potentials which unveil the presence of exact solutions. We use the analytic results to investigate how to control the energy and charge to make the Q-balls stable. (orig.)

  2. Exact angular momentum projection based on cranked HFB solution

    Energy Technology Data Exchange (ETDEWEB)

    Enami, Kenichi; Tanabe, Kosai; Yosinaga, Naotaka [Saitama Univ., Urawa (Japan). Dept. of Physics

    1998-03-01

    Exact angular momentum projection of cranked HFB solutions is carried out. It is reconfirmed from this calculation that cranked HFB solutions reproduce the intrinsic structure of deformed nucleus. The result also indicates that the energy correction from projection is important for further investigation of nuclear structure. (author)

  3. Exact solutions for classical Yang-Mills fields

    CERN Document Server

    Frasca, Marco

    2014-01-01

    Some years ago we displayed a set of classical solutions for the classical Yang-Mills field theory having the property to satisfy a dispersion relation typical of a massive theory. But such solutions seemed to be exact only in the Landau gauge making all the argument an asymptotic one for the most general case of a generic gauge. These solutions can be used to describe the vacuum of the quantum Yang-Mills theory and so, to prove that they are always exact can grant a general framework to build a quantum field theory. Here we show that these solutions are always exact changing just the normalization factor. The components of the field become separated on a generic gauge being all equal just in the Landau gauge.

  4. Exact Solitary Wave Solution in the ZK-BBM Equation

    Directory of Open Access Journals (Sweden)

    Juan Zhao

    2014-01-01

    Full Text Available The traveling wave solution for the ZK-BBM equation is considered, which is governed by a nonlinear ODE system. The bifurcation structure of fixed points and bifurcation phase portraits with respect to the wave speed c are analyzed by using the dynamical system theory. Furthermore, the exact solutions of the homoclinic orbits for the nonlinear ODE system are obtained which corresponds to the solitary wave solution curve of the ZK-BBM equation.

  5. Relativit\\'e g\\'en\\'erale: solutions exactes stationnaires

    CERN Document Server

    Clément, Gérard

    2011-01-01

    After a brief summary of the foundations of general relativity, we will concentrate on the stationary exact solutions of the Einstein and Einstein-Maxwell equations. A number of these solutions can be interpreted as black holes, corresponding to a special spacetime geometry. Then, we will show that the reformulation of the stationary Einstein-Maxwell equations as a gravitating sigma model provides us with a powerful tool to generate new solutions.

  6. Exact interior solutions in 2 + 1-dimensional spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Rahaman, Farook; Bhar, Piyali [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Biswas, Ritabrata [Indian Institute of Engineering Sceince and Technology Shibpur, Howrah, West Bengal (India); Usmani, A.A. [Aligarh Muslim University, Department of Physics, Aligarh, Uttar Pradesh (India)

    2014-04-15

    We provide a new class of exact solutions for the interior in 2 + 1-dimensional spacetime. The solutions obtained for the perfect fluid model both with and without cosmological constant (Λ) are found to be regular and singularity free. It assumes very simple analytical forms that help us to study the various physical properties of the configuration. Solutions without Λ are found to be physically acceptable. (orig.)

  7. F-theory Superspace

    CERN Document Server

    Linch, William D

    2015-01-01

    We consider, at the linearized level, the superspace formulation of lower-dimensional F-theory. In particular, we describe the embedding of 3D Type II supergravity of the superstring, or 4D, N=1 supergravity of M-theory, into the corresponding F-theory in full detail, giving the linearized action and gauge transformations in terms of the prepotential. This manifestly supersymmetric formulation reveals some features not evident from a component treatment, such as Weyl and local S-supersymmetry invariances. The linearized multiplet appears as a super 3-form (just as that for the manifestly T-dual theory is a super 2-form), reflecting the embedding of M-theory (as the T-dual theory embeds Type II supergravity). We also give the embedding of matter multiplets into this superspace, and derive the F-constraint from the gauge invariance of the gauge invariance.

  8. Searching Exact Solutions for Compact Stars in Braneworld:. a Conjecture

    Science.gov (United States)

    Ovalle, J.

    In the context of the braneworld, a method to find consistent solutions to Einstein's field equations in the interior of a spherically symmetric, static and non-uniform stellar distribution with Weyl stresses is developed. This method, based on the fact that any braneworld stellar solution must have the general relativity solution as a limit, produces a constraint which reduces the degrees of freedom on the brane. Hence the nonlocality and non-closure of the braneworld equations can be overcome. The constraint found is physically interpreted as a necessary condition to regain general relativity, and a particular solution for it is used to find an exact and physically acceptable analytical internal solution to no-uniform stellar distributions on the brane. It is shown that such an exact solution is possible due to the fact that bulk corrections to pressure, density and a metric component are a null source of anisotropic effects on the brane. A conjecture is proposed regarding the possibility of finding physically relevant exact solutions to non-uniform stellar distributions on the brane.

  9. An exact solution of Haugan's binary pulsar equation of motion

    Science.gov (United States)

    Weinstein, M.; Mor, A.

    1988-05-01

    In his work on the post-Newtonian arrival-time analysis for a pulsary binary system, Haugan (1985) derived and integrated the two-body equation of the motion of the pulsar. The purpose of the present study is to show that there is an exact solution to this nonlinear equation, without any need of far-reaching assumptions and neglected nonlinear terms.

  10. Analyzing Multi-Field Tunneling With Exact Bounce Solutions

    CERN Document Server

    Aravind, Aditya; Lorshbough, Dustin; Paban, Sonia

    2014-01-01

    We study multi-field tunneling using exact solutions for additive potentials. We introduce a binomial potential with non-integer powers that could be considered a generalization of the $4D$ Fubini instanton potential. Using scaling arguments, we show that for multi-field potentials taller and wider barriers may still lead to a smaller bounce action.

  11. Feynman graph solution to Wilson's exact renormalization group

    CERN Document Server

    Sonoda, H

    2003-01-01

    We introduce a new prescription for renormalizing Feynman diagrams. The prescription is similar to BPHZ, but it is mass independent, and works in the massless limit as the MS scheme with dimensional regularization. The prescription gives a diagrammatic solution to Wilson's exact renormalization group differential equation.

  12. Exact Solutions of the Photon Equation in some Rotating Universes

    CERN Document Server

    Aydogdu, O; Korunur, M; Salti, M

    2005-01-01

    In this paper exact solutions of the photon equation are presented and the second order differential equation form of the Maxwell equations in some rotating universes is found to show the equivalence with the Photon equation which is obtained the same form for the same universes.

  13. Exact periodic solution in coupled nonlinear Schrodinger equations

    Institute of Scientific and Technical Information of China (English)

    Li Qi-Liang; Chen Jun-Lang; Sun Li-Li; Yu Shu-Yi; Qian Sheng

    2007-01-01

    The coupled nonlinear Schrodinger equations (CNLSEs) of two symmetrical optical fibres are nonintegrable, however the transformed CNLSEs have integrability. Integrability of the transformed CNLSEs is proved by the Hamilton dynamics theory and Galilei transform. Making use of a transform for CNLSEs and using the ansatz with Jacobi elliptic function form, this paper obtains the exact optical pulse solutions.

  14. Exact solutions for some nonlinear partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Peng, Yan-Ze

    2003-08-11

    Exact solutions to some nonlinear partial differential equations, including (2+1)-dimensional breaking soliton equation, sine-Gordon equation and double sine-Gordon equation, are studied by means of the mapping method proposed by the author recently. Many new results are presented. A simple review of the method is finally given.

  15. Gravitational waves as exact solutions of Einstein field equations

    Energy Technology Data Exchange (ETDEWEB)

    Vilasi, G [Dipartimento di Fisica, Universita di Salerno Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Gruppo Collegato di Salerno Via S. Allende, I-84081 Baronissi (Salerno) (Italy)

    2007-11-15

    Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra of Killing fields are described. A sub-class of these gravitational fields have a wave-like character; it is shown that they have spin-1.

  16. Exact solution to surface displacement associated with sources ...

    African Journals Online (AJOL)

    user

    International Journal of Engineering, Science and Technology ... Usually an exact solution to the surface displacement in an elastic half space is available for ..... to (ζ1 , ζ 2 ,ζ3 ) by means of the transformation (2.1), i.e, the station (x, y,-h) on.

  17. Instability and exact multiplicity of solutions of semilinear equations

    Directory of Open Access Journals (Sweden)

    Philip Korman

    2000-10-01

    Full Text Available For a class of two-point boundary-value problems we use bifurcation theory to show that a solution is unstable under a simple, geometric in nature, assumption on the non-linear term. As an application we obtain some new exact multiplicity results.

  18. Exact solutions for classical Yang-Mills fields

    OpenAIRE

    2014-01-01

    We provide a set of exact solutions of the classical Yang-Mills equations. They have the property to satisfy a massive dispersion relation and hold in all gauges. These solutions can be used to describe the vacuum of the quantum Yang-Mills theory and so, they provide a general framework to build a quantum field theory. The components of the field become separated on a generic gauge but are all equal just in the Lorenz (Landau) gauge.

  19. Nonlocal Symmetries and Exact Solutions for PIB Equation

    Science.gov (United States)

    Xin, Xiang-Peng; Miao, Qian; Chen, Yong

    2012-09-01

    In this paper, the symmetry group of the (2+1)-dimensional Painlevé integrable Burgers (PIB) equations is studied by means of the classical symmetry method. Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.

  20. Exact solutions to a nonlinear dispersive model with variable coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Yin Jun [Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074 (China); Lai Shaoyong [Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074 (China)], E-mail: laishaoy@swufe.edu.cn; Qing Yin [Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074 (China)

    2009-05-15

    A mathematical technique based on an auxiliary differential equation and the symbolic computation system Maple is employed to investigate a prototypical and nonlinear K(n, n) equation with variable coefficients. The exact solutions to the equation are constructed analytically under various circumstances. It is shown that the variable coefficients and the exponent appearing in the equation determine the quantitative change in the physical structures of the solutions.

  1. Nonlocal Symmetries and Exact Solutions for PIB Equation

    Institute of Scientific and Technical Information of China (English)

    辛祥鹏; 苗倩; 陈勇

    2012-01-01

    In this paper, the symmetry group of the is studied by means of the classical symmetry method (2+l)-dimensionM Painlevd integrable Burgers (PIB) equations Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.

  2. The exact solution of an octagonal rectangle triangle random tiling

    CERN Document Server

    De Gier, J; Gier, Jan de; Nienhuis, Bernard

    1996-01-01

    We present a detailed calculation of the recently published exact solution of a random tiling model possessing an eight-fold symmetric phase. The solution is obtained using Bethe Ansatz and provides closed expressions for the entropy and phason elastic constants. Qualitatively, this model has the same features as the square-triangle random tiling model. We use the method of P. Kalugin, who solved the Bethe Ansatz equations for the square-triangle tiling, which were found by M. Widom.

  3. Stable and Critical Noncohesive Coulomb Wedges: Exact Elastic Solutions

    Science.gov (United States)

    Wang, K.; Hu, Y.

    2004-12-01

    The theory of critically tapered Coulomb wedge has been successfully applied to model active fold-and-thrust belts or submarine accretionary prisms. Brittle mountain building is episodic in nature, controlled by changes in basal friction, erosion and sedimentation, and hydrogeology. Sediment accretion may be modulated by great subduction earthquakes. Between deformation episodes and/or during transition between compressional and extensional tectonics, the Coulomb wedges are stable (i.e., supercritical), to which the critical taper theory does not apply. In this work, we provide an exact elastic solution for stable wedges based on Airy stress functions. The stress equilibrium equation and definition of basal friction and basal and internal pore fluid pressure ratios are exactly the same as those used for Dahlen's [1984] exact solution for critical noncohesive Coulomb wedges, but internal friction μ becomes irrelevant. Given elastic - perfectly Coulomb-plastic rheology, for stresses in a wedge on the verge of Coulomb failure there must co-exist a critical taper solution involving μ and a unique equivalent elastic solution not involving μ . Our elastic solution precisely reduces to Dahlen's critical taper solution for critical conditions. For stable conditions, normal stress perpendicular to the surface slope σ z and shear stress τ xz are identical with those in a critical taper, but the slope-parallel normal stress is different. The elastic solution is also generally applicable to purely elastic wedges and useful for modeling geodetic observations. A stable noncohesive Coulomb wedge differs from a general elastic wedge in that its upper and lower surfaces stay at zero curvature during loading. Dahlen, F.A. (1984), Noncohesive critical Coulomb wedges: An exact solution, JGR, 89, 10,125-10,133.

  4. Quantifying risks with exact analytical solutions of derivative pricing distribution

    Science.gov (United States)

    Zhang, Kun; Liu, Jing; Wang, Erkang; Wang, Jin

    2017-04-01

    Derivative (i.e. option) pricing is essential for modern financial instrumentations. Despite of the previous efforts, the exact analytical forms of the derivative pricing distributions are still challenging to obtain. In this study, we established a quantitative framework using path integrals to obtain the exact analytical solutions of the statistical distribution for bond and bond option pricing for the Vasicek model. We discuss the importance of statistical fluctuations away from the expected option pricing characterized by the distribution tail and their associations to value at risk (VaR). The framework established here is general and can be applied to other financial derivatives for quantifying the underlying statistical distributions.

  5. Exact Solutions for Models of Cultural Transmission and Network Rewiring

    CERN Document Server

    Evans, T S

    2006-01-01

    We look at the evolution through rewiring of the degree distribution of a network so the number edges is constant. This is exactly equivalent to the evolution of probability distributions in models of cultural transmission with drift and innovation, or models of homogeneity in genes in the presence of mutation. We show that the mean field equations in the literature are incomplete and provide the full equations. We then give an exact solution for both their long time solution and for their approach to equilibrium. Numerical results show these are excellent approximations and confirm the characteristic simple inverse power law distributions with a large scale cutoff under certain conditions. The alternative is that we reach a completely homogeneous solution. We consider how such processes may arise in practice, using a recent Minority Game study as an example.

  6. Exact solutions and zero modes in scalar field theory

    CERN Document Server

    Frasca, Marco

    2013-01-01

    We provide a set of exact solutions in field theory of scalar fields with $Z_2$ symmetry that involve Jacobi elliptic functions. These solutions have the interesting property to provide massive waves even if one starts from a massless equation. We analyze them classically providing also exact solutions to the corresponding equations for the Green functions needed to completely solve them in a strong coupling limit. This is accomplished using a functional expansion into powers of the current. It is shown that the spontaneous breaking of the $Z_2$ symmetry is due to the existence of a zero mode that persists also in the case of the Higgs mechanism. In this latter case, the zero mode seems to play a role similar to the Goldstone boson in the breaking of a continuous symmetry and so, it should be important at lower momenta as a long range excitation.

  7. A static axisymmetric exact solution of f(R)-gravity

    Energy Technology Data Exchange (ETDEWEB)

    Gutierrez-Pineres, Antonio C., E-mail: acgutierrez@correo.nucleares.unam.mx [Facultad de Ciencias Basicas, Universidad Tecnologica de Bolivar, CO 131001 Cartagena de Indias (Colombia); Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A.P. 70-543, 04510 Mexico D.F. (Mexico); Lopez-Monsalvo, Cesar S., E-mail: cesar.slm@correo.nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A.P. 70-543, 04510 Mexico D.F. (Mexico)

    2013-01-29

    We present an exact, axially symmetric, static, vacuum solution for f(R)-gravity in Weyl's canonical coordinates. We obtain a general explicit expression for the dependence of df(R)/dR upon the r and z coordinates and then the corresponding explicit form of f(R), which must be consistent with the field equations. We analyze in detail the modified Schwarzschild solution in prolate spheroidal coordinates. Finally, we study the curvature invariants and show that, in the case of f(R){ne}R, this solution corresponds to a naked singularity.

  8. Exact travelling wave solutions of nonlinear partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish) Suez Canal University, AL-Arish 45111 (Egypt)]. E-mail: asoliman_99@yahoo.com; Abdou, M.A. [Theoretical Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: m_abdou_eg@yahoo.com

    2007-04-15

    An extended Fan-sub equation method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. The key idea of this method is to take full advantage of the general elliptic equation, involving five parameters, which has more new solutions and whose degeneracies can lead to special sub equation involving three parameters. As an illustration of the extended Fan method, more new solutions are obtained for three models namely, generalized KdV, Drinfeld-Sokolov system and RLW equation.

  9. Exact traveling soliton solutions for the scalar Qiao equation

    Science.gov (United States)

    Abdoulkary, Saïdou; Aboubakar, Mahamoudou; Aboukar; Mohamadou, Alidou; Beda, Tibi

    2015-01-01

    We investigate exact traveling wave solutions of the scalar Qiao equation proposed by Li and Qiao (2010 J. Math. Phys. 51 042703) using the generalized auxiliary equation method. This equation is known to have bi-Hamiltonian structure and Lax pair, which imply integrability of the equation for a fixed value of k. Symmetries of the scalar Qiao equation and its solutions are also considered. The obtained solutions include kink and antikink solitons, bright and dark solitons, singular solutions and exponential solutions. This method could be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in physics. This work could be also relevant for numerical studies of the scalar Qiao equation.

  10. Exact, Schwarzschild-like solution for Yang-Mills theory

    Energy Technology Data Exchange (ETDEWEB)

    Singleton, D.

    1995-04-01

    Exploiting the connection between general relativity and Yang-Mills theory an exact, Schwarzchild-like solution is given for an SU(N) gauge field coupled to a scalar field in the Bogomolny, Prasad, Sommerfield limit. The SU(2) solution is found using the second order Euler-Lagrange formalism, while the SU(N) generalization is given using the first order Bogomolny formalism. In analogy with the Schwarzschild solution of general relativity, these Yang-Mills solutions possess an event horizon with respect to the SU(N) charge. It is conjectured that this may be the confinement mechanism for QCD, since just as a Schwarzschild black hole will permanently confine anything which carries the charge of general relativity (mass-energy), so this Yang-Mills solution will confine any particle which carries the SU(N) charge.

  11. A new method of generating exact inflationary solutions

    CERN Document Server

    Schunck, F E; Franz E Schunck; Eckehard W Mielke

    1994-01-01

    The mechanism of the initial inflation of the universe is based on gravitationally coupled scalar fields \\phi. Various scenarios are distinguished by the choice of an {\\it effective self--interaction potential} U(\\phi) which simulates a {\\it temporarily} non--vanishing {\\em cosmological term}. Using the Hubble expansion parameter H as a new ``time" coordinate, we can formally derive the {\\it general} Robertson--Walker metric for a {\\em spatially flat} cosmos. Our new method provides a classification of allowed inflationary potentials and is broad enough to embody all known {\\it exact} solutions involving one scalar field as special cases. Moreover, we present new inflationary and deflationary exact solutions and can easily predict the influence of the form of U(\\phi) on density perturbations.

  12. New exact travelling wave solutions of bidirectional wave equations

    Indian Academy of Sciences (India)

    Jonu Lee; Rathinasamy Sakthivel

    2011-06-01

    The surface water waves in a water tunnel can be described by systems of the form [Bona and Chen, Physica D116, 191 (1998)] \\begin{equation*} \\begin{cases} v_t + u_x + (uv)_x + au_{x x x} − bv_{x x t} = 0,\\\\ u_t + v_x + u u_x + cv_{x x x} − d u_{x x t} = 0, \\end{cases} \\tag{1} \\end{equation*} where , , and d are real constants. In general, the exact travelling wave solutions will be helpful in the theoretical and numerical study of the nonlinear evolution systems. In this paper, we obtain exact travelling wave solutions of system (1) using the modified tanh–coth function method with computerized symbolic computation.

  13. On the Exact Solution of Wave Equations on Cantor Sets

    Directory of Open Access Journals (Sweden)

    Dumitru Baleanu

    2015-09-01

    Full Text Available The transfer of heat due to the emission of electromagnetic waves is called thermal radiations. In local fractional calculus, there are numerous contributions of scientists, like Mandelbrot, who described fractal geometry and its wide range of applications in many scientific fields. Christianto and Rahul gave the derivation of Proca equations on Cantor sets. Hao et al. investigated the Helmholtz and diffusion equations in Cantorian and Cantor-Type Cylindrical Coordinates. Carpinteri and Sapora studied diffusion problems in fractal media in Cantor sets. Zhang et al. studied local fractional wave equations under fixed entropy. In this paper, we are concerned with the exact solutions of wave equations by the help of local fractional Laplace variation iteration method (LFLVIM. We develop an iterative scheme for the exact solutions of local fractional wave equations (LFWEs. The efficiency of the scheme is examined by two illustrative examples.

  14. Some exact BPS solutions for exotic vortices and monopoles

    Science.gov (United States)

    Ramadhan, Handhika S.

    2016-07-01

    We present several analytical solutions of BPS vortices and monopoles in the generalized Abelian Maxwell-Higgs and Yang-Mills-Higgs theories, respectively. These models have recently been extensively studied and several exact solutions have already been obtained in [1,2]. In each theory, the dynamics is controlled by the additional two positive scalar-field-dependent functions, f (| ϕ |) and w (| ϕ |). For the case of vortices, we work in the ordinary symmetry-breaking Higgs potential, while for the case of monopoles we have the ordinary condition of the Prasad-Sommerfield limit. Our results generalize the exact solutions found previously. We also present solutions for BPS vortices with higher winding number. These solutions suffer from the condition that w (| ϕ |) has negative value at some finite range of r, but we argue that since it satisfies the weaker positive-value conditions then the corresponding energy density is still positive-definite and, thus, they are acceptable BPS solutions.

  15. Exact solutions for nonlinear partial fractional differential equations

    Institute of Scientific and Technical Information of China (English)

    Khaled A.Gepreel; Saleh Omran

    2012-01-01

    In this article,we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations.We use the improved (G’/G)-expansion function method to calculate the exact solutions to the time-and space-fractional derivative foam drainage equation and the time-and space-fractional derivative nonlinear KdV equation.This method is efficient and powerful for solving wide classes of nonlinear evolution fractional order equations.

  16. New Exact Solutions for New Model Nonlinear Partial Differential Equation

    Directory of Open Access Journals (Sweden)

    A. Maher

    2013-01-01

    Full Text Available In this paper we propose a new form of Padé-II equation, namely, a combined Padé-II and modified Padé-II equation. The mapping method is a promising method to solve nonlinear evaluation equations. Therefore, we apply it, to solve the combined Padé-II and modified Padé-II equation. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions, and elliptic functions.

  17. Symmetries and Exact Solutions of the Breaking Soliton Equation

    Institute of Scientific and Technical Information of China (English)

    陈美; 刘希强

    2011-01-01

    With the aid of the classical Lie group method and nonclassical Lie group method, we derive the classical Lie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS) equation. Using the symmetries, we find six classical similarity reductions and two nonclassical similarity reductions of the BS equation. Varieties of exact solutions of the BS equation are obtained by solving the reduced equations.

  18. The exact fundamental solution for the Benes tracking problem

    Science.gov (United States)

    Balaji, Bhashyam

    2009-05-01

    The universal continuous-discrete tracking problem requires the solution of a Fokker-Planck-Kolmogorov forward equation (FPKfe) for an arbitrary initial condition. Using results from quantum mechanics, the exact fundamental solution for the FPKfe is derived for the state model of arbitrary dimension with Benes drift that requires only the computation of elementary transcendental functions and standard linear algebra techniques- no ordinary or partial differential equations need to be solved. The measurement process may be an arbitrary, discrete-time nonlinear stochastic process, and the time step size can be arbitrary. Numerical examples are included, demonstrating its utility in practical implementation.

  19. Exact solutions in multidimensional gravity with antisymmetric forms

    CERN Document Server

    Ivashchuk, V D

    2001-01-01

    This topical review deals with a multidimensional gravitational model containing dilatonic scalar fields and antisymmetric forms. The manifold is chosen in the form M = M_0 x M_1 x ...x M_n, where M_i are Einstein spaces (i >0). The sigma-model approach and exact solutions in the model are reviewed and the solutions with p-branes (e.g. Majumdar-Papapetrou-type, cosmological, spherically symmetric, black-brane and Freund-Rubin-type ones) are considered.

  20. Exact Solution in the New Inflation Scenario with Induced Gravity

    Institute of Scientific and Technical Information of China (English)

    WANG Wen-Fu

    2001-01-01

    Taking the Hubble parameter directly as a function of the scalar field instead of as a function of time,H = H( ), we present a new exact solution in the new inflation model with induced gravity. This includes solution which is inflation for end, and develops smoothly towards radiation-like evolution for ≥ end. The inflation is driven by the evolution of the field with inflation potential, V( ) = λ 2 v2)2.density, ns, is computed and ns lies well inside the limits set by the cosmic background explorer (COBE) satellite.the dex of the scalar effective cosmological constant Aeff tends to zero when inflation ends.``

  1. Conformal Invariance and the exact solution of BFKL equations

    CERN Document Server

    Navelet, H

    1997-01-01

    The conformal invariance properties of the QCD Pomeron in the transverse plane allow us to give an explicit analytical expression for the solution of the BFKL equations both in the transverse coordinate and momentum spaces. This result is obtained from the solution of the conformal eigenvectors in the mixed representation in terms of two conformal blocks, each block being the product of an holomorphic times an antiholomorphic function. This property is used to give an exact expression for the QCD dipole multiplicities and dipole-dipole cross-sections in the whole parameter space, proving the equivalence between the BFKL and dipole representations of the QCD Pomeron.

  2. Scalar triplet on a domain wall: an exact solution

    CERN Document Server

    Gani, Vakhid A; Radomskiy, Roman V

    2016-01-01

    We study a model with a real scalar Higgs field and a scalar triplet field that allows existence of a topological defect -- a domain wall. The wall breaks the global $O(3)$ symmetry of the model, which gives rise to non-Abelian orientational degrees of freedom. We found an exact analytic solution that describes a domain wall with a localized configuration of the triplet field on it. This solution enables one to calculate contributions to the action from the orientational and translational degrees of freedom of the triplet field. We also study the linear stability of the domain wall with the triplet field switched off.

  3. On the Exact Solution of a Generalized Polya Process

    Directory of Open Access Journals (Sweden)

    Hidetoshi Konno

    2010-01-01

    Full Text Available There are two types of master equations in describing nonequilibrium phenomena with memory effect: (i the memory function type and (ii the nonstationary type. A generalized Polya process is studied within the framework of a non-stationary type master equation approach. For a transition-rate with an arbitrary time-dependent relaxation function, the exact solution of a generalized Polya process is obtained. The characteristic features of temporal variation of the solution are displayed for some typical time-dependent relaxation functions reflecting memory in the systems.

  4. Exact Solution in Chaotic Inflation Model with Negative Potential

    Institute of Scientific and Technical Information of China (English)

    王文福

    2003-01-01

    New exact solution to the Einstein equations that describe the evolution of cosmological chaotic inflation model is derived. The inflation is driven by the evolution of scalar field with negative potential V( )=-Vo +1/2m2ψ2.This includes the solution which is exponential inflation for ψo >ψ>ψf , and then develops smoothly towards the radiation-like evolution for ψ<ψf. The spectral indices of the scalar density ns and the gravitational wave fluctuations ng are computed. The value of ns lies well inside the limits set by the cosmic background explorer satellite.

  5. Non-uniform Braneworld Stars: an Exact Solution

    CERN Document Server

    Ovalle, J

    2008-01-01

    The first exact interior solution to Einstein's field equations for a static and non-uniform braneworld star with local and non-local bulk terms is presented. It is shown that the bulk Weyl scalar ${\\cal U}(r)$ is always negative inside the stellar distribution, in consequence it reduces both the effective density and the effective pressure. It is found that the anisotropy generated by bulk gravity effect has an acceptable physical behaviour inside the distribution. Using a Reissner-N\\"{o}rdstrom-like exterior solution, the effects of bulk gravity on pressure and density are found through matching conditions.

  6. Critical exact solutions for self-gravitating Dirac fields

    CERN Document Server

    Cianci, Roberto; Vignolo, Stefano

    2016-01-01

    We consider the Einstein-Dirac field equations describing a self-gravitating massive neutrino, looking for axially-symmetric exact solutions; in the search of general solutions, we find some that are specific and which have critical features, such as the fact that the space-time curvature turns out to be flat and the spinor field gives rise to a vanishing bi-linear scalar $\\overline{\\psi}\\psi=0$ with non-vanishing bi-linear pseudo-scalar $i\\overline{\\psi}\\gamma^5\\psi\

  7. Conformal invariance and new exact solutions of the elastostatics equations

    Science.gov (United States)

    Chirkunov, Yu. A.

    2017-03-01

    We fulfilled a group foliation of the system of n-dimensional (n ≥ 2) Lame equations of the classical static theory of elasticity with respect to the infinite subgroup contained in normal subgroup of main group of this system. It permitted us to move from the Lame equations to the equivalent unification of two first-order systems: automorphic and resolving. We obtained a general solution of the automorphic system. This solution is an n-dimensional analogue of the Kolosov-Muskhelishvili formula. We found the main Lie group of transformations of the resolving system of this group foliation. It turned out that in the two-dimensional and three-dimensional cases, which have a physical meaning, this system is conformally invariant, while the Lame equations admit only a group of similarities of the Euclidean space. This is a big success, since in the method of group foliation, resolving equations usually inherit Lie symmetries subgroup of the full symmetry group that was not used for the foliation. In the three-dimensional case for the solutions of the resolving system, we found the general form of the transformations similar to the Kelvin transformation. These transformations are the consequence of the conformal invariance of the resolving system. In the three-dimensional case with a help of the complex dependent and independent variables, the resolving system is written as a simple complex system. This allowed us to find non-trivial exact solutions of the Lame equations, which direct for the Lame equations practically impossible to obtain. For this complex system, all the essentially distinct invariant solutions of the maximal rank we have found in explicit form, or we reduced the finding of those solutions to the solving of the classical one-dimensional equations of the mathematical physics: the heat equation, the telegraph equation, the Tricomi equation, the generalized Darboux equation, and other equations. For the resolving system, we obtained double wave of a

  8. Some exact BPS solutions for exotic vortices and monopoles

    CERN Document Server

    Ramadhan, Handhika S

    2015-01-01

    We present several analytical solutions of BPS vortices and monopoles in the generalized Abelian Maxwell-Higgs and Yang-Mills-Higgs theories, respectively. These models have recently been extensively studied and several exact solutions have already been obtained in~\\cite{Casana:2014qfa, Casana:2013lna}. In each theory, the dynamics is controlled by the additional two positive scalar-field-dependent functions, $f(|\\phi|)$ and $w(|\\phi|)$. For the case of vortices, we work in the ordinary symmetry-breaking Higgs potential, while for the case of monopoles we have the ordinary condition of the Prasad-Sommerfield limit. Our results generalize that of exact solutions found previously. We also present solutions for BPS vortices with higher winding number. These solutions suffer from the condition that $w(|\\phi|)$ has negative value at some finite range of $r$, but we argue that since it satisfies the weaker positive-value conditions then the corresponding energy density is still positive-definite and, thus, they are...

  9. Stokes Waves Revisited: Exact Solutions in the Asymptotic Limit

    CERN Document Server

    Davies, Megan

    2016-01-01

    Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic secular variation in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long standing theoretical insufficiency by invoking a compact exact $n$-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third ordered perturbative solution, that leads to a seamless extension to higher order (e.g. fifth order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desir...

  10. Exact axisymmetric solutions for laminated transversely isotropic piezoelectric circular plate (Ⅰ)——Exact solutions for piezoelectric circular plate

    Institute of Scientific and Technical Information of China (English)

    丁皓江; 徐荣桥; 国凤林

    1999-01-01

    Based on three-dimensional elastic equations for piezoelectric materials, the state equations for piezoelectric circular plate under axisymmetric deformation are derived. Applying Hankel transform to them and letting the free boundary terms resulting from Hankel transform be zero, a set of ordinary differential equations with constant coefficients and associated boundary conditions are obtained. Furthermore, two exact solutions corresponding to generalized rigid slipping and generalized elastic simple support are deduced. Then, the governing equations obtained reduce to equations for axisymmetric problem of transversely isotropic circular plate. Under the two types of boundary conditions of elastic simple support and rigid slipping, exact solutions are derived. Finally, numerical results are presented and applicability of the classical plate theory is discussed.

  11. Superspace geometry and the minimal, non minimal, and new minimal supergravity multiplets

    Energy Technology Data Exchange (ETDEWEB)

    Girardi, G.; Grimm, R.; Mueller, M.; Wess, J.

    1984-11-01

    We analyse superspace constraints in a systematic way and define a set of natural constraints. We give a complete solution of the Bianchi identities subject to these constraints and obtain a reducible, but not fully reducible multiplet. By additional constraints it can be reduced to either the minimal nonminimal or new minimal multiplet. We discuss the superspace actions for the various multiplets.

  12. Exact Spherical Wave Solutions to Maxwell's Equations with Applications

    Science.gov (United States)

    Silvestri, Guy G.

    Electromagnetic radiation from bounded sources represent an important class of physical problems that can be solved for exactly. However, available texts on this subject almost always resort to approximate solution techniques that not only obscure the essential features of the problem but also restrict application to limited ranges of observation. This dissertation presents exact solutions for this important class of problems and demonstrates how these solutions can be applied to situations of genuine physical interest, in particular, the design of device structures with prespecified emission characteristics. The strategy employed is to solve Maxwell's equations in the spherical coordinate system. In this system, fundamental parameters such as electric and magnetic multipole moments fall out quite naturally. Expressions for radiated power, force, and torque assume especially illuminating and simple forms when expressed in terms of these multipole moments. All solutions are derived ab initio using first-principles arguments exclusively. Two operator-equations that receive particularly detailed treatment are the vector Helmholtz equation for the time-independent potential vec a and the "covariant divergence" equation for the energy-momentum-stress tensor T^{mu nu}. An application of classical formulas, as modified by the requirements of statistical mechanics, to the case of heated blackbodies leads to inquiries into the foundations of quantum mechanics and their relation to classical field theory. An application of formulas to various emission structures (spherically-shaped antennas, surface diffraction gratings, collimated beams) provides a basis upon which to characterize these structures in an exact sense, and, ultimately, to elicit clues as to their optimum design.

  13. Optimum intermediate fibers for reducing interconnection loss: exact solution.

    Science.gov (United States)

    Yablon, Andrew D; Sumetsky, M

    2007-03-15

    We derive an exact analytical solution for a transmission line of N single-mode intermediate optical fibers that minimize the interconnection loss between any two dissimilar fiber modes that are well described by that paraxial scalar wave equation. Our solution shows that N optimum intermediate fibers reduce the original interconnection loss by a factor of least 1/(N+1) and that the total interconnection loss is only a function of N and the original direct interconnection loss. Our solution is not restricted to axisymmetric fibers or mode fields and therefore could be useful for reducing the interconnection loss between microstructured optical fibers, between certain slab waveguides, or between fibers and optical sources or detectors.

  14. Supersymmetric Spacetimes from Curved Superspace

    CERN Document Server

    Kuzenko, Sergei M

    2015-01-01

    We review the superspace technique to determine supersymmetric spacetimes in the framework of off-shell formulations for supergravity in diverse dimensions using the case of 3D N=2 supergravity theories as an illustrative example. This geometric formalism has several advantages over other approaches advocated in the last four years. Firstly, the infinitesimal isometry transformations of a given curved superspace form, by construction, a finite-dimensional Lie superalgebra, with its odd part corresponding to the rigid supersymmetry transformations. Secondly, the generalised Killing spinor equation, which must be obeyed by the supersymmetry parameters, is a consequence of the more fundamental superfield Killing equation. Thirdly, general rigid supersymmetric theories on a curved spacetime are readily constructed in superspace by making use of the known off-shell supergravity-matter couplings and restricting them to the background chosen. It is the superspace techniques which make it possible to generate arbitra...

  15. Exact Solution in Chaotic Inflation Model with Potential Minima

    Institute of Scientific and Technical Information of China (English)

    WANG Wen-Fu

    2001-01-01

    Taking the cosmological expansion rate directly as a function of field , H = H( ), we present a new exact solution to Einstein's equations that describe the evolution of cosmological chaotic inflation model. The inflation is driven by the evolution of scalar field with inflation potential V( ) = λ 2 v2)2.8 ( 2- 2)2.The spectral indices of the scalar density ns and gravitational wave fluctuations ng are computed. The value of ns lies well inside the limits set by the cosmic background explorer satellite.

  16. A class of exact classical solutions to string theory.

    Science.gov (United States)

    Coley, A A

    2002-12-31

    We show that the recently obtained class of spacetimes for which all of the scalar curvature invariants vanish (which can be regarded as generalizations of pp-wave spacetimes) are exact solutions in string theory to all perturbative orders in the string tension scale. As a result the spectrum of the theory can be explicitly obtained, and these spacetimes are expected to provide some hints for the study of superstrings on more general backgrounds. Since these Lorentzian spacetimes suffer no quantum corrections to all loop orders they may also offer insights into quantum gravity.

  17. Exact Inflationary Solution in String-Motivated Scalar Field Cosmology

    Institute of Scientific and Technical Information of China (English)

    王文福

    2001-01-01

    We present a new exact solution to Einstein's equations that describes the evolution of inflationary universe models. The inflation is driven by the evolution of a scalar field with an approximate two-loop four-dimensional string potential. In this scenario, the inflation began immediately after the epoch governed by quantum gravity and therefore there is no initial singularity. The successful inflation scenario is expected to appear only at two loop order. For a1/|a2| ≥ 90, the spectral index ns of the scalar density fluctuations lies well inside the limits set by the cosmic background explorer satellite and the gravitational wave spectral index is ng≈1.

  18. Exact Solution of a Drop-Push Model for Percolation

    Science.gov (United States)

    Majumdar, Satya N.; Dean, David S.

    2002-08-01

    Motivated by a computer science algorithm known as ``linear probing with hashing,'' we study a new type of percolation model whose basic features include a sequential ``dropping'' of particles on a substrate followed by their transport via a ``pushing'' mechanism. Our exact solution in one dimension shows that, unlike the ordinary random percolation model, the drop-push model has nontrivial spatial correlations generated by the dynamics itself. The critical exponents in the drop-push model are also different from those of the ordinary percolation. The relevance of our results to computer science is pointed out.

  19. Exact solutions and ladder operators for a new anharmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Dong Shihai [Programa de Ingenieria Molecular, Instituto Mexicano del Petroleo, Lazaro Cardenas 152, 07730 Mexico DF (Mexico)]. E-mail: dongsh2@yahoo.com; Sun Guohua [Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, UNAM, A.P. 20-726, Del. Alvaro Obregon, 01000 Mexico DF (Mexico); Lozada-Cassou, M. [Programa de Ingenieria Molecular, Instituto Mexicano del Petroleo, Lazaro Cardenas 152, 07730 Mexico DF (Mexico)

    2005-06-06

    In this Letter, we propose a new anharmonic oscillator and present the exact solutions of the Schrodinger equation with this oscillator. The ladder operators are established directly from the normalized radial wave functions and used to evaluate the closed expressions of matrix elements for some related functions. Some comments are made on the general calculation formula and recurrence relation for off-diagonal matrix elements. Finally, we show that this anharmonic oscillator possesses a hidden symmetry between E(r) and E(ir) by substituting r->ir.

  20. Exact solutions and conserved quantities in f( R, T) Gravity

    Science.gov (United States)

    Sharif, M.; Nawazish, Iqra

    2017-06-01

    This paper explores Noether and Noether gauge symmetries of anisotropic universe model in f( R, T) gravity. We consider two particular models of this gravity and evaluate their symmetry generators as well as associated conserved quantities. We also find exact solution by using cyclic variable and investigate its behavior via cosmological parameters. The behavior of cosmological parameters turns out to be consistent with recent observations which indicates accelerated expansion of the universe. Next we study Noether gauge symmetry and corresponding conserved quantities for both isotropic and anisotropic universe models. We conclude that symmetry generators and the associated conserved quantities appear in all cases.

  1. Exact solutions for the spin tune for model storage rings

    CERN Document Server

    Mane, S R

    2002-01-01

    We present exact analytical expressions for the spin tune for arbitrary values of the orbital action for several storage ring models. The models we treat contain Siberian Snakes, the use of which is essential to preserve the polarization of beams in high-energy proton storage rings. Our solutions contain some novel features. We also prove a previously conjectured claim about the behavior of spin tuneshifts in rings with multiple Snakes. The conjecture is based on numerical simulations, but our proof is analytical, and also nonperturbative.

  2. Piezoelectric vibration damping using resonant shunt circuits: an exact solution

    Science.gov (United States)

    Soltani, P.; Kerschen, G.; Tondreau, G.; Deraemaeker, A.

    2014-12-01

    The objective of this paper is to propose an exact closed-form solution to the {{H}∞ } optimization of piezoelectric materials shunted with inductive-resistive passive electrical circuits. Realizing that Den Hartog's method which imposes fixed points of equal height in the receptance transfer function is approximate, the parameters of the piezoelectric tuned vibration absorber are calculated through the direct minimization of the maxima of the receptance. The method is applied to a one-degree-of-freedom primary oscillator considering various values of the electromechanical coupling coefficients.

  3. Exact solutions of certain nonlinear chemotaxis diffusion reaction equations

    Indian Academy of Sciences (India)

    MISHRA AJAY; KAUSHAL R S; PRASAD AWADHESH

    2016-05-01

    Using the auxiliary equation method, we obtain exact solutions of certain nonlinear chemotaxis diffusion reaction equations in the presence of a stimulant. In particular, we account for the nonlinearities arising not only from the density-dependent source terms contributed by the particles and the stimulant but also from the coupling term of the stimulant. In addition to this, the diffusion of the stimulant and the effect of long-range interactions are also accounted for in theconstructed coupled differential equations. The results obtained here could be useful in the studies of several biological systems and processes, e.g., in bacterial infection, chemotherapy, etc.

  4. Scattering of two photons from two distant qubits: exact solution

    Energy Technology Data Exchange (ETDEWEB)

    Laakso, Matti; Pletyukhov, Mikhail [Institute for Theory of Statistical Physics, RWTH Aachen, 52056 Aachen (Germany)

    2015-07-01

    We consider the inelastic scattering of two photons from two qubits separated by an arbitrary distance and coupled to a one-dimensional transmission line. We present an exact, analytical solution to the problem, and use it to explore a particular configuration of qubits which is transparent to single-photon scattering, thus highlighting non-Markovian effects of inelastic two-photon scattering: Strong two-photon interference and momentum dependent photon (anti)bunching. This latter effect can be seen as an inelastic generalization of the Hong-Ou-Mandel effect.

  5. Exact solution of an evolutionary model without aging

    Science.gov (United States)

    Onody, Roberto N.; de Medeiros, Nazareno G. F.

    1999-09-01

    We introduce an age-structured asexual population model containing all the relevant features of evolutionary aging theories. Beneficial as well as deleterious mutations, heredity, and arbitrary fecundity are present and managed by natural selection. An exact solution without aging is found. We show that fertility is associated with generalized forms of the Fibonacci sequence, while mutations and natural selection are merged into an integral equation which is solved by Fourier series. Average survival probabilities and Malthusian growth exponents are calculated and indicate that the system may exhibit mutational meltdown. The relevance of the model in the context of fissile reproduction groups like many protozoa and coelenterates is discussed.

  6. Exact solutions to model surface and volume charge distributions

    Science.gov (United States)

    Mukhopadhyay, S.; Majumdar, N.; Bhattacharya, P.; Jash, A.; Bhattacharya, D. S.

    2016-10-01

    Many important problems in several branches of science and technology deal with charges distributed along a line, over a surface and within a volume. Recently, we have made use of new exact analytic solutions of surface charge distributions to develop the nearly exact Boundary Element Method (neBEM) toolkit. This 3D solver has been successful in removing some of the major drawbacks of the otherwise elegant Green's function approach and has been found to be very accurate throughout the computational domain, including near- and far-field regions. Use of truly distributed singularities (in contrast to nodally concentrated ones) on rectangular and right-triangular elements used for discretizing any three-dimensional geometry has essentially removed many of the numerical and physical singularities associated with the conventional BEM. In this work, we will present this toolkit and the development of several numerical models of space charge based on exact closed-form expressions. In one of the models, Particles on Surface (ParSur), the space charge inside a small elemental volume of any arbitrary shape is represented as being smeared on several surfaces representing the volume. From the studies, it can be concluded that the ParSur model is successful in getting the estimates close to those obtained using the first-principles, especially close to and within the cell. In the paper, we will show initial applications of ParSur and other models in problems related to high energy physics.

  7. Critical exact solutions for self-gravitating Dirac fields

    Energy Technology Data Exchange (ETDEWEB)

    Cianci, Roberto; Fabbri, Luca; Vignolo, Stefano [Universita di Genova, DIME Sez. Metodi e Modelli Matematici, Genova (Italy)

    2016-11-15

    We consider the Einstein-Dirac field equations describing a self-gravitating massive neutrino, looking for axially symmetric exact solutions; in the search of general solutions, we find some that are specific and which have critical features, such as the fact that the space-time curvature turns out to be flat and the spinor field gives rise to a vanishing bi-linear scalar ψψ =0 with non-vanishing bi-linear pseudo-scalar iψγ{sup 5}ψ ≠ 0: because in quantum-field theory general computational methods are built on plane-wave solutions, for which the bi-linear pseudo-scalar vanishes while the bi-linear scalar does not vanish, then the solutions we found cannot be treated with the usual machinery of quantum-field theory. This means that for the Einstein-Dirac system there exist admissible solutions which nevertheless cannot be quantized with the common prescriptions; we regard this situation as yet another issue of tension between Einstein gravity and quantum principles. Possible ways to quench this tension can be seen either in enlarging the validity of quantum-field theory or by restricting the space of the solutions of the Einstein-Dirac system of field equations. (orig.)

  8. Exact Cosmological Solutions in Modified Brans--Dicke Theory

    CERN Document Server

    Rasouli, S M M

    2016-01-01

    In this paper, we obtain exact cosmological vacuum solutions for an extended FLRW homogenous and isotropic Brans-Dicke (BD) universe in five dimensions for all values of the curvature index. Then, by employing the equations associated to a modified Brans-Dicke theory (MBDT) [1], we construct the physics on a four-dimensional hypersurface. We show that the induced matter obeys the equation of state of a fluid of a barotropic type. We discuss the properties of such an induced matter for some values of the equation of state parameter and analyze in detail their corresponding solutions. To illustrate the cosmological behaviors of the solutions, we contrast our solutions with those present the standard Brans-Dicke theory. We retrieve that, in MBDT scenario, it is impossible to find a physically acceptable solution associated to the negative curvature for both the dust-dominated and radiation-dominated universes. However, for a spatially flat and closed universes, we argue that our obtained solutions are more gener...

  9. Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models

    CERN Document Server

    Cordova, Clay; Popolitov, Alexandr; Shakirov, Shamil

    2016-01-01

    We find an exact solution to strongly-coupled matrix models with a single-trace monomial potential. Our solution yields closed form expressions for the partition function as well as averages of Schur functions. The results are fully factorized into a product of terms linear in the rank of the matrix and the parameters of the model. We extend our formulas to include both logarthmic and finite-difference deformations, thereby generalizing the celebrated Selberg and Kadell integrals. We conjecture a formula for correlators of two Schur functions in these models, and explain how our results follow from a general orbifold-like procedure that can be applied to any one-matrix model with a single-trace potential.

  10. Exact solutions and physical analogies for unidirectional flows

    CERN Document Server

    Bazant, Martin Z

    2016-01-01

    Unidirectional flow, exemplified by Hagen-Poiseuille flow in a circular pipe, is the simplest phenomenon of fluid mechanics. Its mathematical description, the Dirichlet problem for Poisson's equation in two dimensions with constant forcing, arises in many physical contexts, such as the torsion of elastic beams, first solved by de Saint-Venant and extended to arbitrary domains by Muskhelishvilli. In this article, we unify and extend the literature by identifying fifteen physical analogies for unidirectional flow and describing their common mathematical structure. We show how to construct approximate geometries that admit exact solutions, by adding harmonic functions to quadratic forms or truncating eigenfunction expansions, and we discuss the difficulty of the evaluating the general contour-integral solution for a given geometry. We prove that the remarkable geometrical interpretation of Poiseuille flow in an equilateral pipe, as the product of the distances from an interior point to the sides, is only shared ...

  11. Scalar triplet on a domain wall: an exact solution

    Science.gov (United States)

    Gani, Vakhid A.; Lizunova, Mariya A.; Radomskiy, Roman V.

    2016-04-01

    We study a model with a real scalar Higgs field and a scalar triplet field that allows existence of a topological defect — a domain wall. The wall breaks the global O(3) symmetry of the model, which gives rise to non-Abelian orientational degrees of freedom. We found an exact analytic solution that describes a domain wall with a localized configuration of the triplet field on it. This solution enables one to calculate contributions to the action from the orientational and translational degrees of freedom of the triplet field. We also study the linear stability of the domain wall with the triplet field switched off. We obtain that degrees of freedom localized on the wall can appear or do not appear depending on the parameters of the model.

  12. Exact solutions and physical analogies for unidirectional flows

    Science.gov (United States)

    Bazant, Martin Z.

    2016-06-01

    Unidirectional flow is the simplest phenomenon of fluid mechanics. Its mathematical description, the Dirichlet problem for Poisson's equation in two dimensions with constant forcing, arises in many physical contexts, such as the torsion of elastic beams, first solved by de Saint-Venant for complex shapes. Here the literature is unified and extended by identifying 17 physical analogies for unidirectional flow and describing their common mathematical structure. Besides classical analogies in fluid and solid mechanics, applications are discussed in stochastic processes (first passage in two dimensions), pattern formation (river growth by erosion), and electrokinetics (ion transport in nanochannels), which also involve Poisson's equation with nonconstant forcing. Methods are given to construct approximate geometries that admit exact solutions, by adding harmonic functions to quadratic forms or by truncating eigenfunction expansions. Exact solutions for given geometries are also derived by conformal mapping. We prove that the remarkable geometrical interpretation of Poiseuille flow in an equilateral triangular pipe (the product of the distances from an interior point to the sides) is only shared by parallel plates and unbounded equilateral wedges (with the third side hidden behind the apex). We also prove Onsager reciprocity for linear electrokinetic phenomena in straight pores of arbitrary shape and surface charge, based on the mathematics of unidirectional flow.

  13. Integration in superspace using distribution theory

    Energy Technology Data Exchange (ETDEWEB)

    Coulembier, K; De Bie, H; Sommen, F [Clifford Research Group, Department of Mathematical Analysis Faculty of Engineering, Ghent University, Krijgslaan 281, 9000 Gent (Belgium)], E-mail: Coulembier@cage.ugent.be, E-mail: Hendrik.DeBie@UGent.be, E-mail: fs@cage.ugent.be

    2009-10-02

    In this paper, a new class of Cauchy integral formulae in superspace is obtained, using formal expansions of distributions. This allows us to solve five open problems in the study of harmonic and Clifford analysis in superspace.

  14. Properties of exact solution of second-order differential equation with pantograph delay

    Institute of Scientific and Technical Information of China (English)

    李冬松; 白红; 刘明珠

    2002-01-01

    This paper is concerned with properties of exact solution of pantograph delay equation y′′(t)=ay′(t)+by(t)+cy(qt), 0<q<1. Firstly, the existence and uniqueness of the exact solution of equations are proved, and then the condition is investigated which guarantee the exact solution is asymptotic stable.

  15. An exact solution of the slow-light problem

    CERN Document Server

    Rybin, A V; Bishop, A R

    2004-01-01

    We investigate propagation of a slow-light soliton in atomic vapors and Bose-Einstein condensates described by the nonlinear Lambda-model. We show that the group velocity of the soliton monotonically decreases with the intensity of the controlling laser field, which decays exponentially after the laser is switched off. The shock wave of the vanishing controlling field overtakes the slow soliton and stops it, while the optical information is recorded in the medium in the form of spatially localized polarization. We find an explicit exact solution describing the whole process within the slowly varying amplitude and phase approximation. Our results point to the possibility of addressing spatially localized memory formations and moving these memory bits along the medium in a controllable fashion.

  16. Some Exact Solutions of Magnetized viscous model in String Cosmology

    CERN Document Server

    Singh, C P

    2012-01-01

    In this paper we study anisotropic Bianchi-V universe with magnetic field and bulk viscous fluid in string cosmology. Exact solutions of the field equations are obtained by using the equation of state for a cloud of strings and a relationship between bulk viscous coefficient and expansion scalar. The bulk viscous coefficient is assumed to be inversely proportional to the expansion scalar. It is interesting to examine the effects of magnetized bulk viscous string model in early and late stages of the evolution of the universe. This paper investigates the different string models like geometrical(Nambu string), Takabayashi (p-string) and Reddy string models by taking certain physical conditions. The introduction of magnetic field or bulk viscosity or both results in rapid change in scale factors as well as in the classical potential. The presence of viscosity prevents the universe to be empty in its future evolution. The physical and geometrical aspects of each string model are discussed in detail.

  17. Exact solutions for hydrodynamic interactions of two squirming spheres

    CERN Document Server

    Papavassiliou, Dario

    2016-01-01

    We provide exact solutions of the Stokes equations for a squirming sphere close to a no-slip surface, both planar and spherical, and for the interactions between two squirmers, in three dimensions. These allow the hydrodynamic interactions of swimming microscopic organisms with confining boundaries, or each other, to be determined for arbitrary separation and, in particular, in the close proximity regime where approximate methods based on point singularity descriptions cease to be valid. We give a detailed description of the circular motion of an arbitrary squirmer moving parallel to a no-slip spherical boundary or flat free surface at close separation, finding that the circling generically has opposite sense at free surfaces and at solid boundaries. While the asymptotic interaction is symmetric under head-tail reversal of the swimmer, in the near field microscopic structure can result in significant asymmetry. We also find the translational velocity towards the surface for a simple model with only the lowest...

  18. Exactness

    Institute of Scientific and Technical Information of China (English)

    许涛

    2004-01-01

    M r.Sm ith liked to be exact. O ne day when he was w alking in thestreet a m an cam e over and asked him E xcuse m e but w here's the , : “ ,nearest bookshop ?” The nearest bookshop Y ou have to cross a bridge and then turn “ ?to the right. ” A nd is the bridge long “ ?” Thirty m eters. “ ” The m an thanked him and went towards the bridge. Suddenly heheard som eone running after him . Stop M r.Sm ith w as shouting. I'm sorry. I just rem em bered ...

  19. Logical gaps in the approximate solutions of the social learning game and an exact solution.

    Science.gov (United States)

    Dai, Wenjie; Wang, Xin; Di, Zengru; Wu, Jinshan

    2014-01-01

    After the social learning models were proposed, finding solutions to the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built either upon an ad-hoc argument or a twisted Bayesian analysis of the games. Here, we present logical gaps in those solutions and offer an exact solution of our own. We also introduce a minor extension to the original game so that not only logical differences but also differences in action outcomes among those solutions become visible.

  20. Logical gaps in the approximate solutions of the social learning game and an exact solution.

    Directory of Open Access Journals (Sweden)

    Wenjie Dai

    Full Text Available After the social learning models were proposed, finding solutions to the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built either upon an ad-hoc argument or a twisted Bayesian analysis of the games. Here, we present logical gaps in those solutions and offer an exact solution of our own. We also introduce a minor extension to the original game so that not only logical differences but also differences in action outcomes among those solutions become visible.

  1. Dual solution of Casson fluid over a porous medium: Exact solutions with extra boundary condition

    Science.gov (United States)

    Khan, Najeeb Alam; Khan, Sidra

    2016-12-01

    In this article we calculate the exact solution of the steady flow of non-Newtonian Casson fluid, over a stretching/shrinking sheet. The governing partial differential equations (PDEs) are transformed into ordinary differential equation (ODE) by using similarity transformation and then solved analytically by utilizing the exact solution. The closed form unique solution is obtained in the case of stretching sheet whereas for shrinking sheet unique and dual solutions are obtained. Influences of Casson fluid and suction/injection parameter on dimensionless velocity function are discussed and plotted graphically; also the effects of skin friction coefficient are presented in graphical form. Comparisons of current solutions with previous study are also made for the verification of the present study.

  2. Exact travelling wave solutions for four forms of nonlinear Klein-Gordon equations

    Energy Technology Data Exchange (ETDEWEB)

    Sirendaoreji [College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, Inner Mongolia (China)]. E-mail: siren@imnu.edu.cn

    2007-04-09

    A variable separated equation and its solutions are used to construct the exact travelling wave solutions for four forms of nonlinear Klein-Gordon equations. The solutions previously obtained by the tanh and sech method are recovered. New and more exact travelling wave solutions including solitons, kink and anti-kink, bell and anti-bell solitary wave solutions, periodic solutions, singular solutions and exponential solutions are found.

  3. Exact solution of the classical mechanical quadratic Zeeman effect

    Indian Academy of Sciences (India)

    Sambhu N Datta; Anshu Pandey

    2007-06-01

    We address the curious problem of quadratic Zeeman effect at the classical mechanical level. The problem has been very well understood for decades, but an analytical solution of the equations of motion is still to be found. This state of affairs persists because the simultaneous presence of the Coulombic and quadratic terms lowers the dynamical symmetry. Energy and orbital angular momentum are still constants of motion. We find the exact solutions by introducing the concept of an image ellipse. The quadratic effect leads to a dilation of space–time, and a one-to-one correspondence is observed for pairs of physical quantities like energy and angular momentum, and the maximum and minimum distances from the Coulomb center for the Zeeman orbit and the corresponding pairs for the image ellipse. Thus, instead of finding additional conserved quantities, we find constants of motion for an additional dynamics, namely, the image problem. The trajectory is open, in agreement with Bertrand's theorem, but necessarily bound. A stable unbound trajectory does not exist for real values of energy and angular momentum. The radial distance, the angle covered in the plane of the orbit, and the time are uniquely determined by introducing further the concept of an image circle. While the radial distance is defined in a closed form as a transcendental function of the image-circular angle, the corresponding orbit angle and time variables are found in the form of two convergent series expansions. The latter two variables are especially contracted, thereby leading to a precession of the open cycles around the Coulomb center. It is expected that the space–time dilation effect observed here would somehow influence the solution of the quantum mechanical problem at the non-relativistic level.

  4. Quantum algebra of $N$ superspace

    CERN Document Server

    Hatcher, N; Stephany, J

    2006-01-01

    We identify the quantum algebra of position and momentum operators for a quantum system in superspace bearing an irreducible representation of the super Poinca\\'e algebra. This algebra is noncommutative for the position operators. We use the properties of superprojectors in D=4 $N$ superspace to construct explicit position and momentum operators satisfying the algebra. They act on wave functions corresponding to different supermultiplets classified by its superspin. We show that the quantum algebra associated to the massive superparticle is a particular case described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently.

  5. On conformal supergravity and harmonic superspace

    CERN Document Server

    Butter, Daniel

    2015-01-01

    This paper describes a fully covariant approach to harmonic superspace. It is based on the conformal superspace description of conformal supergravity and involves extending the supermanifold M^{4|8} by the tangent bundle of CP^1. The resulting superspace M^{4|8} x TCP^1 can be identified in a certain gauge with the conventional harmonic superspace M^{4|8} x S^2. This approach not only makes the connection to projective superspace transparent, but simplifies calculations in harmonic superspace significantly by eliminating the need to deal directly with supergravity prepotentials. As an application of the covariant approach, we derive from harmonic superspace the full component action for the sigma model of a hyperkahler cone coupled to conformal supergravity. Further applications are also sketched.

  6. New Exact Solutions for (1 + 1)-Dimensional Dispersion-Less System

    Institute of Scientific and Technical Information of China (English)

    WANG Xian-Jun; Naranmandula; FU Jing-Li; HU Jian-Guo; BAO Gang; Tubuxin

    2008-01-01

    Using improved homogeneous balance method, we obtain complex function form new exact solutions for the (1 + l)-dimensional dispersion-less system, and from the exact solutions we derive real function form solution of the field u. Based on this real function form solution, we find some new interesting coherent structures by selecting arbitrary functions appropriately.

  7. Symmetric Teleparallel Gravity: Some Exact Solutions and Spinor Couplings

    Science.gov (United States)

    Adak, Muzaffer; Sert, Özcan; Kalay, Mestan; Sari, Murat

    2013-12-01

    In this paper, we elaborate on the symmetric teleparallel gravity (STPG) written in a non-Riemannian space-time with nonzero nonmetricity, but zero torsion and zero curvature. First, we give a prescription for obtaining the nonmetricity from the metric in a peculiar gauge. Then, we state that under a novel prescription of parallel transportation of a tangent vector in this non-Riemannian geometry, the autoparallel curves coincide with those of the Riemannian space-times. Subsequently, we represent the symmetric teleparallel theory of gravity by the most general quadratic and parity conserving Lagrangian with lagrange multipliers for vanishing torsion and curvature. We show that our Lagrangian is equivalent to the Einstein-Hilbert Lagrangian for certain values of coupling coefficients. Thus, we arrive at calculating the field equations via independent variations. Then, we obtain in turn conformal, spherically symmetric static, cosmological and pp-wave solutions exactly. Finally, we discuss a minimal coupling of a spin-1/2 field to STPG.

  8. Some exact solutions of magnetized viscous model in string cosmology

    Indian Academy of Sciences (India)

    C P Singh

    2014-07-01

    In this paper, we study anisotropic Bianchi-V Universe with magnetic field and bulk viscous fluid in string cosmology. Exact solutions of the field equations are obtained by using the equation of state (EoS) for a cloud of strings, and a relationship between bulk viscous coefficient and scalar expansion. The bulk viscous coefficient is assumed to be inversely proportional to the expansion scalar. It is interesting to examine the effects of magnetized bulk viscous string model in early and late stages of evolution of the Universe. This paper presents different string models like geometrical (Nambu string), Takabayasi (p-string) and Reddy string models by taking certain physical conditions. We discuss the nature of classical potential for viscous fluid with and without magnetic field. The presence of bulk viscosity stops the Universe from becoming empty in its future evolution. It is observed that the Universe expands with decelerated rate in the presence of viscous fluid with magnetic field whereas, it expands with marginal inflation in the presence of viscous fluid without magnetic field. The other physical and geometrical aspects of each string model are discussed in detail.

  9. Exact Integral Solutions for Two-Phase Flow

    Science.gov (United States)

    McWhorter, David B.; Sunada, Daniel K.

    1990-03-01

    Exact integral solutions for the horizontal, unsteady flow of two viscous, incompressible fluids are derived. Both one-dimensional and radial displacements are calculated with full consideration of capillary drive and for arbitrary capillary-hydraulic properties. One-dimensional, unidirectional displacement of a nonwetting phase is shown to occur increasingly like a shock front as the pore-size distribution becomes wider. This is in contrast to the situation when an inviscid nonwetting phase is displaced. The penetration of a nonwetting phase into porous media otherwise saturated by a wetting phase occurs in narrow, elongate distributions. Such distributions result in rapid and extensive penetration by the nonwetting phase. The process is remarkably sensitive to the capillary-hydraulic properties that determine the value of knw/kw at large wetting phase saturations, a region in which laboratory measurements provide the least resolution. The penetration of a nonwetting phase can be expected to be dramatically affected by the presence of fissures, worm holes, or other macropores. Calculations for radial displacement of a nonwetting phase resident at a small initial saturation show the displacement to be inefficient. The fractional flow of the nonwetting phase falls rapidly and, for a specific example, becomes 1% by the time one pore volume of water has been injected.

  10. Exact Traveling Wave Solutions for Wick-Type Stochastic Schamel KdV Equation

    Directory of Open Access Journals (Sweden)

    Hossam A. Ghany

    2014-01-01

    Full Text Available F-expansion method is proposed to seek exact solutions of nonlinear partial differential equations. By means of Hermite transform, inverse Hermite transform, and white noise analysis, the variable coefficients and Wick-type stochastic Schamel KdV equations are completely described. Abundant exact traveling wave solutions for variable coefficients Schamel KdV equations are given. These solutions include exact stochastic Jacobi elliptic functions, trigonometric functions, and hyperbolic functions solutions.

  11. Exact solutions of some nonlinear partial differential equations using functional variable method

    Indian Academy of Sciences (India)

    A Nazarzadeh; M Eslami; M Mirzazadeh

    2013-08-01

    The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm Kadomtsev–Petviashvili equation and the higher-order nonlinear Schrödinger equation. By using this useful method, we found some exact solutions of the above-mentioned equations. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. It is shown that the proposed method is effective and general.

  12. Formulation of supergravity without superspace

    CERN Document Server

    Ferrara, S

    1979-01-01

    Supergravity, the particle theory which unifies under a unique gauge principle the quantum-mechanical concept of spin and space-time geometry, is formulated in terms of quantities defined over Minkowski space-time. 'l'he relation between this formulation and the fonnulation which uses superspace, the space-time supplemented by spinning degrees of freedom, is also briefly discussed.

  13. Orientifolding in N = 2 Superspace

    NARCIS (Netherlands)

    Robles-Llana, D.; Rocek, M.; Saueressig, Frank; Theis, U.; Vandoren, S.

    2007-01-01

    We discuss orientifold projections on superspace effective actions for hypermultiplets. We present a simple and new mechanism that allows one to find the K¨ahler potential and complex structure for the N = 1 theory directly in terms of the parent N = 2 theory. As an application, we demonstrate our m

  14. EXACT SOLITARY WAVE SOLUTIONS TO A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS USING DIRECT ALGEBRAIC METHOD

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.

  15. New explicit and exact solutions of the Benney-Kawahara-Lin equation

    Institute of Scientific and Technical Information of China (English)

    Xie Yuan-Xi

    2009-01-01

    In this paper, we present a combination method of constructing the explicit and exact solutions of nonlinear partial differential equations. And as an illustrative example, we apply the method to the Benney-Kawahara-Lin equation and derive its many explicit and exact solutions which are all new solutions.

  16. An Exact Solution to the Two-Particle Boltzmann Equation System for Maxwell Gases

    Institute of Scientific and Technical Information of China (English)

    布仁满都拉; 赵迎春

    2012-01-01

    An exact solution to the two-particle Boltzmann equation system for Maxwell gases is obtained with use of Bobylev approach.The relationship between the exact solution and the self-similar solution of the boltzmann equation is also given.

  17. Numerical and Exact Solution of Buckling Load For Beam on Elastic Foundation

    Directory of Open Access Journals (Sweden)

    Roland JANČO

    2013-06-01

    Full Text Available In this paper we will be presented the exact solution of buckling load for supported beam on elastic foundation. Exact solution will be compared with numerical solution by FEM in our code in Matlab. Implementation of buckling to FEM will be presented here.

  18. Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

    Science.gov (United States)

    Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

    2015-07-01

    Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

  19. A Series of Exact Solutions of (2+1)-Dimensional CDGKS Equation

    Institute of Scientific and Technical Information of China (English)

    YANG Zong-Hang

    2006-01-01

    An algebraic method with symbolic computation is devised to uniformly construct a series of exact solutions of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawda equation. The solutions obtained in this paper include solitary wave solutions, rational solutions, triangular periodic solutions, Jacobi and Weierstrass doubly periodic solutions. Among them, the Jacobi periodic solutions exactly degenerate to the solutions at a certain limit condition. Compared with most existing tanh method, the method used here can give new and more general solutions. More importantly, this method provides a guideline to classify the various types of the solution according to some parameters.

  20. Spherically-symmetric, cold collapse: the exact solutions and a comparison with self-similar solutions

    CERN Document Server

    Coughlin, Eric R

    2016-01-01

    We present the exact solutions for the collapse of a spherically-symmetric, cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These solutions exhibit a number of remarkable features, including the self-consistent formation of and subsequent accretion onto a central point mass. A number of specific examples are provided, and we show that Penston's solution of pressureless, self-similar collapse is recovered for polytropic density profiles; importantly, however, we demonstrate that the time over which this solution holds is fleetingly narrow, implying that much of the collapse proceeds non-self-similarly. We show that our solutions can naturally incorporate turbulent pressure support, and we investigate the evolution of overdensities -- potentially generated by such turbulence -- as the collapse proceeds. Finally, we analyze the evolution of the angular velocity and magnetic fields in the limit that their ...

  1. Exact solutions of the time-fractional Fisher equation by using modified trial equation method

    Science.gov (United States)

    Tandogan, Yusuf Ali; Bildik, Necdet

    2016-06-01

    In this study, modified trial equation method has been proposed to obtain precise solutions of nonlinear fractional differential equation. Using the modified test equation method, we obtained some new exact solutions of the time fractional nonlinear Fisher equation. The obtained results are classified as a soliton solution, singular solutions, rational function solutions and periodic solutions.

  2. The geometry of branes and extended superspaces

    Energy Technology Data Exchange (ETDEWEB)

    Chryssomalakos, C. E-mail: chryss@lie3.ific.uv.es; Azcarraga, J.A. de E-mail: azcarrag@lie1.ific.uv.es; Izquierdo, J.M. E-mail: izquierd@fta.uva.es; Perez Bueno, J.C. E-mail: pbueno@lie.ific.uv.es

    2000-02-14

    We argue that a description of supersymmetric extended objects from a unified geometric point of view requires an enlargement of superspace. To this aim we study in a systematic way how superspace groups and algebras arise from Grassmann spinors when these are assumed to be the only primary entities. In the process, we recover generalized space-time superalgebras and extensions of supersymmetry found earlier. The enlargement of ordinary superspace with new parameters gives rise to extended superspace groups, on which manifestly supersymmetric actions may be constructed for various types of p-branes, including D-branes (given by Chevalley-Eilenberg cocycles) with their Born-Infeld fields. This results in a field/extended superspace democracy for superbranes: all brane fields appear as pull-backs from a suitable target superspace. Our approach also clarifies some facts concerning the origin of the central charges for the different p-branes.

  3. Exact solution of the relativistic quantum Toda chain

    CERN Document Server

    Zhang, Xin; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng

    2016-01-01

    The relativistic quantum Toda chain model is studied with the generalized algebraic Bethe Ansatz method. By employing a set of local gauge transformations, proper local vacuum states can be obtained for this model. The exact spectrum and eigenstates of the model are thus constructed simultaneously.

  4. Orientifolding in N=2 superspace

    Energy Technology Data Exchange (ETDEWEB)

    Robles-Llana, D.; Saueressig, F.; Vandoren, S. [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Utrecht (Netherlands); Rocek, M. [C.N. Yang Institute for Theoretical Physics, Stony Brook University, NY 11794-3840 (United States); Theis, U. [Institute for Theoretical Physics, Friedrich-Schiller-University Jena, 07743 Jena (Germany)

    2007-05-15

    We discuss orientifold projections on superspace effective actions for hypermultiplets. We present a simple and new mechanism that allows one to find the Kaehler potential and complex structure for the N=1 theory directly in terms of the parent N=2 theory. As an application, we demonstrate our method for Calabi-Yau orientifold compactifications of type IIB superstrings. (Abstract Copyright [2007], Wiley Periodicals, Inc.)

  5. Super-Higgs in superspace

    Energy Technology Data Exchange (ETDEWEB)

    McGarrie, Moritz [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Tallarita, Gianni [Queen Mary Univ. London (United Kingdom). School of Physics and Astronomy

    2012-01-15

    We determine the effective gravitational couplings in superspace whose components reproduce the supergravity Higgs effect for the constrained Goldstino multiplet. It reproduces the known Gravitino sector whilst constraining the off-shell completion. We show that these components arise by computing the effective action. This may be useful for phenomenological studies and model building: We give an example of its application to multiple Goldstini. (orig.)

  6. Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation

    CERN Document Server

    Denicol, Gabriel S; Martinez, Mauricio; Noronha, Jorge; Strickland, Michael

    2014-01-01

    We present an exact solution to the Boltzmann equation which describes a system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion for arbitrary shear viscosity to entropy density ratio. This new solution is constructed by considering the conformal map between Minkowski space and the direct product of three dimensional de Sitter space with a line. The resulting solution respects SO(3)_q x SO(1,1) x Z_2 symmetry. We compare the exact kinetic solution with exact solutions of the corresponding macroscopic equations with the same symmetry that were obtained from the kinetic theory in ideal and second-order viscous hydrodynamic approximations.

  7. An Exact Formal Solution to Reaction-Diffusion Equations from Biomathematics

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    We study the exact formal solution to the simplified Keller-Segel system modelling chemotaxis. The method we use is series expanding. The main result is to attain the formal solution to the simplified Keller-Segel system.

  8. Unified derivation of exact solutions to the relativistic Coulomb problem: Lie algebraic approach

    Science.gov (United States)

    Panahi, H.; Baradaran, M.; Savadi, A.

    2015-10-01

    Exact algebraic solutions of the D-dimensional Dirac and Klein-Gordon equations for the Coulomb potential are obtained in a unified treatment. It is shown that two cases are reducible to the same basic equation, which can be solved exactly. Using the Lie algebraic approach, the general exact solutions of the problem are obtained within the framework of representation theory of the sl(2) Lie algebra.

  9. New Exact Solutions of the Integrable Broer-Kaup Equations in (2+1)-Dimensional Spaces

    Institute of Scientific and Technical Information of China (English)

    LI De-Sheng; ZHANG Hong-Qing

    2004-01-01

    In this paper,by improving some procedure of extended tanh-function method,some new exact solutions to the integrable Broer-Kaup equations in(2 + 1)-dimensional spaces are obtained,which include soliton-like solutions,solitary wave solutions,trigonometric function solutions,and rational solutions.

  10. New explicit exact solutions to a nonlinear dispersive-dissipative equation

    Institute of Scientific and Technical Information of China (English)

    Naranmandula; Wang Ke-Xie

    2004-01-01

    Using the first-integral method, we obtain a series of new explicit exact solutions such as exponential function solutions, triangular function solutions, singular solitary wave solution and kink solitary wave solution of a nonlinear dispersive-dissipative equation, which describes weak nonlinear ion-acoustic waves in plasma consisting of cold ions and warm electrons.

  11. Exact discrete soliton solutions of quintic discrete nonlinear Schr(o)dinger equation

    Institute of Scientific and Technical Information of China (English)

    Li Hua-Mei; Wu Feng-Min

    2005-01-01

    By using the extended hyperbolic function approach, we have studied a quintic discrete nonlinear Schrodinger equation and obtained new exact localized solutions, including the discrete bright soliton solution, dark soliton solution,alternating phase bright soliton solution and alternating phase dark soliton solution, if a special constraint is imposed on the coefficients of the equation.

  12. New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schr(o)dinger Equation

    Institute of Scientific and Technical Information of China (English)

    YANG Qin; DAI Chao-Qing; ZHANG Jie-Fang

    2005-01-01

    Some new exact travelling wave and period solutions of discrete nonlinear Schrodinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differentialdifferent models.

  13. On Exact Solutions to Partial Differential Equations by the Modified Homotopy Perturbation Method

    Institute of Scientific and Technical Information of China (English)

    Gang YANG; Ru-yun CHEN; Luo-gen YAO

    2012-01-01

    Based on the modified homotopy perturbation method (MHPM),exact solutions of certain partial differential equations are constructed by separation of variables and choosing the finite terms of a series in p as exact solutions.Under suitable initial conditions,the PDE is transformed into an ODE.Some illustrative examples reveal the efficiency of the proposed method.

  14. Exact periodic wave and soliton solutions in two-component Bose-Einstein condensates

    Institute of Scientific and Technical Information of China (English)

    Li Hua-Mei

    2007-01-01

    We present several families of exact solutions to a system of coupled nonlinear Schr(o)dinger equations. The model describes a binary mixture of two Bose-Einstein condensates in a magnetic trap potential. Using a mapping deformation method, we find exact periodic wave and soliton solutions, including bright and dark soliton pairs.

  15. Exact Numerical Solutions of Bose-Hubbard Model

    Institute of Scientific and Technical Information of China (English)

    ZHANG Dan; PAN Feng

    2004-01-01

    Hamiltonian of a one-dimensional Bose-Hubbard model is re-formulated by using differential realization of the boson algebra. Energy matrices can then be generated systematically by using a Mathematica package. The output can be taken as the input of other diagonalization codes. As examples, exact energy eigenvalues and the corresponding wavefunctions for some cases are obtained with a Fortran diagonalization code. Phase transition of the model is analyzed.

  16. Exact solution of an su(n) spin torus

    CERN Document Server

    Hao, Kun; Li, Guang-Liang; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng

    2016-01-01

    The trigonometric su(n) spin chain with anti-periodic boundary condition (su(n) spin torus) is demonstrated to be Yang-Baxter integrable. Based on some intrinsic properties of the R-matrix, certain operator product identities of the transfer matrix are derived. These identities and the asymptotic behavior of the transfer matrix together allow us to obtain the exact eigenvalues in terms of an inhomogeneous T-Q relation via the off-diagonal Bethe Ansatz.

  17. Exact solution of an su(n) spin torus

    Science.gov (United States)

    Hao, Kun; Cao, Junpeng; Li, Guang-Liang; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng

    2016-07-01

    The trigonometric su(n) spin chain with anti-periodic boundary condition (su(n) spin torus) is demonstrated to be Yang-Baxter integrable. Based on some intrinsic properties of the R-matrix, certain operator product identities of the transfer matrix are derived. These identities and the asymptotic behavior of the transfer matrix together allow us to obtain the exact eigenvalues in terms of an inhomogeneous T  -  Q relation via the off-diagonal Bethe Ansatz.

  18. Exact solutions for some nonlinear systems of partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Darwish, A.A. [Department of Mathematics, Faculty of Science, Helwan University (Egypt)], E-mail: profdarwish@yahoo.com; Ramady, A. [Department of Mathematics, Faculty of Science, Beni-Suef University (Egypt)], E-mail: aramady@yahoo.com

    2009-04-30

    A direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear systems of partial differential equations (PDEs) is used and implemented in a computer algebraic system. New solutions for some nonlinear partial differential equations (NLPDEs) are obtained. Graphs of the solutions are displayed.

  19. The hyperbolic Allen-Cahn equation: exact solutions

    Science.gov (United States)

    Nizovtseva, I. G.; Galenko, P. K.; Alexandrov, D. V.

    2016-10-01

    Using the first integral method, a general set of analytical solutions is obtained for the hyperbolic Allen-Cahn equation. The solutions are presented by (i) the class of continual solutions described by \\tanh -profiles for traveling waves of the order parameter, and (ii) the class of singular solutions which exhibit unbounded discontinuity in the profile of the order parameter at the origin of the coordinate system. It is shown that the solutions include the previous analytical results for the parabolic Allen-Cahn equation as a limited class of \\tanh -functions, in which the inertial effects are omitted.

  20. Observational Constraints on New Exact Inflationary Scalar-field Solutions

    CERN Document Server

    Barrow, John D

    2016-01-01

    An algorithm is used to generate new solutions of the scalar field equations in homogeneous and isotropic universes. Solutions can be found for pure scalar fields with various potentials in the absence and presence of spatial curvature and other perfect fluids. A series of generalisations of the Chaplygin gas and bulk viscous cosmological solutions for inflationary universes are found. We also show how the Hubble slow-roll parameters can be calculated using the solution algorithm and we compare these inflationary solutions with the observational data provided by the Planck 2015 collaboration in order to constraint and rule out some of these models.

  1. Application of differential constraint method to exact solution of second-grade fluid

    Institute of Scientific and Technical Information of China (English)

    Dao-xiang ZHANG; Su-xiao FENG; Zhi-ming LU; Yu-lu LIU

    2009-01-01

    A differential constraint method is used to obtain analytical solutions of a second-grade fluid flow. By using the first-order differential constraint condition, exact solutions of Poiseuille flows, jet flows and Couette flows subjected to suction or blowing forces, and planar elongational flows are derived. In addition, two new classes of exact solutions for a second-grade fluid flow are found. The obtained exact solutions show that the non-Newtonian second-grade flow behavior depends not only on the material viscosity but also on the material elasticity. Finally, some boundary value problems are discussed.

  2. New Exact Explicit Nonlinear Wave Solutions for the Broer-Kaup Equation

    Directory of Open Access Journals (Sweden)

    Zhenshu Wen

    2014-01-01

    Full Text Available We study the nonlinear wave solutions for the Broer-Kaup equation. Many exact explicit expressions of the nonlinear wave solutions for the equation are obtained by exploiting the bifurcation method and qualitative theory of dynamical systems. These solutions contain solitary wave solutions, singular solutions, periodic singular solutions, and kink-shaped solutions, most of which are new. Some previous results are extended.

  3. Searching Exact Solutions for Compact Stars in Braneworld: a conjecture

    OpenAIRE

    2007-01-01

    In the context of the braneworld, a method to find consistent solutions to Einstein's field equations in the interior of a spherically symmetric, static and non uniform stellar distribution with Weyl stresses is developed. This method, based in the fact that any braneworld stellar solution must have the general relativity solution as a limit, produces a constraint which reduces the degrees of freedom on the brane. Hence the non locality and non closure of the braneworld equations can be overc...

  4. A family of exact solutions for unpolarized Gowdy models

    CERN Document Server

    Obregón, O; Obregon, Octavio; Ryan, Michael P.

    1998-01-01

    Unpolarized Gowdy models are inhomogeneous cosmological models that depend on time and one spatial variable and have complicated nonlinear equations of motion. There are two topologies associated with these models, a three-torus and a one-sphere cross a two-sphere. The three-torus models have been used for numerical studies because it seems difficult to find analytic solutions to their nonlinear Einstein equations. The one-sphere cross tow-sphere models have even more complicated equations, but at least one family of analytic solutions can be given as a reinterpretation of known solutions. Various properties of this family of solutions are studied.

  5. Exact anisotropic viscous fluid solutions of Einstein's equations

    Science.gov (United States)

    Goenner, H. F. M.; Kowalewski, F.

    1989-05-01

    A method for obtaining anisotropic, rotationless viscous fluid matter solutions of Bianchi type I and Segré type [1, 111] with the barotropic equation of state is presented. Solutions for which the anisotropy decreases exponentially or with a power law as well as solutions with average Hubble parameterH ˜t -1 are discussed. Also, a class of solutions with constant anisotropy and Bianchi type VIh is found. The dominant energy condition holds and the transport coefficients show the right sign.

  6. Exact solution of quantum gravity in 1 + 1 dimensions

    Science.gov (United States)

    Rajeev, S. G.

    1982-06-01

    Quantum gravity in 1 + 1 dimensions, with zero cosmological constant is formulated, including contributions from all possible topologies. The spectrum and the S-matrix are calculated exactly. Pure gravity is found to exist in a disordered phase, dominated by topologically non-trivial configurations. In the presence of fermionic matter fields, space-time can undergo a phase transition to an ordered phase. It is a pleasure to thank Professor A.P. Balachandran, Professor R. Shankar and Professor A. Ashtekar, and C.G. Trahern, V.P. Nair and V. Rodgers.

  7. Exact solutions for the 2d one component plasma

    CERN Document Server

    Andersen, Timothy D

    2011-01-01

    The 2d one component gas of pointlike charges in a uniform neutralizing background interacting with a logarithmic potential is a common model for plasmas. In its classical equilibrium statistics at fixed temperature (canonical ensemble) it is formally related to certain types of random matrices with Gaussian distribution and complex eigenvalues. In this paper, I present an exact integration of this ensemble for $N$ such particles (or alternatively $N\\times N$ matrices) for all complex temperatures, a significant open problem in statistical physics for several decades.

  8. Exact Solutions of the Photon Equation in Anisotropic Spacetimes

    CERN Document Server

    Havare, A; Aydogdu, O; Salti, M; Yetkin, T; Havare, Ali; Korunur, Murat; Aydogdu, Oktay; Salti, Mustafa; Yetkin, Taylan

    2005-01-01

    In this paper we study solution of the photon equation (the Massless Duffin-Kemmer-Petiau equation (mDKP)) in anisotropic expanding the Bianchi-I type spacetime using the Fourier analyze method. The harmonic oscillator behavior of the solutions is found. It is shown that Maxwell equations are equivalent to the photon equation.

  9. New Exact Solutions to NLS Equation and Coupled NLS Equations

    Institute of Scientific and Technical Information of China (English)

    FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo

    2004-01-01

    A transformation is introduced on the basis of the projective Riccati equations, and it is applied as an intermediate in expansion method to solve nonlinear Schrodinger (NLS) equation and coupled NLS equations. Many kinds of envelope travelling wave solutions including envelope solitary wave solution are obtained, in which some are found for the first time.

  10. The exact solutions to (2+1)-dimensional nonlinear Schrǒdinger equation

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jin-liang; WANG Ming-liang; FANG Zong-de

    2004-01-01

    By using the extended F-expansion method, the exact solutions,including periodic wave solutions expressed by Jacobi elliptic functions, for (2+1)-dimensional nonlinear Schrǒdinger equation are derived. In the limit cases, the solitary wave solutions and the other type of traveling wave solutions for the system are obtained.

  11. Exact Solutions for a Higher-Order Nonlinear Schr(o)dinger Equation in Atmospheric Dynamics

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    By giving prior assumptions on the form of the solutions, we succeed to find several exact solutions for a higher-order nonlinear Schrodinger equation derived from one important model in the study of atmospheric and ocean dynamical systems. Our analytical solutions include bright and dark solitary waves, and periodical solutions, which can be used to explain atmospheric phenomena.

  12. A method for constructing exact solutions and application to Benjamin Ono equation

    Institute of Scientific and Technical Information of China (English)

    Wang Zhen; Li De-Sheng; Lu Hui-Fang; Zhang Hong-Qing

    2005-01-01

    By using an improved projective Riccati equation method, this paper obtains several types of exact travelling wave solutions to the Benjamin Ono equation which include multiple soliton solutions, periodic soliton solutions and Weierstrass function solutions. Some of them are found for the first time. The method can be applied to other nonlinear evolution equations in mathematical physics.

  13. New Families of Exact Solutions for (2+1)-Dimensional Broer-Kaup System

    Institute of Scientific and Technical Information of China (English)

    ZHAO Hong; BAI Cheng-Lin; HAN Ji-Guang

    2005-01-01

    Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions, are obtained.

  14. Exact Shock Solution of a Coupled System of Delay Differential Equations: A Car-Following Model

    Science.gov (United States)

    Tutiya, Yohei; Kanai, Masahiro

    2007-08-01

    In this letter, we present exact shock solutions of a coupled system of delay differential equations, which was introduced as a traffic-flow model called car-following model. We use the Hirota method, originally developed in order to solve soliton equations. The relevant delay differential equations have been known to allow exact solutions expressed by elliptic functions with periodic boundary conditions. In the present work, however, shock solutions are obtained with open boundaries, representing the stationary propagation of a traffic jam.

  15. AUTO-DARBOUX TRANSFORMATION AND EXACT SOLUTIONS OF THE BRUSSELATOR REACTION DIFFUSION MODEL

    Institute of Scientific and Technical Information of China (English)

    闫振亚; 张鸿庆

    2001-01-01

    Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known.Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine- cosine method, more exact solutions are found which contain soliton solutions.

  16. Testing the Cactus code on exact solutions of Einstein field equations

    OpenAIRE

    Vulcanov, D.; M. Alcubierre

    2002-01-01

    The article presents a series of numerical simulations of exact solutions of the Einstein equations performed using the Cactus code, a complete 3-dimensional machinery for numerical relativity. We describe an application (''''thorn'') for the Cactus code that can be used for evolving a variety of exact solutions, with and without matter, including solutions used in modern cosmology for modeling the early stages of the universe. Our main purpose has been to test the Cactus code on these well-k...

  17. Prandtl's Boundary Layer Equation for Two-Dimensional Flow: Exact Solutions via the Simplest Equation Method

    Directory of Open Access Journals (Sweden)

    Taha Aziz

    2013-01-01

    Full Text Available The simplest equation method is employed to construct some new exact closed-form solutions of the general Prandtl's boundary layer equation for two-dimensional flow with vanishing or uniform mainstream velocity. We obtain solutions for the case when the simplest equation is the Bernoulli equation or the Riccati equation. Prandtl's boundary layer equation arises in the study of various physical models of fluid dynamics. Thus finding the exact solutions of this equation is of great importance and interest.

  18. Exact solutions for logistic reaction-diffusion equations in biology

    Science.gov (United States)

    Broadbridge, P.; Bradshaw-Hajek, B. H.

    2016-08-01

    Reaction-diffusion equations with a nonlinear source have been widely used to model various systems, with particular application to biology. Here, we provide a solution technique for these types of equations in N-dimensions. The nonclassical symmetry method leads to a single relationship between the nonlinear diffusion coefficient and the nonlinear reaction term; the subsequent solutions for the Kirchhoff variable are exponential in time (either growth or decay) and satisfy the linear Helmholtz equation in space. Example solutions are given in two dimensions for particular parameter sets for both quadratic and cubic reaction terms.

  19. Exact time-localized solutions in Vacuum String Field Theory

    CERN Document Server

    Bonora, L; Santos, R J S; Tolla, D D

    2004-01-01

    We address the problem of finding star algebra projectors that exhibit localized time profiles. We use the double Wick rotation method, starting from an Euclidean (unconventional) lump solution, which is characterized by the Neumann matrix being the conventional one for the continuous spectrum, while the inverse of the conventional one for the discrete spectrum. This is still a solution of the projector equation and we show that, after inverse Wick-rotation, its time profile has the desired localized time dependence. We study it in detail in the low energy regime (field theory limit) and in the extreme high energy regime (tensionless limit) and show its similarities with the rolling tachyon solution.

  20. Exact solution of some linear matrix equations using algebraic methods

    Science.gov (United States)

    Djaferis, T. E.; Mitter, S. K.

    1977-01-01

    A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

  1. 5D Lovelock gravity: new exact solutions with torsion

    CERN Document Server

    Cvetković, B

    2016-01-01

    We investigate Lovelock gravity in five dimensions in first order formalism. We construct a new class of solutions: BTZ black ring with(out) torsion. We show that our solution with torsion exists in the different sector of the Lovelock gravity compared to Lovelock Chern-Simons and the sector investigated by Canfora et al. We compute conserved charges of the solutions by using Nester's formula, and confirm the results by canonical method. We show that the theory linearized around the background with torsion possesses additional degrees of freedom compared to general relativity.

  2. Exact solutions to quadratic gravity generated by a conformal method

    CERN Document Server

    Pravda, Vojtech; Podolsky, Jiri; Svarc, Robert

    2016-01-01

    We study the role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one non-linear partial differential equation for the conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. We show that all spacetimes conformal to Kundt are either Kundt or Robinson--Trautmann, and we provide explicit Kundt and Robinson--Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.

  3. Exact half-BPS type IIB interface solutions I: local solution and supersymmetric Janus

    Energy Technology Data Exchange (ETDEWEB)

    D' Hoker, Eric; Estes, John; Gutperle, Michael [Department of Physics and Astronomy, University of California, Los Angeles, CA 90095 (United States)

    2007-06-15

    The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold AdS{sub 4} x S{sup 2} x S{sup 2} x {sigma} with SO(2, 3) x SO(3) x SO(3) symmetry in terms of two holomorphic functions on a Riemann surface {sigma}, which generally has a boundary. This is achieved by reducing the BPS equations using the above symmetry requirements, proving that all solutions of the BPS equations solve the full Type IIB supergravity field equations, mapping the BPS equations onto a new integrable system akin to the Liouville and Sine-Gordon theories, and mapping this integrable system to a linear equation which can be solved exactly. Amongst the infinite class of solutions, a non-singular Janus solution is identified which provides the AdS/CFT dual of the maximally supersymmetric Yang-Mills interface theory discovered recently. The construction of general classes of globally non-singular solutions, including fully back-reacted AdS{sub 5} x S{sup 5} and supersymmetric Janus doped with D5 and/or NS5 branes, is deferred to a companion paper.

  4. A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Ji Juan-Juan

    2017-01-01

    Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

  5. New exact perfect fluid solutions of Einstein's equations. II

    Science.gov (United States)

    Uggla, Claes; Rosquist, Kjell

    1990-12-01

    A family of new spatially homogeneous Bianchi type VIh perfect fluid solutions of the Einstein equations is presented. The fluid flow is orthogonal to the spatially homogeneous hypersurfaces, and the pressure is proportional to the energy density.

  6. Exact Solutions of Bogoyavlenskii Coupled KdV Equations

    Institute of Scientific and Technical Information of China (English)

    HUHeng-Chun; LOUSen-Yue

    2004-01-01

    The special soliton solutions of Bogoyavlenskii coupled KdV equations are obtained by means of the standard Weiss-Tabor -Carnvale Painleve' truncation expansion and the nonstandard truncation of a modified Conte's invariant Painlevé expansion.

  7. EXACT SOLUTIONS FOR MAGNETOHYDRODYNAMIC FLOW IN A ROTATING FLUID

    Institute of Scientific and Technical Information of China (English)

    S.Asghar; Masood Khan; A.M.Siddiqui; T.Hayat

    2002-01-01

    An analytical solution is obtained for the flow due to solid-body rotations of an oscillating porous disk and of a fluid at infinity. Neglecting the induced magnetic field, the effects of the transversely applied magnetic field on the flow are studied. Further, the flow confined between two disks is also discussed. It is found that an infinite number of solutions exist for the flow confined between two disks.

  8. Analytical exact solution of the non-linear Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da [Universidade de Brasilia (UnB), DF (Brazil). Inst. de Fisica. Grupo de Fisica e Matematica

    2011-07-01

    Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)

  9. Homogenous Balance Method and Exact Analytical Solutions for Whitham-Broer-Kaup Equations in Shallow Water

    Institute of Scientific and Technical Information of China (English)

    XIAZhi

    2004-01-01

    Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.

  10. Some new exact solutions to the Burgers-Fisher equation and generalized Burgers-Fisher equation

    Institute of Scientific and Technical Information of China (English)

    Jiang Lu; Guo Yu-Cui; Xu Shu-Jiang

    2007-01-01

    Some new exact solutions of the Burgers-Fisher equation and generalized Burgers-Fisher equation have been obtained by using the first integral method. These solutions include exponential function solutions, singular solitary wave solutions and some more complex solutions whose figures are given in the article. The result shows that the first integral method is one of the most effective approaches to obtain the solutions of the nonlinear partial differential equations.

  11. Exact Solutions to Extended Nonlinear Schr(o)dinger Equation in Monomode Optical Fiber

    Institute of Scientific and Technical Information of China (English)

    BAI Cheng-Lin; ZHAO Hong; Wang Wei-Tao

    2006-01-01

    By using the generally projective Riccati equation method, more new exact travelling wave solutions to extended nonlinear Schr(o)dinger equation (NLSE), which describes the femtosecond pulse propagation in monomode optical fiber, are found, which include bright soliton solution, dark soliton solution, new solitary waves, periodic solutions, and rational solutions. The finding of abundant solution structures for extended NLSE helps to study the movement rule of femtosecond pulse propagation in monomode optical fiber.

  12. Mushy-zone model with an exact solution

    Energy Technology Data Exchange (ETDEWEB)

    Solomon, A. D.; Wilson, D. G.; Alexiades, V.

    1982-04-01

    In this paper we propose a very simple model of a mushy zone which admits of an explicit solution. To our knowledge, it is the only instance where an actual observation of the mushy zone width and structure is used as a partial basis for the model definition. The model rests upon two unknown parameters. The first determines the relation between the equilibrium temperature gradient and the mushy zone width. The second depends upon the dendritic structure in the mushy zone, and is related to the solid fraction. Both can be estimated from experiments. We will limit ourselves to defining the model, presenting its closed form solution, and giving tables from which the solution can be found explicitly. It is shown that in most cases the predicted mushy zone is of very negligible importance.

  13. Three-dimensional dilatonic gravity's rainbow: Exact solutions

    Science.gov (United States)

    Hossein Hendi, Seyed; Eslam Panah, Behzad; Panahiyan, Shahram

    2016-10-01

    Deep relations of dark energy scenario and string theory results into dilaton gravity, on the one hand, and the connection between quantum gravity and gravity's rainbow, on the other hand, motivate us to consider three-dimensional dilatonic black hole solutions in gravity's rainbow. We obtain two classes of the solutions, which are polynomial and logarithmic forms. We also calculate conserved and thermodynamic quantities, and examine the first law of thermodynamics for both classes. In addition, we study thermal stability and show that one of the classes is thermally stable while the other one is unstable.

  14. Three-dimensional dilatonic gravity's rainbow: Exact solutions

    Science.gov (United States)

    Hossein Hendi, Seyed; Eslam Panah, Behzad; Panahiyan, Shahram

    2016-10-01

    Deep relations of dark energy scenario and string theory results into dilaton gravity, on the one hand, and the connection between quantum gravity and gravity's rainbow, on the other hand, motivate us to consider three-dimensional dilatonic black hole solutions in gravity's rainbow. We obtain two classes of the solutions, which are polynomial and logarithmic forms. We also calculate conserved and thermodynamic quantities, and examine the first law of thermodynamics for both classes. In addition, we study thermal stability and show that one of the classes is thermally stable while the other one is unstable.

  15. Families of exact solutions of a 2D gravity model minimally coupled to electrodynamics

    CERN Document Server

    Moayedi, S K

    2001-01-01

    Three families of exact solutions for 2-dimensional gravity minimally coupled to electrodynamics are obtained in the context of ${\\cal R}=T$ theory. It is shown, by supersymmetric formalism of quantum mechanics, that the quantum dynamics of a neutral bosonic particle on static backgrounds with both varying curvature and electric field is exactly solvable.

  16. Exact solutions of the high dimensional hard-core Fermi-Hubbard model

    Institute of Scientific and Technical Information of China (English)

    潘峰; 戴连荣

    2001-01-01

    A simple algebraic approach to exact solutions of the hard-core Fermi-Hubbard model is proposed. Excitation energies and the corresponding wavefunctions of the hard-core Fermi-Hubbard model with nearest neighbor hopping cases in high dimension are obtained by using this method, which manifests that the model is exactly solvable in any dimension.

  17. Some Exact Solutions of the Semilocal Popov Equations with Many Flavors

    CERN Document Server

    Kim, Chanju

    2015-01-01

    In 2+1 dimensional nonrelativistic Chern-Simons gauge theories on $S^2$ which has a global $SU(M)$ symmetry, the semilocal Popov vortex equations are obtained as Bogomolny equations by minimizing the energy in the presence of a uniform external magnetic field. We study the equations with many flavors and find several families of exact solutions. The equations are transformed to the semilocal Liouville equations for which some exact solutions are known. In this paper, we find new exact solutions of the semilocal Liouville equations. Using these solutions, we construct solutions to the semilocal Popov equations. The solutions are expressed in terms of one or more arbitrary rational functions on $S^2$. Some simple solutions reduce to $CP^{M-1}$ lump configurations.

  18. Exact and variational solutions of 3D eigenmodes in high gain FELs [Exact and variational solutions of 3D eigenmodes in high gain free electron lasers

    Energy Technology Data Exchange (ETDEWEB)

    Xie, Ming [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

    2000-05-18

    Exact solution and variational approximation of eigenmodes in high gain FELs are presented. These eigenmodes specify transverse profiles and exponential growth rates of the laser field before saturation. They are self-consistent solutions of coupled Maxwell–Vlasov equations describing FEL interaction taking into account the effects due to energy spread, emittance and betatron oscillations of the electron beam, as well as diffraction and optical guiding of the laser field. A new formalism of scaling is introduced and based on which solutions in various limiting cases are discussed. Additionally, a fitting formula is obtained from interpolating the variational solution for quick calculation of exponential growth rate of the fundamental mode.

  19. EXACT SOLITARY WAVE SOLUTIONS OF THETWO NONLINEAR EVOLUTION EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    ZhuYanjuan; ZhangChunhua

    2005-01-01

    The solitary wave solutions of the combined KdV-mKdV-Burgers equation and the Kolmogorov-Petrovskii-Piskunov equation are obtained by means of the direct algebra method, which can be generalized to deal with high dimensional nonlinear evolution equations.

  20. Exact String-Like Solutions in Conformal Gravity

    CERN Document Server

    Verbin, Y

    2010-01-01

    The Cylindrically-symmetric static vacuum equations of Conformal Gravity are solved for the case of additional boost symmetry along the axis. We present the complete family of solutions which describe the exterior gravitational field of line sources in Conformal Gravity. We also analyze the null geodesics in these spaces.

  1. Exact Jacobian Elliptic Function Solutions to sinh-Gordon Equation

    Institute of Scientific and Technical Information of China (English)

    FU Zun-Tao; LIU Shi-Kuo; LIU Shi-Da

    2006-01-01

    In this paper, two transformations are introduced to solve sinh-Gordon equation by using the knowledge of elliptic equation and Jacobian elliptic functions.It is shown that different transformations are required in order to obtain more kinds of solutions to the sinh-Gordon equation.

  2. Exact Solutions for Fractional Differential-Difference Equations by an Extended Riccati Sub-ODE Method

    Institute of Scientific and Technical Information of China (English)

    FENG Qing-Hua

    2013-01-01

    In this paper,an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann-Liouville derivative.By a fractional complex transformation,a given fractional differential-difference equation can be turned into another differential-difference equation of integer order.The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system.As a result,some new exact solutions including hyperbolic function solutions,trigonometric function solutions and rational solutions are established.

  3. Exact Solutions for Fractional Differential-Difference Equations by an Extended Riccati Sub-ODE Method

    Science.gov (United States)

    Feng, Qing-Hua

    2013-05-01

    In this paper, an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann—Liouville derivative. By a fractional complex transformation, a given fractional differential-difference equation can be turned into another differential-difference equation of integer order. The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system. As a result, some new exact solutions including hyperbolic function solutions, trigonometric function solutions and rational solutions are established.

  4. A Large Class of Exact Solutions to the One-Dimensional Schrodinger Equation

    Science.gov (United States)

    Karaoglu, Bekir

    2007-01-01

    A remarkable property of a large class of functions is exploited to generate exact solutions to the one-dimensional Schrodinger equation. The method is simple and easy to implement. (Contains 1 table and 1 figure.)

  5. Adomian Decomposition Method and Exact Solutions of the Perturbed KdV Equation

    Institute of Scientific and Technical Information of China (English)

    WU Bin; LOU Sen-Yue

    2002-01-01

    The Adomian decomposition method is used to solve the Cauchy problem of the perturbed KdV equation.Three types of exact solitary wave solutions are reobtained via the A domian's approach by selecting the initial conditionsappropriately.

  6. New Exact Solutions for a Class of Nonlinear Coupled Differential Equations

    Institute of Scientific and Technical Information of China (English)

    ZHAO Hong; GUO Jun; BAI Cheng-Lin; HAN Ji-Guang

    2005-01-01

    More new exact solutions for a class of nonlinear coupled differential equations are obtained by using a direct and efficient hyperbola function transform method based on the idea of the extended homogeneous balance method.

  7. Painlevé analysis and exact solutions of a modified Boussinesq equation

    CERN Document Server

    Liu, Q P

    1995-01-01

    We consider a modified Boussinesq type equation. The Painlev\\'{e} test of the WTC method is performed for this equation and it shows that the equation has weak Painlev\\'{e} property. Some exact solutions are constructed.

  8. Adomian Decomposition Method and Exact Solutions of the Perturbed KdV Equation

    Institute of Scientific and Technical Information of China (English)

    WuBin; LOUSen-Yue

    2002-01-01

    The Adomian decomposition method is used to solve the Cauchy problem of the perturbed KdV equation.Three types of exact solitary wave solutions are reobtained via the Adomian's approach by selcting the initial conditions appropriately.

  9. Exact multiplicity of solutions to perturbed logistic type equations on a symmetric domain

    Institute of Scientific and Technical Information of China (English)

    LIU Ping; SHI JunPing; WANG YuWen

    2008-01-01

    We apply the imperfect bifurcation theory in Banach spaces to study the exact multiplicity of solutions to a perturbed logistic type equations on a symmetric spatial domain.We obtain the precise bifurcation diagrams.

  10. Exact multiplicity of solutions to perturbed logistic type equations on a symmetric domain

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    We apply the imperfect bifurcation theory in Banach spaces to study the exact multiplicity of solutions to a perturbed logistic type equations on a symmetric spatial domain. We obtain the precise bifurcation diagrams.

  11. Exact solutions of a class of fractional Hamiltonian equations involving Caputo derivatives

    Energy Technology Data Exchange (ETDEWEB)

    Baleanu, Dumitru [Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Ankara 06530 (Turkey); Trujillo, Juan J [Departamento de Analisis Matematico, University of La Laguna, 38271 La Laguna, Tenerife (Spain)], E-mail: dumitru@cankaya.edu.tr, E-mail: JTrujill@ullmat.es, E-mail: baleanu@venus.nipne.ro

    2009-11-15

    The fractional Hamiltonian equations corresponding to the Lagrangians of constrained systems within Caputo derivatives are investigated. The fractional phase space is obtained and the exact solutions of some constrained systems are obtained.

  12. Bäcklund Transformation and New Exact Solutions of the Sharma-Tasso-Olver Equation

    Directory of Open Access Journals (Sweden)

    Lin Jianming

    2011-01-01

    Full Text Available The Sharma-Tasso-Olver (STO equation is investigated. The Painlevé analysis is efficiently used for analytic study of this equation. The Bäcklund transformations and some new exact solutions are formally derived.

  13. Exact Traveling Wave Solutions for a Kind of Generalized Ginzburg-Landau Equation

    Institute of Scientific and Technical Information of China (English)

    LIU Cheng-Shi

    2005-01-01

    Using a complete discrimination system for polynomials, new exact traveling wave solutions for generalized Ginzburg-Landau equation are obtained. The method has general meaning for many similar problems.

  14. Exact solution of the Klein Gordon equation in the presence of a minimal length

    CERN Document Server

    Jana, T K

    2009-01-01

    We obtain exact solutions of the (1+1) dimensional Klein Gordon equation with linear vector and scalar potentials in the presence of a minimal length. Algebraic approach to the problem has also been studied.

  15. Exact Solutions for a Coupled Korteweg-de Vries System

    Science.gov (United States)

    Zuo, Da-Wei; Jia, Hui-Xian

    2016-11-01

    Korteweg-de Vries (KdV)-type equation can be used to characterise the dynamic behaviours of the shallow water waves and interfacial waves in the two-layer fluid with gradually varying depth. In this article, by virtue of the bilinear forms, rational solutions and three kind shapes (soliton-like, kink and bell, anti-bell, and bell shapes) for the Nth-order soliton-like solutions of a coupled KdV system are derived. Propagation and interaction of the solitons are analyzed: (1) Potential u shows three kind of shapes (soliton-like, kink, and anti-bell shapes); Potential v exhibits two type of shapes (soliton-like and bell shapes); (2) Interaction of the potentials u and v both display the fusion phenomena.

  16. Exact Scalar-Tensor Cosmological Solutions via Noether Symmetry

    CERN Document Server

    Belinchón, J A; Mak, M K

    2016-01-01

    In this paper, we investigate the Noether symmetries of a generalized scalar-tensor, Brans-Dicke type cosmological model, in which we consider explicit scalar field dependent couplings to the Ricci scalar, and to the scalar field kinetic energy, respectively. We also include the scalar field self-interaction potential into the gravitational action. From the condition of the vanishing of the Lie derivative of the gravitational cosmological Lagrangian with respect to a given vector field we obtain three cosmological solutions describing the time evolution of a spatially flat Friedman-Robertson-Walker Universe filled with a scalar field. The cosmological properties of the solutions are investigated in detail, and it is shown that they can describe a large variety of cosmological evolutions, including models that experience a smooth transition from a decelerating to an accelerating phase.

  17. Exact Anisotropic Solutions of the Generalized TOV Equation

    CERN Document Server

    Riazi, Nematollah; Sajadi, S Naseh; Assyaee, S Shahrokh

    2015-01-01

    We explore gravitating relativistic spheres composed of an anisotropic, barotropic uid. We assume a bi-polytropic equation of state which has a linear and a power-law terms. The generalized Tolman-Oppenheimer-Volkoff (TOV) equation which describes the hydrostatic equilibrium is obtained. The full system of equations are solved for solutions which are regular at the origin and asymptotically flat. Conditions for the appearance of horizon and a basic treatment of stability are also discussed.

  18. NEW EXACT SOLUTIONS TO KdV EQUATIONS WITH VARIABLE COEFFICIENTS OR FORCING

    Institute of Scientific and Technical Information of China (English)

    付遵涛; 刘式达; 刘式适; 赵强

    2004-01-01

    Jacobi elliptic function expansion method is extended to construct the exact solutions to another kind of KdV equations, which have variable coefficients or forcing terms. And new periodic solutions obtained by this method can be reduced to the solitontyped solutions under the limited condition.

  19. ABUNDANT EXACT SOLUTION STRUCTURES OF THE NIZHNIK-NOVIKOV-VESELOV EQUATION

    Institute of Scientific and Technical Information of China (English)

    张解放

    2001-01-01

    Using the extended homogeneous balance method, we have obtained abundant exact solution structures of a (2+ 1)-dimensional integrable model, the Nizhnik-Novikov-Veselov equation. By means of leading order terms analysis,the nonlinear transformations of the Nizhnik-Novikov-Veselov equation are given first, and then some special types of single solitary wave solution and multisoliton-like solutions are constructed.

  20. Exact Solutions of the Two-Dimensional Discrete Nonlinear Schr\\"odinger Equation with Saturable Nonlinearity

    CERN Document Server

    Khare, Avinash; Samuelsen, Mogens R; Saxena, Avadh; 10.1088/1751-8113/43/37/375209

    2010-01-01

    We show that the two-dimensional, nonlinear Schr\\"odinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the effective Peierls-Nabarro barrier for the pulse-like soliton solution is zero.

  1. STUDY ON EXACT ANALYTICAL SOLUTIONS FOR TWO SYSTEMS OF NONLINEAR EVOLUTION EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    闫振亚; 张鸿庆

    2001-01-01

    The homogeneous balance method was improved and applied to two systems of nonlinear evolution equations. As a result, several families of exact analytic solutions are derived by some new ansatzs. These solutions contain Wang's and Zhang's results and other new types of analytical solutions, such as rational fraction solutions and periodic solutions. The way can also be applied to solve more nonlinear partial differential equations.

  2. PAINLEV PROPERTY OF BURGERS-KDV EQUATION AND ITS EXACT SOLUTIONS

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    In this paper, we introduce the Painlev property of the Burgers-KdV equation. Two types of exact solutions to the equation are obtained by the standard truncated expansion metIn this paper, we introduce the Painlev property of the Burgers-KdV equation. Two types of exact solutions to the equation are obtained by the standard truncated expansion method and the extended standard truncated expansion method, respectively.hod and the extended standard truncated expansion method, respectively.

  3. Exact Travelling Solutions of Discrete sine-Gordon Equation via Extended Tanh-Function Approach

    Institute of Scientific and Technical Information of China (English)

    DAI Chao-Qing; ZHANG Jie-Fang

    2006-01-01

    In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach.

  4. A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit

    CERN Document Server

    Denicol, Gabriel S; Martinez, Mauricio; Noronha, Jorge; Strickland, Michael

    2014-01-01

    We present an exact solution of the relativistic Boltzmann equation for a system undergoing boost-invariant longitudinal and azimuthally symmetric transverse flow ("Gubser flow"). The resulting exact non-equilibrium dynamics is compared to 1st- and 2nd-order relativistic hydrodynamic approximations for various shear viscosity to entropy density ratios. This novel solution can be used to test the validity and accuracy of different hydrodynamic approximations in conditions similar to those generated in relativistic heavy-ion collisions.

  5. Exact solution for the unforced Duffing oscillator with cubic and quintic nonlinearities

    OpenAIRE

    Beléndez,Augusto; Beléndez Vázquez, Tarsicio; Martínez Guardiola, Francisco Javier; Pascual Villalobos, Carolina; Álvarez López, Mariela Lázara; Arribas Garde, Enrique

    2016-01-01

    The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, unforced cubic–quintic Duffing oscillator is solved exactly, providing exact expressions for the period and the solution. The period is given in terms of the complete elliptic integral of the first kind and the solution involves Jacobi elliptic functions. Some particular cases obtained varying the parameters that characterize this oscillator are presented and discussed. The behaviour of the per...

  6. Exact Solution of Unsteady Flow of Viscoelastic Fluid in a Pipe with Fractional Maxwell Model

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The unsteady flow of viscoelastic fluid in a cylindrical pipe was investigated using the fractional Maxwell model. Two special cases of unsteady pipe flow were expressed. The first is start-up flow, and the second is oscillating flow. The exact solution of start-up flow under a constant pressure gradient was obtained by using the theories of Laplace transform and Fourier-Bessel series for fractional derivatives. The exact solution of oscillating flow was obtained by utilizing the separation of variables.

  7. Complex Tanh-Function Expansion Method and Exact Solutions to Two Systems of Nonlinear Wave Equations

    Institute of Scientific and Technical Information of China (English)

    ZHANGJin-Liang; WANGMing-Liang

    2004-01-01

    The complex tanh-function expansion method was presented recently, and it can be applied to derive exact solutions to the Schroedinger-type nonlinear evolution equations directly without transformation. In this paper,the complex tanh-function expansion method is applied to derive the exact solutions to the general coupled nonlinear evolution equations. Zakharov system and a long-short-wave interaction system are considered as examples, and the new applications of the complex tanh-function expansion method are shown.

  8. Constructing exact solutions to discrete systems with the trial function method

    Institute of Scientific and Technical Information of China (English)

    Taogetusang Sirendaoerji

    2008-01-01

    Based on the homogenous balance method and the trial function method, several trial function methods composed of exponential functions are proposed and applied to nonlinear discrete systems. With the help of symbolic computation system, the new exact solitary wave solutions to discrete nonlinear mKdV lattice equation, discrete nonlinear (2+1) dimensional Toda lattice equation, Ablowitz-Ladik-lattice system are constructed.The method is of significance to seek exact solitary wave solutions to other nonlinear discrete systems.

  9. Exact Solutions of Discrete Complex Cubic Ginzburg-Landau Equation and Their Linear Stability

    Institute of Scientific and Technical Information of China (English)

    张金良; 刘治国

    2011-01-01

    The discrete complex cubic Ginzburg-Landau equation is an important model to describe a number of physical systems such as Taylor and frustrated vortices in hydrodynamics and semiconductor laser arrays in optics. In this paper, the exact solutions of the discrete complex cubic Ginzburg-Landau equation are derived using homogeneous balance principle and the GI/G-expansion method, and the linear stability of exact solutions is discussed.

  10. Complex Tanh-Function Expansion Method and Exact Solutions to Two Systems of Nonlinear Wave Equations

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jin-Liang; WANG Ming-Liang

    2004-01-01

    The complex tanh-function expansion method was presented recently, and it can be applied to derive exact solutions to the Schrodinger-type nonlinear evolution equations directly without transformation. In this paper,the complex tanh-function expansion method is applied to derive the exact solutions to the general coupled nonlinear evolution equations. Zakharov system and a long-short-wave interaction system are considered as examples, and the new applications of the complex tanh-function expansion method are shown.

  11. Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system

    CERN Document Server

    Cherniha, Roman

    2010-01-01

    Q-conditional symmetries of the classical Lotka-Volterra system in the case of one space variable are completely described and a set of such symmetries in explicit form is constructed. The relevant non-Lie ans\\"atze to reduce the classical Lotka-Volterra systems with correctly-specified coefficients to ODE systems and examples of new exact solutions are found. A possible biological interpretation of some exact solutions is presented.

  12. Exact solutions of a Flat Full Causal Bulk viscous FRW cosmological model through factorization

    CERN Document Server

    Cornejo-Pérez, O

    2012-01-01

    We study the classical flat full causal bulk viscous FRW cosmological model through the factorization method. The method allows to find some new exact parametric solutions for different values of the viscous parameter $s$. Special attention is given to the well known case $s=1/2$, for which the cosmological model admits scaling symmetries. Also, some exact parametric solutions for $s=1/2$ are obtained through the Lie group method.

  13. Exact Solutions of Chemically Reactive Solute Distribution in MHD Boundary Layer Flow over a Shrinking Surface

    Institute of Scientific and Technical Information of China (English)

    Chandaneswar Midya

    2012-01-01

    An analytical study of the distribution of a reactant solute undergoing a first-order chemical reaction in the boundary layer flow of an electrically conducting incompressible Buid over a linearly shrinking surface is presented. The Row is permeated by an externally applied magnetic Geld normal to the plane of the flow. The equations governing the Row and concentration Reid are reduced into a set of nonlinear ordinary differential equations using similarity variables. Closed form exact solutions of the reduced concentration equation are obtained for both prescribed power-law surface concentration (PSC) and power-law wall mass flux (PMF) as boundary conditions. The study reveals that the concentration over a shrinking sheet is signiRcantly different from that of a stretching surface. It s found that te solute boundary layer thickness is enhanced with the increasing values of the Schmidt number and the power-law index parameter, but decreases with enhanced vaJues of magnetic and reaction rate parameters for the PSC case. For the PMF case, the solute boundary layer thickness decreases with the increase of the Schmidt number, magnetic and reaction rate parameter for power-law index parameter n = 0. Negative solute boundary layer thickness is observed for the PMF case when n = 1 and 2, and these facts may not be realized in real-world applications.%An analytical study of the distribution of a reactant solute undergoing a first-order chemical reaction in the boundary layer flow of an electrically conducting incompressible fluid over a linearly shrinking surface is presented.The flow is permeated by an externally applied magnetic field normal to the plane of the flow.The equations governing the flow and concentration field are reduced into a set of nonlinear ordinary differential equations using similarity variables.Closed form exact solutions of the reduced concentration equation are obtained for both prescribed power-law surface concentration (PSC) and power-law wall

  14. New methods to provide exact solutions for some unidirectional motions of rate type fluids

    Directory of Open Access Journals (Sweden)

    Fetecau Corina

    2016-01-01

    Full Text Available Based on three immediate consequences of the governing equations corresponding to some unidirectional motions of rate type fluids, new motion problems are tackled for exact solutions. For generality purposes, exact solutions are developed for shear stress boundary value problems of generalized Burgers fluids. Such solutions, for which the shear stress instead of its differential expressions is given on the boundary, are lack in the literature for such fluids. Consequently, the first exact solutions for motions of rate type fluids induced by an infinite plate or a circular cylinder that applies a constant shear f or an oscillating shear f sin(ωt to the fluid are here presented. In addition, all steady-state solutions can easily be reduced to known solutions for second grade and Newtonian fluids.

  15. The exact solution of the Schrödinger equation with a polynomially spatially varying mass

    Science.gov (United States)

    Bednarik, Michal; Cervenka, Milan

    2017-07-01

    The Schrödinger equation with a position-dependent mass (SEPDM) is employed in many areas of quantum physics. Exact solutions for the SEPDM lie at the center of interest of the professional public because it helps us to understand the behavior of quantum particles in the cases in which their mass varies spatially. For this purpose, we used the mass function represented by a quartic polynomial and a quadratic potential function, which extends the current class of exact solutions of the SEPDM. The exact analytical solution of the problem is expressed as a linear combination of local Heun functions. Heun's equation contains many parameters, resulting in its general nature. We studied how limit changes in some of these parameters will affect the solution of the SEPDM. The obtained solutions are particularly suitable for the transfer matrix method and solutions of scattering problems; this is demonstrated by the calculation of bound states.

  16. EXACT SOLITRAY WAVE SOLUTIONS AND SINGULAR SOLUTIONS TO THE TWO-DIMENSIONAL NONLINEAR DISSIPATIVE-DISPERSIVE SYSTEM

    Institute of Scientific and Technical Information of China (English)

    李志斌; 陈天华

    2002-01-01

    An algorithm for constructing exact solitary wave solutions and singular solutions for a class of nonlinear dissipative-dispersive system is presented. With the aid of symbolic manipulation system Maple, some explicit solutions are obtained for the system in physically interesting but non-integrable cases.

  17. Exact Solutions of a Generalized Weighted Scale Free Network

    Directory of Open Access Journals (Sweden)

    Li Tan

    2013-01-01

    Full Text Available We investigate a class of generalized weighted scale-free networks, where the new vertex connects to m pairs of vertices selected preferentially. The key contribution of this paper is that, from the standpoint of random processes, we provide rigorous analytic solutions for the steady state distributions, including the vertex degree distribution, the vertex strength distribution and the edge weight distribution. Numerical simulations indicate that this network model yields three power law distributions for the vertex degrees, vertex strengths and edge weights, respectively.

  18. Exact solutions of multi-term fractional diffusion-wave equations with Robin type boundary conditions

    Institute of Scientific and Technical Information of China (English)

    Xiao-jing LIU; Ji-zeng WANG; Xiao-min WANG; You-he ZHOU

    2014-01-01

    General exact solutions in terms of wavelet expansion are obtained for multi-term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differ-ential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method.

  19. N=2 Conformal Superspace in Four Dimensions

    CERN Document Server

    Butter, Daniel

    2011-01-01

    We develop the geometry of four dimensional N=2 superspace where the entire conformal algebra of SU(2,2|2) is realized linearly in the structure group rather than just the SL(2,C) x U(2)_R subgroup of Lorentz and R-symmetries, extending to N=2 our prior result for N=1 superspace. This formulation explicitly lifts to superspace the existing methods of the N=2 superconformal tensor calculus; at the same time the geometry, when degauged to SL(2,C) x U(2)_R, reproduces the existing formulation of N=2 conformal supergravity constructed by Howe.

  20. The exact solutions of nonlinear problems by Homotopy Analysis Method (HAM

    Directory of Open Access Journals (Sweden)

    Hafiz Abdul Wahab

    2016-06-01

    Full Text Available The present paper presents the comparison of analytical techniques. We establish the existence of the phenomena of the noise terms in the perturbation series solution and find the exact solution of the nonlinear problems. If the noise terms exist, the Homotopy Analysis method gives the same series solution as in Adomian Decomposition Method as well as homotopy Perturbation Method (Wahab et al, 2015 and we get the exact solution using the initial guess in Homotopy Analysis Method using the results obtained by Adomian Decomposition Method.

  1. Exact solutions of the two-dimensional discrete nonlinear Schrodinger equation with saturable nonlinearity

    DEFF Research Database (Denmark)

    Khare, A.; Rasmussen, K. O.; Samuelsen, Mogens Rugholm

    2010-01-01

    We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the e......We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show...

  2. A new exact anisotropic solution of embedding class one

    Energy Technology Data Exchange (ETDEWEB)

    Maurya, S.K.; Smitha, T.T. [University of Nizwa, Department of Mathematical and Physical Sciences, College of Arts and Science, Nizwa (Oman); Gupta, Y.K. [Raj Kumar Goel Institute of Technology, Department of Mathematics, Ghaziabad (India); Rahaman, Farook [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India)

    2016-07-15

    We have presented a new anisotropic solution of Einstein's field equations for compact-star models. Einstein's field equations are solved by using the class-one condition (S.N. Pandey, S.P. Sharma, Gen. Relativ. Gravit. 14, 113 (1982)). We constructed the expression for the anisotropy factor (Δ) by using the pressure anisotropy condition and thereafter we obtained the physical parameters like energy density, radial and transverse pressure. These models parameters are well-behaved inside the star and satisfy all the required physical conditions. Also we observed the very interesting result that all physical parameters depend upon the anisotropy factor (Δ). The mass and radius of the present compact-star models are quite compatible with the observational astrophysical compact stellar objects like Her X-1, RXJ 1856-37, SAX J1808.4-3658(SS1), SAX J1808.4-3658(SS2). (orig.)

  3. Approach to exact solutions of cosmological perturbations: Tachyon field inflation

    Science.gov (United States)

    Herrera, Ramón; Pérez, Roberto G.

    2016-03-01

    An inflationary universe scenario in the context of a tachyon field is studied. This study is carried out using an ansatz for the effective potential of cosmological perturbations U (η ). We describe in great detail the analytical solutions of the scalar and tensor perturbations for two different Ansätze for the effective potential of cosmological perturbations: Easther's model and an effective potential similar to power-law inflation. Also, we find from the background equations that the effective tachyonic potentials V (φ ) in both models satisfy the properties of a tachyonic potential. We consider the recent data from the Planck to constrain the parameters in our effective potential generating the cosmological perturbations.

  4. Two exact solutions of the DPL non-Fourier heat conduction equation with special conditions

    Institute of Scientific and Technical Information of China (English)

    Youtong Zhang; Changsong Zheng; Yongfeng Liu; Liang Shao; Chenhua Gou

    2009-01-01

    This paper presents two exact explicit solutions for the three dimensional dual-phase lag (DLP) heat conduction equation, during the derivation of which the method of trial and error and the authors' previous experiences are utilized. To the authors' knowledge, most solutions of 2D or 3D DPL models available in the literature are obtained by numerical methods, and there are few exact solutions up to now. The exact solutions in this paper can be used as benchmarks to validate numerical solutions and to develop numerical schemes, grid generation methods and so forth.In addition, they are of theoretical significance since they correspond to physically possible situations. The main goal of this paper is to obtain some possible exact explicit solutions of the dual-phase lag heat conduction equation as the benchmark solutions for computational heat transfer, rather than specific solutions for some given initial and boundary conditions. Therefore, the initial and boundary conditions are indeterminate before derivation and can be deduced from the solutions afterwards. Actually, all solutions given in this paper can be easily proven by substituting them into the governing equation.

  5. Painlevé Integrability and New Exact Solutions of the (4 + 1-Dimensional Fokas Equation

    Directory of Open Access Journals (Sweden)

    Sheng Zhang

    2015-01-01

    Full Text Available The Painlevé integrability of the (4+1-dimensional Fokas equation is verified by the WTC method of Painlevé analysis combined with a new and more general transformation. By virtue of the truncated Painlevé expansion, two new exact solutions with arbitrary differentiable functions are obtained. Thanks to the arbitrariness of the included functions, the obtained exact solutions not only possess rich spatial structures but also help to bring about two-wave solutions and three-wave solutions. It is shown that the transformation adopted in this work plays a key role in testing the Painlevé integrability and constructing the exact solutions of the Fokas equation.

  6. The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations

    Directory of Open Access Journals (Sweden)

    Yadong Shang

    2012-01-01

    Full Text Available This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type for n and E, the solitary wave solutions of kink-type for E and bell-type for n, the singular traveling wave solutions, periodic wave solutions of triangle functions, Jacobi elliptic function doubly periodic solutions, and Weierstrass elliptic function doubly periodic wave solutions. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.

  7. An Algebraic Method for Constructing Exact Solutions to Difference-Differential Equations

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    In this paper, we present a method to solve difference differential equation(s). As an example, we apply this method to discrete KdV equation and Ablowitz-Ladik lattice equation. As a result, many exact solutions are obtained with the help of Maple including soliton solutions presented by hyperbolic functions sinh and cosh, periodic solutions presented by sin and cos and rational solutions. This method can also be used to other nonlinear difference-differential equation(s).

  8. Exact solution of unsteady flow generated by sinusoidal pressure gradient in a capillary tube

    Directory of Open Access Journals (Sweden)

    M. Abdulhameed

    2015-12-01

    Full Text Available In this paper, the mathematical modeling of unsteady second grade fluid in a capillary tube with sinusoidal pressure gradient is developed with non-homogenous boundary conditions. Exact analytical solutions for the velocity profiles have been obtained in explicit forms. These solutions are written as the sum of the steady and transient solutions for small and large times. For growing times, the starting solution reduces to the well-known periodic solution that coincides with the corresponding solution of a Newtonian fluid. Graphs representing the solutions are discussed.

  9. Superforms in six-dimensional superspace

    Energy Technology Data Exchange (ETDEWEB)

    Arias, Cesar [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago de Chile (Chile); III, William D. Linch [Center for String and Particle Theory, Department of Physics,University of Maryland at College Park,College Park, MD 20742-4111 (United States); Ridgway, Alexander K. [Department of Physics, California Institute of Technology,Pasadena, CA 91125 (United States)

    2016-05-03

    We investigate the complex of differential forms in curved, six-dimensional, N=(1,0) superspace. The superconformal group acts on this complex by super-Weyl transformations. An ambi-twistor-like representation of a second conformal group arises on a pure spinor subspace of the cotangent space. The p-forms are defined by super-Weyl-covariant tensor fields on this pure spinor subspace. The on-shell dynamics of such fields is superconformal. We construct the superspace de Rham complex by successively obstructing the closure of forms. We then extend the analysis to composite forms obtained by wedging together forms of lower degree. Finally, we comment on applications to integration in curved superspace and propose a superspace formulation of the abelian limit of the non-abelian tensor hierarchy of N=(1,0) superconformal models.

  10. New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Yusuf Pandir

    2013-01-01

    Full Text Available We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE, we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.

  11. Coupled Nonlinear Schr(o)dinger Equation: Symmetries and Exact Solutions

    Institute of Scientific and Technical Information of China (English)

    LIU Ping; LOU Sen-Yue

    2009-01-01

    The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schr(o)dinger (CNLS) equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.

  12. Lienard Equation and Exact Solutions for Some Soliton-Producing Nonlinear Equations

    Institute of Scientific and Technical Information of China (English)

    ZHANG Wei-Guo; CHANG Qian-Shun; ZHANG Qi-Ren

    2004-01-01

    In this paper, we first consider exact solutions for Lienard equation with nonlinear terms of any order. Then,explicit exact bell and kink profile solitary-wave solutions for many nonlinear evolution equations are obtained by means of results of the Lienard equation and proper deductions, which transform original partial differential equations into the Lienard one. These nonlinear equations include compound KdV, compound KdV-Burgers, generalized Boussinesq,generalized KP and Ginzburg-Landau equation. Some new solitary-wave solutions are found.

  13. Exact solution of a delay difference equation modeling traffic flow and their ultra-discrete limit

    OpenAIRE

    Matsuya, Keisuke; Kanai, Masahiro

    2015-01-01

    We consider a car-following model described by a delay difference equation and give its exact solutions that present propagation of a traffic jam. This model is a discrete-time version of the delayed optimal-velocity model; in the continuum limit, we recover the delay differential equation for this model and the exact solutions as well. We then work in the ultra-discrete limit, obtaining a delay cellular-automaton model, which successfully inherits the solutions. Also the dispersion relation ...

  14. EXACT SOLUTION OF AN EXTERNAL CIRCULAR CRACK IN A PIEZOELECTRIC SOLID SUBJECTED TO SHEAR LOADING

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    A three-dimensional, exact analysis is presented in this paperfor the problem of an external circular crack in a transversely isotropic piezoelectric medium subjected to arbitrary antisymmetric shear loading. A recently proposed general solution of three-dimensional piezoelectricity is employed. It is shown that four quasi harmonic functions involved in the general solution can be represented by just one complex potential. Previous results in potential theory are then used to obtain the exact solution of the problem. For point shear loading, Green's functions for the elastoelectric field are derived in terms of elementary functions.

  15. Exact solutions of the Wheeler-DeWitt equation and the Yamabe construction

    CERN Document Server

    Ita, Eyo

    2014-01-01

    Exact solutions of the Wheeler-DeWitt equation of the full theory of four dimensional gravity of Lorentzian signature are obtained. They are characterized by Schr\\"odinger wavefunctionals having support on 3-metrics of constant spatial scalar curvature, and thus contain two full physical field degrees of freedom in accordance with the Yamabe construction. These solutions are moreover Gaussians of minimum uncertainty and they are naturally associated with a rigged Hilbert space. In addition, in the limit the regulator is removed, exact 3-dimensional diffeomorphism and local gauge invariance of the solutions are recovered.

  16. Exact solutions of the Wheeler–DeWitt equation and the Yamabe construction

    Energy Technology Data Exchange (ETDEWEB)

    Ita III, Eyo Eyo, E-mail: ita@usna.edu [Physics Department, US Naval Academy, Annapolis, MD (United States); Soo, Chopin, E-mail: cpsoo@mail.ncku.edu.tw [Department of Physics, National Cheng Kung University, Taiwan (China)

    2015-08-15

    Exact solutions of the Wheeler–DeWitt equation of the full theory of four dimensional gravity of Lorentzian signature are obtained. They are characterized by Schrödinger wavefunctionals having support on 3-metrics of constant spatial scalar curvature, and thus contain two full physical field degrees of freedom in accordance with the Yamabe construction. These solutions are moreover Gaussians of minimum uncertainty and they are naturally associated with a rigged Hilbert space. In addition, in the limit the regulator is removed, exact 3-dimensional diffeomorphism and local gauge invariance of the solutions are recovered.

  17. Exact solutions and particle creation for nonconformal scalar fields in homogeneous isotropic cosmological models

    CERN Document Server

    Pavlov, Yu V

    2013-01-01

    The problem is solved of describing scale factors of a homogeneous isotropic spaces-time such that the exact solution for the scalar field with a nonconformal coupling to curvature can be obtained from solutions for the conformally coupled field by redefining the mass and momentum. Explicit expressions for dependence of time from the large-scale factor are presented in the form of Abelian integrals in these cases. The exact solution for a scalar field with Gauss-Bonnet type coupling with curvature is received and it is shown that the corresponding nonconformal additions can dominate at the particles creation by gravitational field.

  18. Testing The Cactus code on exact solutions of the Einstein field equations

    CERN Document Server

    Vulcanov, D N; Vulcanov, Dumitru N.; Alcubierre, Miguel

    2001-01-01

    We discuss a series of numerical simulations of exact solutions of the Einstein equations performed using the Cactus code, a complete 3-dimensional machinery for numerical relativity. We describe an application (``thorn'') for the Cactus code that can be used for evolving a variety of exact solutions, with and without matter, including solutions used in modern cosmology for modelling the early stages of the universe. Our main purpose has been to test the Cactus code on these well-known examples, focusing mainly on the stability and convergence of the code.

  19. Exact solutions for quantum mechanical particle with spin 1 in the external homogeneous magnetic field

    CERN Document Server

    Kisel, V V; Red'kov, V M

    2010-01-01

    With the use of the general covariant matrix 10-dimensional Petiau -- Duffin -- Kemmer formalism in cylindrical coordinates and tetrad there are constructed exact solutions of the quantum-mechanical equation for a particle with spin 1 in presence of an external homogeneous magnetic field. There are separated three linearly independent types of solutions; in each case the formula for energy levels has been found.

  20. Nonlinear differential equations with exact solutions expressed via the Weierstrass function

    NARCIS (Netherlands)

    Kudryashov, NA

    2004-01-01

    A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear di

  1. An hp-adaptive strategy for the solution of the exact kernel curved wire Pocklington equation

    NARCIS (Netherlands)

    Lahaye, D.; Hemker, P.W.

    2007-01-01

    In this paper we introduce an adaptive method for the numerical solution of the Pocklington integro-differential equation with exact kernel for the current induced in a smoothly curved thin wire antenna. The hp-adaptive technique is based on the representation of the discrete solution, which is expa

  2. New exact solutions of the generalized Zakharov–Kuznetsov modified equal-width equation

    Indian Academy of Sciences (India)

    Yusuf Pandir

    2014-06-01

    In this paper, new exact solutions, including soliton, rational and elliptic integral function solutions, for the generalized Zakharov–Kuznetsov modified equal-width equation are obtained using a new approach called the extended trial equation method. In this discussion, a new version of the trial equation method for the generalized nonlinear partial differential equations is offered.

  3. Exact solutions of the Fokker-Planck equation for the Malthus-Verhulst model

    Science.gov (United States)

    Brey, J. J.; Aizpuru, C.; Morillo, M.

    1987-04-01

    A class of particular solutions of the Fokker-Planck equation associated with the Malthus-Verhulst model is obtained. These time-dependent solutions are exact and allow us to study the evolution of both the distribution function and the moments. A careful analysis is carried out for the two simplest cases, showing the different possible types of relaxation.

  4. Exact Solutions of the SU(2) Yang-Mills-Higgs Theory

    CERN Document Server

    Teh, R

    2001-01-01

    Some exact static solutions of the SU(2) Yang-Mills-Higgs theory are presented. These solutions do not satisfy the first order Bogomol'nyi equations, and do not possess finite energy. They are axially symmetric and could possibly represent monopoles and an antimonopole sitting on the z-axis.

  5. The functional variable method for finding exact solutions of some nonlinear time-fractional differential equations

    Indian Academy of Sciences (India)

    Wenjun Liu; Kewang Chen

    2013-09-01

    In this paper, we implemented the functional variable method and the modified Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled KdV system. This method is extremely simple but effective for handling nonlinear time-fractional differential equations.

  6. An Exact Solution and the Pancharatnam Phase for the Generalized Two-Mode Optical System

    Institute of Scientific and Technical Information of China (English)

    侯邦品; 王顺金; 余万伦

    2002-01-01

    Using the algebraic dynamical method, we obtain the exact solution for the generalized two-mode optical system. From the solution, the Pancharatnam phase and the mean values of the number operators of the system are calculated. It is emphasized that the system can be used as a quantum memory.

  7. Some characteristics of three exact solutions of Einstein equations minimally coupled to a Quintessence field

    Institute of Scientific and Technical Information of China (English)

    Zhou Xiao-Hua

    2009-01-01

    We show some characteristics of three exact solutions to Einstein's gravity equation minimally coupled to a Quintessence field.Besides eternal inflation,several other interesting inflationary processes,such as transitory inflation,are obtained in these solutions.Singularity is avoided in some special cases.

  8. EXACT SOLUTIONS FOR GENERAL VARIABLE-COEFFICIENT KdV EQUATION

    Institute of Scientific and Technical Information of China (English)

    LiuXiqiang; JiangSong

    2001-01-01

    By asing the nonclassical method of symmetry reductions, the exact solutions for general variable-coefficient KdV equation with dissipative loss and nonuniformity terms are obtained. When the dissipative loss and nonuniformity terms don't exist, the multisoliton solutions are found and the corresponding Painleve II type equation for the variable-coefficient KdV equation is given.

  9. Exact Solutions for a Nonisospectral and Variable-Coefficient KdV Equation

    Institute of Scientific and Technical Information of China (English)

    DENG Shu-Fang

    2005-01-01

    The bilinear form for a nonisospectral and variable-coefficient KdV equation is obtained and some exact soliton solutions are derived through Hirota method and Wronskian technique. We also derive the bilinear transformation from its Lax pairs and find solutions with the help of the obtained bilinear transformation.

  10. Classification of Exact Solutions for Some Nonlinear Partial Differential Equations with Generalized Evolution

    Directory of Open Access Journals (Sweden)

    Yusuf Pandir

    2012-01-01

    Full Text Available We obtain the classification of exact solutions, including soliton, rational, and elliptic solutions, to the one-dimensional general improved Camassa Holm KP equation and KdV equation by the complete discrimination system for polynomial method. In discussion, we propose a more general trial equation method for nonlinear partial differential equations with generalized evolution.

  11. Quantum transport in 1d systems via a master equation approach: numerics and an exact solution

    CERN Document Server

    Znidaric, Marko

    2010-01-01

    We discuss recent findings about properties of quantum nonequilibrium steady states. In particular we focus on transport properties. It is shown that the time dependent density matrix renormalization method can be used successfully to find a stationary solution of Lindblad master equation. Furthermore, for a specific model an exact solution is presented.

  12. Exact bright and dark spatial soliton solutions in saturable nonlinear media

    Energy Technology Data Exchange (ETDEWEB)

    Calvo, Gabriel F. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain); Belmonte-Beitia, Juan [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: Juan.Belmonte@uclm.es; Perez-Garcia, Victor M. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales, Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), E.T.S.I. Industriales, Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)

    2009-08-30

    We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schroedinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.

  13. The fractional coupled KdV equations: Exact solutions and white noise functional approach

    Institute of Scientific and Technical Information of China (English)

    Hossam A.Ghany; A.S.Okb El Bab; A.M.Zabel; Abd-Allah Hyder

    2013-01-01

    Variable coefficients and Wick-type stochastic fractional coupled KdV equations are investigated.By using the modified fractional sub-equation method,Hermite transform,and white noise theory the exact travelling wave solutions and white noise functional solutions are obtained,including the generalized exponential,hyperbolic,and trigonometric types.

  14. Exact Solutions of Two-dimensional and Tri-dimensional Consolidation Equations

    CERN Document Server

    Di Francesco, Romolo

    2011-01-01

    The exact solution of Terzaghi's consolidation equation has further highlighted the limits of this theory in the one-dimensional field as, like Taylor's approximate solution, it overestimates the decay times of the phenomenon; on the other hand, one only needs to think about the accumulation pattern of sedimentary-basin soils to understand how their internal structure fits in more with the model of transversely isotropic medium, so as to result in the development of two- and three-dimensional consolidation models. This is the reason why, using Terzaghi's theory and his exact solution as starting point, two-dimensional and three-dimensional consolidation equations have been proposed, in an attempt to find their corresponding exact solutions which constitute more reliable forecasting models. Lastly, results show how this phenomenon is predominantly influenced by the dimensions of the horizontal plane affected by soil consolidation and permeabilities that behave according to three coordinate axes.

  15. Exact Solution of Mutator Model with Linear Fitness and Finite Genome Length

    Science.gov (United States)

    Saakian, David B.

    2017-08-01

    We considered the infinite population version of the mutator phenomenon in evolutionary dynamics, looking at the uni-directional mutations in the mutator-specific genes and linear selection. We solved exactly the model for the finite genome length case, looking at the quasispecies version of the phenomenon. We calculated the mutator probability both in the statics and dynamics. The exact solution is important for us because the mutator probability depends on the genome length in a highly non-trivial way.

  16. Unified treatment of a class of spherically symmetric potentials: quasi-exact solution

    CERN Document Server

    Panahi, Hossein

    2016-01-01

    In this paper, we investigate the Schr\\"odinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all models give rise to the same basic differential equation, which is expressible as an element of the universal enveloping algebra of sl(2). Then, we obtain the general exact solutions of the problem by employing the representation theory of sl(2) Lie algebra.

  17. The Klein–Gordon–Zakharov equations with the positive fractional power terms and their exact solutions

    Indian Academy of Sciences (India)

    JINLIANG ZHANG; WUQIANG HU; YU MA

    2016-12-01

    In this paper, the famous Klein–Gordon–Zakharov (KGZ) equations are first generalized, and the new special types of KGZ equations with the positive fractional power terms (gKGZE) are presented. In order to derive exact solutions of the new special gKGZE, subsidiary higher-order ordinary differential equations (sub-ODEs) with the positive fractional power terms are introduced, and with the aid of the sub-ODE, exact solutions of four special types of the gKGZE are derived, which are the bell-type solitary wave solution, the algebraicsolitary wave solution, the kink-type solitary wave solution and the sinusoidal travelling wave solution, provided that the coefficients of gKGZE satisfy certain constraint conditions.

  18. Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

    Science.gov (United States)

    Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua

    2016-12-01

    Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205

  19. Exact Schwarzschild-like solution for SU(N) gauge theory

    Science.gov (United States)

    Singleton, D.

    1996-09-01

    In this paper we extend our previously discovered exact solution for an SU(2) Yang-Mills-Higgs theory, to the general group SU(N+1). Using the first-order formalism of Bogomolny, an exact, spherically symmetric solution for the gauge and scalar fields is found. This solution is similar to the Schwarzschild solution of general relativity, in that the gauge and scalar fields become infinite on a spherical shell of radius r 0= K. However in the Schwarzschild case the singularity at the event horizon is a coordinate singularity while for the present solution the singularity is a true singularity. It is speculated that this solution may give a confinement mechanism for non-Abelian gauge theories, since any particle which carries the SU(N+1) charge would become permanently trapped inside the region r< r 0.

  20. New exact solutions of sixth-order thin-film equation

    Directory of Open Access Journals (Sweden)

    Wafaa M. Taha

    2014-01-01

    Full Text Available TheG′G-expansion method is used for the first time to find traveling-wave solutions for the sixth-order thin-film equation, where related balance numbers are not the usual positive integers. New types of exact traveling-wave solutions, such as – solitary wave solutions, are obtained the sixth-order thin-film equation, when parameters are taken at special values.

  1. NEW EXPLICIT AND EXACT TRAVELLING WAVE SOLUTIONS FOR A COMPOUND KdV-BURGERS EQUATION

    Institute of Scientific and Technical Information of China (English)

    XIA TIE-CHENG; ZHANG HONG-QING; YAN ZHEN-YA

    2001-01-01

    In this paper, new explicit and exact travelling wave solutions for a compound KdV-Burgers equation are obtained by using the hyperbola function method and the Wu elimination method, which include new solitary wave solutions and periodic solutions. Particularly important cases of the equation, such as the compound KdV, mKdV-Burgers and mKdV equations can be solved by this method. The method can also solve other nonlinear partial differential equations.

  2. A new family of exact and rotating solutions of fireball hydrodynamics

    CERN Document Server

    Csörgő, T

    2013-01-01

    A new class of analytic, exact, rotating, self-similar and surprisingly simple solutions of non-relativistic hydrodynamics are presented for a three-dimensionally expanding, spheroidally symmetric fireball. These results generalize earlier, non-rotating solutions for ellipsoidally symmetric fireballs with directional, three-dimensional Hubble flows. The solutions are presented for a general class of equations of state that includes the lattice QCD equations of state and may feature inhomogeneous temperature and corresponding density profiles.

  3. New exact solutions of the non-homogeneous Burgers equation in (1+1) dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Schulze-Halberg, Axel [Department of Science, University of Colima, Bernal Diaz del Castillo 340, Colima Villas San Sebastian, C P 28045, Colima (Mexico)

    2007-04-15

    We construct an invertible transformation between the non-homogeneous Burgers equation (NBE) and the stationary Schroedinger equation in (1+1) dimensions. By means of this transformation, each solution of the stationary Schroedinger equation generates a fully time-dependent solution of the NBE. As applications we derive exact solutions of the NBE for general power-law nonhomogeneities, generalizing former results on the linear case.

  4. Exact solutions of the (3+1)-dimensional space-time fractional Jimbo-Miwa equation

    Science.gov (United States)

    Aksoy, Esin; Guner, Ozkan; Bekir, Ahmet; Cevikel, Adem C.

    2016-06-01

    Exact solutions of the (3+1)-dimensional space-time fractional Jimbo-Miwa equation are studied by the generalized Kudryashov method, the exp-function method and the (G'/G)-expansion method. The solutions obtained include the form of hyperbolic functions, trigonometric and rational functions. These methods are effective, simple, and many types of solutions can be obtained at the same time.

  5. Exact periodic wave solutions to the generalized Nizhnik-Novikov-Veselov equation

    Indian Academy of Sciences (India)

    Yan-Ze Peng

    2005-02-01

    The extended mapping method with symbolic computation is developed to obtain exact periodic wave solutions to the generalized Nizhnik{Novikov{Veselov equation. Limit cases are studied and new solitary wave solutions and triangular periodic wave solutions are obtained. The method is applicable to a large variety of non-linear partial differential equations, as long as odd- and even-order derivative terms do not coexist in the equation under consideration.

  6. Exact solutions for nonlinear variants of Kadomtsev–Petviashvili (, ) equation using functional variable method

    Indian Academy of Sciences (India)

    M Mirzazadeh; M Eslami

    2013-12-01

    Studying compactons, solitons, solitary patterns and periodic solutions is important in nonlinear phenomena. In this paper we study nonlinear variants of the Kadomtsev–Petviashvili (KP) and the Korteweg–de Vries (KdV) equations with positive and negative exponents. The functional variable method is used to establish compactons, solitons, solitary patterns and periodic solutions for these variants. This method is a powerful tool for searching exact travelling solutions in closed form.

  7. A Family of Interesting Exact Solutions of the Sine-Gordon Equation

    Institute of Scientific and Technical Information of China (English)

    HUANG De-Bin; LIU Zeng-Rong; WANG Li-Lian

    2000-01-01

    By using AKNS [Phys. Rev. Lett. 31 (1973) 125] system and introducing the wave function, a family of interesting exact solutions of the sine-Gordon equation are constructed. These solutions seem to be some soliton, kink, and anti-kink ones respectively for the different choice of the spectrum, whereas due to the interaction between two traveling-waves they have some properties different from usual soliton, kink, and anti-kink solutions.

  8. New exact solutions to the generalized KdV equation with generalized evolution

    Indian Academy of Sciences (India)

    Yongan Xie; Shengqiang Tang; Dahe Feng

    2012-04-01

    In this paper, by using a transformation and an application of Fan subequation, we study a class of generalized Korteweg–de Vries (KdV) equation with generalized evolution. As a result, more types of exact solutions to the generalized KdV equation with generalized evolution are obtained, which include more general single-hump solitons, multihump solitons, kink solutions and Jacobian elliptic function solutions with double periods.

  9. Exact stationary solutions independent of energy for strongly nonlinear stochastic systems of multiple degrees of freedom

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    A new procedure is proposed to construct strongly nonlinear systems of multiple degrees of freedom subjected to parametric and/or external Gaussian white noises, whose exact stationary solutions are independent of energy. Firstly, the equivalent Fokker-Planck-Kolmogorov (FPK) equations are derived by using exterior differentiation. The main difference between the equivalent FPK equation and the original FPK equation lies in the additional arbitrary antisymmetric diffusion matrix. Then the exact stationary solutions and the structures of the original systems can be obtained by using the coefficients of antisymmetric diffusion matrix. The obtained exact stationary solutions, which are generally independent of energy, are for the most general class of strongly nonlinear stochastic systems multiple degrees of freedom (MDOF) so far, and some classes of the known ones dependent on energy belong to the special cases of them.

  10. Interaction and charge transfer between dielectric spheres: exact and approximate analytical solutions

    CERN Document Server

    Lindén, Fredrik; Zettergren, Henning

    2016-01-01

    We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones.

  11. Exact Solutions of Degree Distributions for Random Birth-and-Death Networks

    CERN Document Server

    Zhang, Xiaojun; Rayman-Bacchus, Lez

    2015-01-01

    In this paper, a general random birth-and-death network model (RBDN) is considered, in which at each time step, a new node is added into the network with probability p or an existing node is deleted from the network with probability q=1-p. For different p (1>p>1/2, 0exact solutions. First, a homogeneous Markov chain with two variables based on stochastic process rules (SPR) is employed and its state transformation equations are provided for solving the degree distributions of RBDN. Then for different p, the different degree distribution equations are determined, and the exact solutions of the degree distributions are obtained by the probability generating function approach. Computation simulations are used to verify these exact solutions.

  12. Agent-based model for the h-index - Exact solution

    CERN Document Server

    Żogała-Siudem, Barbara; Cena, Anna; Gagolewski, Marek

    2015-01-01

    The Hirsch's $h$-index is perhaps the most popular citation-based measure of the scientific excellence. In 2013 G. Ionescu and B. Chopard proposed an agent-based model for this index to describe a publications and citations generation process in an abstract scientific community. With such an approach one can simulate a single scientist's activity, and by extension investigate the whole community of researchers. Even though this approach predicts quite well the $h$-index from bibliometric data, only a solution based on simulations was given. In this paper, we complete their results with exact, analytic formulas. What is more, due to our exact solution we are able to simplify the Ionescu-Chopard model which allows us to obtain a compact formula for $h$-index. Moreover, a simulation study designed to compare both, approximated and exact, solutions is included. The last part of this paper presents evaluation of the obtained results on a real-word data set.

  13. Exact stationary solutions independent of energy for strongly nonlinear stochastic systems of multiple degrees of freedom

    Institute of Scientific and Technical Information of China (English)

    HUANG ZhiLong; JIN XiaoLing

    2009-01-01

    A new procedure is proposed to construct strongly nonlinear systems of multiple degrees of freedom subjected to parametric and/or external Gaussian white noises,whose exact stationary solutions are independent of energy.Firstly,the equivalent Fokker-Planck-Kolmogorov(FPK)equations are derived by using exterior differentiation.The main difference between the equivalent FPK equation and the original FPK equation lies in the additional arbitrary antisymmetric diffusion matrix.Then the exact stationary solutions and the structures of the original systems can be obtained by using the coefficients of antisymmetric diffusion matrix.The obtained exact stationary solutions,which are generally independent of energy,are for the most general class of strongly nonlinear stochastic systems multiple degrees of freedom(MDOF)so far,and some classes of the known ones dependent on energy belong to the special cases of them.

  14. Exact solutions to the Mo-Papas and Landau-Lifshitz equations.

    Science.gov (United States)

    Rivera, R; Villarroel, D

    2002-10-01

    Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics.

  15. Exact solutions for scalar field cosmology in f(R) gravity

    CERN Document Server

    Maharaj, S D; Chervon, S V; Nikolaev, A V

    2016-01-01

    We look for exact solutions in scalar field cosmology. To achieve this we use $f(R)$ modified gravity with a scalar field and do not specify the the form of the $f(R)$ function. In particular, we study Friedmann universe assuming that acceleration of the scalar curvature is negligible. We first present solutions for special cases and then the general solution. Using initial conditions which represent the universe at the present epoch, we evaluated the constants of integration. This allows for the comparison of the scale factor in the new solutions with that of the $\\Lambda CDM$ solution, thereby affecting the age of the universe in $f(R)$ gravity.

  16. High-order exact solutions for pseudo-plane ideal flows

    Science.gov (United States)

    Sun, Che

    2016-08-01

    A steady pseudo-plane ideal flow (PIF) model is derived from the 3D Euler equations under Boussinesq approximation. The model is solved analytically to yield high-degree polynomial exact solutions. Unlike quadratic flows, the cubic and quartic solutions display reduced geometry in the form of straightline jet, circular vortex, and multipolar strain field. The high-order circular-vortex solutions are vertically aligned and even the non-aligned multipolar strain-field solutions display vertical concentricity. Such geometry reduction is explained by an analytical theorem stating that only straightline jet and circular vortex have functional solutions to the PIF model.

  17. Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods

    Directory of Open Access Journals (Sweden)

    Özkan Güner

    2014-01-01

    Full Text Available We apply the functional variable method, exp-function method, and (G′/G-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE in the sense of the modified Riemann-Liouville derivative. As a result, some new exact solutions for them are obtained. The results show that these methods are very effective and powerful mathematical tools for solving nonlinear fractional equations arising in mathematical physics. As a result, these methods can also be applied to other nonlinear fractional differential equations.

  18. Lie symmetry analysis and exact solutions of the quasi-geostrophic two-layer problem

    CERN Document Server

    Bihlo, Alexander

    2010-01-01

    The quasi-geostrophic two-layer model is of superior interest in dynamic meteorology since it is one of the easiest ways to study baroclinic processes in geophysical fluid dynamics. The complete set of point symmetries of the two-layer equations is determined. An optimal set of one- and two-dimensional inequivalent subalgebras of the maximum Lie invariance algebra is constructed. On the basis of these subalgebras we exhaustively carry out group-invariant reduction and compute various classes of exact solutions. Where possible, reference to the physical meaning of the exact solutions is given.

  19. New Exact Solutions of Boussinesq Equation%Boussinesq 方程新的精确解

    Institute of Scientific and Technical Information of China (English)

    杨琼芬; 杜先云; 杨立娟

    2011-01-01

    以齐次平衡原则和试探函数法为基础,给出函数变换与双线性算子相结合的方法,构造了Boussinesq方程新的精确解.%Based on the homogeneous balance principle and the trial function method, a method for combining function transformation with bilinear operator is proposed. . And the method is applied to construct new exact solutions of Boussinesq equation. This method can be used to find new exact solutions to other nonlinear evolution equations.

  20. Regarding on the exact solutions for the nonlinear fractional differential equations

    Directory of Open Access Journals (Sweden)

    Kaplan Melike

    2016-01-01

    Full Text Available In this work, we have considered the modified simple equation (MSE method for obtaining exact solutions of nonlinear fractional-order differential equations. The space-time fractional equal width (EW and the modified equal width (mEW equation are considered for illustrating the effectiveness of the algorithm. It has been observed that all exact solutions obtained in this paper verify the nonlinear ordinary differential equations which was obtained from nonlinear fractional-order differential equations under the terms of wave transformation relationship. The obtained results are shown graphically.

  1. Construction and exact solution of a nonlinear quantum field model in quasi-higher dimension

    Energy Technology Data Exchange (ETDEWEB)

    Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

    2015-10-15

    Nonperturbative exact solutions are allowed for quantum integrable models in one space-dimension. Going beyond this class we propose an alternative Lax matrix approach, exploiting the hidden multi-space–time concept in integrable systems and construct a novel nonlinear Schrödinger quantum field model in quasi-two dimensions. An intriguing field commutator is discovered, confirming the integrability of the model and yielding its exact Bethe ansatz solution with rich scattering and bound-state properties. The universality of the scheme is expected to cover diverse models, opening up a new direction in the field.

  2. Exact solutions to the continuous-quality equation for soil organic matter turnover.

    Science.gov (United States)

    Bosatta, Ernesto; Agren, Göran I

    2003-09-07

    All living systems depend on transformations of elements between different states. In particular, the transformation of dead organic matter in the soil (SOM) by decomposers (microbes) releases elements incorporated in SOM and makes the elements available anew to plants. A major problem in analysing and describing this process is that SOM, as the result of the decomposer activity, is a mixture of a very large number of molecules with widely differing chemical and physical properties. The continuous-quality equation (CQE) is a general equation describing this complexity by assigning a continuous-quality variable to each carbon atom in SOM. The use of CQE has been impeded by its complicated mathematics. Here, we show by deriving exact solutions that, at least for some specific cases, there exist solutions to CQE. These exact solutions show that previous approximations have overestimated the rate by which litter decomposes and as a consequence underestimated steady state SOM amounts. The exact and approximate solutions also differ with respect to the parameter space in which they yield finite steady-state SOM amounts. The latter point is important because temperature is one of the parameters and climatic change may move the solution from a region of the parameter space with infinite steady-state SOM to a region of finite steady-state SOM, with potentially large changes in soil carbon stores. We also show that the solution satisfies the Chapman-Kolmogorov theorem. The importance of this is that it provides efficient algorithms for numerical solutions.

  3. Exact axisymmetric solution of laminated transversely isotropic piezoelectric circular plates (Ⅱ)——Exact solution for elastic circular plates and numerical results

    Institute of Scientific and Technical Information of China (English)

    丁皓江; 徐荣桥; 国凤林

    1999-01-01

    Emphasis is placed on purely elastic circular plates. Let the piezoelectric coefficients be equal to zero. Then two sets of uncoupled mechanical and electric equations are obtained and they can be solved independently. Two three-dimensional exact solutions of laminated transversely isotropic circular plate are derived under two boundary conditions, i.e. rigid slipping support and elastic simple support. For isotropic circular plates, the problem of multiple root is treated. At last, some numerical results of piezoelectric and purely elastic circular plates are presented and the applicability of classical plate theory is discussed.

  4. New Exact Solutions of Ion-Acoustic Wave Equations by (G′/G-Expansion Method

    Directory of Open Access Journals (Sweden)

    Wafaa M. Taha

    2013-01-01

    Full Text Available The (G′/G-expansion method is used to study ion-acoustic waves equations in plasma physic for the first time. Many new exact traveling wave solutions of the Schamel equation, Schamel-KdV (S-KdV, and the two-dimensional modified KP (Kadomtsev-Petviashvili equation with square root nonlinearity are constructed. The traveling wave solutions obtained via this method are expressed by hyperbolic functions, the trigonometric functions, and the rational functions. In addition to solitary waves solutions, a variety of special solutions like kink shaped, antikink shaped, and bell type solitary solutions are obtained when the choice of parameters is taken at special values. Two- and three-dimensional plots are drawn to illustrate the nature of solutions. Moreover, the solution obtained via this method is in good agreement with previously obtained solutions of other researchers.

  5. On Five-dimensional Superspaces

    CERN Document Server

    Kuzenko, S M; Kuzenko, Sergei M.; Linch, William D.

    2006-01-01

    Recent one-loop calculations of certain supergravity-mediated quantum corrections in supersymmetric brane-world models employ either the component formulation (hep-th/0305184) or the superfield formalism with only half of the bulk supersymmetry manifestly realized (hep-th/0305169 and hep-th/0411216). There are reasons to expect, however, that 5D supergraphs provide a more efficient setup to deal with these and more involved (in particular, higher-loop) calculations. As a first step toward elaborating such supergraph techniques, we develop in this note a manifestly supersymmetric formulation for 5D globally supersymmetric theories with eight supercharges. Simple rules are given to reduce 5D superspace actions to a hybrid form which keeps manifest only the 4D, N=1 Poincare supersymmetry. (Previously, such hybrid actions were carefully worked out by rewriting the component actions in terms of simple superfields). To demonstrate the power of this formalism for model building applications, two families of off-shel...

  6. New Explicit and Exact Travelling Wave Solutions for Burgers—Kolmogorov—Petrovskii—Piscounov Equations

    Institute of Scientific and Technical Information of China (English)

    XIATie-cheng; ZHANGHong-qing; LIPei-chun

    2003-01-01

    In this paper,many new explicit and exact travelling wave solutions for Burgers-Kolmogorov-Prtrovskii-Piscounov(Burgers-KPP) equations are obtained by using hyperbola function method and Wu-elimination method,which include new singular solitary wave solutions and periodic solutions,Particular important cases of the equation.such as the generalized Burgers-Fisher equation.Burgers-Chaffee-infante equation and KPP equation,the corresponding solutions can be obtained also,The method can also solve other nonliear partial differential equations.

  7. Explicit and exact travelling wave solutions for the generalized derivative Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Huang Dingjiang [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)]. E-mail: hdj8116@163.com; Li Desheng [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China); Department of Mathematics, Shenyang Normal University, Shenyang 110034 (China); Zhang Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)

    2007-02-15

    In this paper, a new auxiliary equation expansion method and its algorithm is proposed by studying a first order nonlinear ordinary differential equation with a sixth-degree nonlinear term. Being concise and straightforward, the method is applied to the generalized derivative Schroedinger equation. As a result, some new exact travelling wave solutions are obtained which include bright and dark solitary wave solutions, triangular periodic wave solutions and singular solutions. This algorithm can also be applied to other nonlinear wave equations in mathematical physics.

  8. The Improved Riccati Equation Method and Exact Solutions to mZK Equation

    Directory of Open Access Journals (Sweden)

    Xiaofeng Li

    2012-01-01

    Full Text Available We utilize the improved Riccati equation method to construct more general exact solutions to nonlinear equations. And we obtain the travelling wave solutions involving parameters, which are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. When the parameters are taken as special values, the method provides not only solitary wave solutions but also periodic waves solutions. The method appears to be easier and more convenient by means of a symbolic computation system. Of course, it is also effective to solve other nonlinear evolution equations in mathematical physics.

  9. Exact solutions for a periodic assembly of bubbles in a Hele-Shaw channel

    CERN Document Server

    Vasconcelos, Giovani L

    2014-01-01

    Exact solutions are reported for a periodic assembly of bubbles steadily co-travelling in a Hele-Shaw channel. The solutions are obtained as conformal mappings from a multiply connected circular domain in an auxiliary complex plane to the flow region in a period cell. The conformal mappings are constructed using the generalized Schwarz-Christoffel formula for multiply connected polygonal domains in terms of products of Schottky-Klein prime functions. It is shown that previous solutions for multiple steady bubbles in a Hele-Shaw cell are all particular cases of the solutions described herein. Examples of specific bubble configurations are discussed.

  10. Exact Operator Solution for Liouville Theory with q a Root of Unity

    CERN Document Server

    Fujiwara, T; Takimoto, Y

    1997-01-01

    The exact operator solution for quantum Liouville theory constructed for the generic quantum deformation parameter q is extended to the case with q being a root of unity. The screening charge operator becomes nilpotent in such cases and arbitrary Liouville exponentials can be obtained in finite polynomials of the screening charge.

  11. Exact solution of a quantum forced time-dependent harmonic oscillator

    Science.gov (United States)

    Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN

    1992-01-01

    The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.

  12. Exact solutions of N-dimensional harmonic oscillator via Laplace transformation

    Institute of Scientific and Technical Information of China (English)

    Chen Gang

    2005-01-01

    The N-dimensional Schrodinger equation for the harmonic oscillator is reduced to a first-order differential equation in terms of the Laplace transformation and the exact bound state solutions are derived. It is shown that this method of solving Schrodinger equation may serve as a substitute for the standard functional, analytical approach also in lower dimensions.

  13. Modified Boussinesq System with Variable Coefficients: Classical Lie Approach and Exact Solutions

    Institute of Scientific and Technical Information of China (English)

    GUPTA R.K.; SINGH K.

    2009-01-01

    The Lie-group formalism is applied to investigate the symmetries of the modified Boussinesq system with variable coefficients. We derived the infinitesimals and the admissible forms of the coefficients that admit the classical symmetry group. The reduced systems of ordinary differential equations deduced from the optimal system of subalgebras are further studied and some exact solutions are obtained.

  14. Almost Surely Asymptotic Stability of Exact and Numerical Solutions for Neutral Stochastic Pantograph Equations

    Directory of Open Access Journals (Sweden)

    Zhanhua Yu

    2011-01-01

    Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.

  15. Exact Solution for the Exterior Field of a Rotating Neutron Star

    CERN Document Server

    Man'ko, V I; Sanabria-Gómez, J D; Manko, Vladimir S.; Mielke, Eckehard W.; Sanabria-Gómez, José D.

    2000-01-01

    A four-parameter class of exact asymptotically flat solutions of the Einstein-Maxwell equations involving only rational functions is presented. It is able to describe the exterior field of a slowly or rapidly rotating neutron star with poloidal magnetic field.

  16. The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions

    DEFF Research Database (Denmark)

    Johannessen, Kim

    2014-01-01

    The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions can be expressed in terms of the Jacobi elliptic functions. The boundary conditions determine the modulus of the Jacobi elliptic functions. The boundary conditions can not be solved analytically...

  17. Exact Solutions of Some (1+1)-Dimensional Nonlinear Evolution Equations

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    By means of the variable separation method, new exact solutions of some (1+1)-dimensional nonlinear evolution equations are obtained. Abundant localized excitations can be found by selecting corresponding arbitrary functions appropriately. Namely, the new soliton-like localized excitations and instanton-like localized excitations are presented.

  18. Exact solutions to three-dimensional time-dependent Schrödinger equation

    Indian Academy of Sciences (India)

    Fakir Chand; S C Mishra

    2007-06-01

    With a view to obtain exact analytic solutions to the time-dependent Schrödinger equation for a few potentials of physical interest in three dimensions, transformation-group method is used. Interestingly, the integrals of motion in the new coordinates turn out to be the desired invariants of the systems.

  19. Exact solutions and conservation laws for a generalized improved Boussinesq equation

    Science.gov (United States)

    Motsepa, Tanki; Khalique, Chaudry Masood

    2016-06-01

    In this paper we study a nonlinear generalized improved Boussinesq equation, which describes nonlinear dispersive wave phenomena. Exact solutions are derived by using the Lie symmetry analysis and the simplest equation methods. Moreover, conservation laws are constructed by using the multiplier method.

  20. Exact Solution to Localized-Induction-Approximation Equation Modeling Smoke Ring Motion

    NARCIS (Netherlands)

    Cieśliński, J.; Gragert, P.K.H.; Sym, A.

    1986-01-01

    We present and discuss a three-parameter class of exact solutions to the localized-induction-approximation equations. These are one-soliton excitations (Bäcklund transforms) of the circular vortex motion. The corresponding generic vortex filament (of infinite or finite length) remains in the

  1. Exact solutions of some fractional differential equations by various expansion methods

    Science.gov (United States)

    Topsakal, Muammer; Guner, Ozkan; Bekir, Ahmet; Unsal, Omer

    2016-10-01

    In this paper, we construct the exact solutions of some nonlinear spacetime fractional differential equations involving modified Riemann-Liouville derivative in mathematical physics and applied mathematics; namely the fractional modified Benjamin-Bona- Mahony (mBBM) and Kawahara equations by using G'/G and (G'/G, 1/G)-expansion methods.

  2. Perturbative Painlevé Analysis of General KdV System and Its Exact Soliton Solutions

    Institute of Scientific and Technical Information of China (English)

    LIN Ji; YE Li-Jun; LI Hua-Mei

    2005-01-01

    Using the standard Painlevé analysis and the perturbative method, the Painlevé test for the logarithmic branch is investigated. Nine arbitrary functions are obtained and the Backlund transformation of the logarithmic branch is given. Using the new type Backlund transformation, many exact solutions are obtained.

  3. Exact solutions for spin-1/2 systems using dynamical manipulation techniques

    CERN Document Server

    Fernández-Cesar, C; Rosas-Ortiz, Oscar

    1997-01-01

    The dynamics of purely spin-1/2 systems in homogeneous magnetic fields is analysed through inverse techniques. The generation of exact solutions using this method is explored. Some cases of the "evolution loops", dynamical processes for which any state evolves cyclically, are presented, and the corresponding geometric phases are evaluated.

  4. Lie symmetries and exact solutions for a short-wave model

    Institute of Scientific and Technical Information of China (English)

    Chen Ai-Yong; Zhang Li-Na; Wen Shuang-Quan

    2013-01-01

    In this paper,the Lie symmetry analysis and generalized symmetry method are performed for a short-wave model.The symmetries for this equation are given,and the phase portraits of the traveling wave systems are analyzed using the bifurcation theory of dynamical systems.The exact parametric representations of four types of traveling wave solutions are obtained.

  5. Exact solutions of the spinor Bethe-Salpeter equation for tightly bound states

    NARCIS (Netherlands)

    Suttorp, L.G.

    1975-01-01

    Exact solutions are obtained for the spinor Bethe-Salpeter equation that describes tightly bound states of spin-/sup 1///sub 2/ fermions with massless-boson exchange. The corresponding coupling constants form a discrete spectrum that depends continuously on the parameters characterizing the type of

  6. Exact solutions of Feinberg–Horodecki equation for time-dependent anharmonic oscillator

    Indian Academy of Sciences (India)

    P K Bera; Tapas Sil

    2013-01-01

    In this work, an alternative treatment known as Nikiforov–Uvarov (NU) method is proposed to find the exact solutions of the Feinberg–Horodecki equation for the time-dependent potentials. The present procedure is illustrated with two examples: (1) time-dependent Wei Hua oscillator, (2) time-dependent Manning–Rosen potential.

  7. Exact solutions of the spinor Bethe-Salpeter equation for tightly bound states

    NARCIS (Netherlands)

    Suttorp, L.G.

    1975-01-01

    Exact solutions are obtained for the spinor Bethe-Salpeter equation that describes tightly bound states of spin-/sup 1///sub 2/ fermions with massless-boson exchange. The corresponding coupling constants form a discrete spectrum that depends continuously on the parameters characterizing the type of

  8. Exact analytic solutions for a Dirac electron moving in graphene under magnetic fields.

    Science.gov (United States)

    Kuru, S; Negro, J; Nieto, L M

    2009-11-11

    Exact analytical solutions for the bound states of a graphene Dirac electron in various magnetic fields with translational symmetry are obtained. In order to solve the time-independent Dirac-Weyl equation the factorization method used in supersymmetric quantum mechanics is adapted to this problem. The behavior of the discrete spectrum, probability and current densities are discussed.

  9. Exact Solutions of Two Coupled Harmonic Oscillators Related to the Sp(4, R) Lie Algebra

    Institute of Scientific and Technical Information of China (English)

    PAN Feng; DAI LianRong

    2001-01-01

    Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4, R) U(2).``

  10. Exact Solutions of the Klein-Gordon Equation with Hylleraas Potential

    CERN Document Server

    Ikot, Akpan N; Ita, Benedict I

    2011-01-01

    We present the exact solution of the Klein-Gordon with Hylleraas Potential using the Nikiforov-Uvarov method. We obtain explicitly the bound state energy eigenvalues and the corresponding eigen function are also obtained and expressed in terms of Jacobi Polynomials

  11. Exact Analytical Solution of the Klein-Gordon Equation in the Generalized Woods-Saxon Potential

    Science.gov (United States)

    Bayrak, O.; Sahin, D.

    2015-09-01

    The exact analytical solution of the Klein-Gordon equation for the spin-0 particles in the generalized Woods-Saxon potential is presented. The bound state energy eigenvalues and corresponding wave functions are obtained in the closed forms. The correlations between the potential parameters and energy eigenvalues are examined for π0 particles.

  12. Exact solutions to the Boltzmann equation by mapping the scattering integral into a differential operator

    Energy Technology Data Exchange (ETDEWEB)

    Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T., E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br, E-mail: ftvdl@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Engenharia Mecanica. Grupo de Pesquisas Radiologicas; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio G., E-mail: phd.marcio@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Tramandai, RS (Brazil). Departamento Interdisciplinar do Campus Litoral Norte

    2015-07-01

    This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)

  13. Exact Analytical Solutions in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length

    Institute of Scientific and Technical Information of China (English)

    CHEN Yong; LI Biao; ZHENG Yu

    2007-01-01

    In the paper, the generalized Riccati equation rational expansion method is presented. Making use of the method and symbolic computation, we present three families of exact analytical solutions of Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Then the dynamics of two anlytical solutions are demonstrated by computer simulations under some selectable parameters including the Feshbach-managed nonlinear coefficient and the hyperbolic secant function coefficient.

  14. New Method for Finding a Series of Exact Solutions to Generalized Breaking Soliton Equation

    Institute of Scientific and Technical Information of China (English)

    BAI Cheng-Lin; GUO Jun; ZHAO Hong

    2005-01-01

    In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like,period-form solutions of nonlinear evolution equations (NEEs). This method is more powerful than the extended tanhfunction method [Phys. Lett. A 277 (2000) 212] and the modified extended tanh-function method [Phys. Lett. A 285 (2001) 355]. Abundant new families of the exact solutions of Bogoyavlenskii's generalized breaking soliton equation are obtained by using this method and symbolic computation system Maple.

  15. New Method for Finding a Series of Exact Solutions to Generalized Breaking Soliton Equation

    Institute of Scientific and Technical Information of China (English)

    BAICheng-Lin; GUOJun; ZHAOHong

    2005-01-01

    In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like,period-form solutions of nonlinear evolution equations (NEEs). This method is more powerful than the extended tanhfunction method [Phys. Left. A 277 (2000) 212] and the modified extended tanh-function method [Phys. Left. A 285 (2001) 355]. Abundant new families of the exact solutions of Bogoyavlenskii's generalized breaking soliton equation are obtained by using this method and symbolic computation system Maple.

  16. Conservation laws and exact solutions of system of Boussinesq-Burgers equations

    Science.gov (United States)

    Akbulut, Arzu; Kaplan, Melike; Taşcan, Filiz

    2017-01-01

    In this work, we study conservation laws that is one of the applications of symmetries. Conservation laws has important place for differential equations and their solutions, also in all physics applications. This study deals with conservation laws of Boussinessq-Burgers equation. We used Noether approach and conservation theorem approach for finding conservation laws for this equation. Also finally, we found exact solutions of this equation by using the modified simple equation method.

  17. Exact bound state solutions of the Klein-Gordon particle in Hulthén potential

    Institute of Scientific and Technical Information of China (English)

    Zhang Min-Cang

    2008-01-01

    In this paper,the Klein-Gordon equation with the spherical symmetric Hulthén potential is turned into a hypergeometric equation and is solved in the framework of function analysis exactly.The corresponding bound state solutions are expressed in terms of the hypergeometric function,and the energy spectrum of the bound states is obtained as a solution to a given equation by boundary constraints.

  18. The Exact Traveling Wave Solutions to Two Integrable KdV6 Equations

    Institute of Scientific and Technical Information of China (English)

    Jibin LI; Yi ZHANG

    2012-01-01

    The exact explicit traveling solutions to the two completely integrable sixthorder nonlinear equations KdV6 are given by using the method of dynamical systems and Cosgrove's work.It is proved that these traveling wave solutions correspond to some orbits in the 4-dimensional phase space of two 4-dimensional dynamical systems.These orbits lie in the intersection of two level sets defined by two first integrals.

  19. Exact traveling wave solution of nonlinear variants of the RLW and the PHI-four equations

    Energy Technology Data Exchange (ETDEWEB)

    Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish), Suez Canal University, AL-Arish 45111 (Egypt); Department of Mathematics, Teacher' s College, Bisha, P.O. Box 551 (Saudi Arabia)], E-mail: asoliman_99@yahoo.com

    2007-08-27

    By means of the modified extended tanh-function (METF) method the multiple traveling wave solutions of some different kinds of nonlinear partial differential equations are presented and implemented in a computer algebraic system. The solutions for the nonlinear equations such as variants of the RLW and variant of the PHI-four equations are exactly obtained and so the efficiency of the method can be demonstrated.

  20. Dynamical behaviours and exact travelling wave solutions of modified generalized Vakhnenko equation

    Indian Academy of Sciences (India)

    JUNJUN XIAO; DAHE FENG; XIA MENG; YUANQUAN CHENG

    2017-01-01

    By using the bifurcation theory of planar dynamical systems and the qualitative theory of differential equations, we studied the dynamical behaviours and exact travelling wave solutions of the modified generalized Vakhnenko equation (mGVE). As a result, we obtained all possible bifurcation parametric sets and many explicit formulas of smooth and non-smooth travelling waves such as cusped solitons, loop solitons, periodic cusp waves, pseudopeakon solitons, smooth periodic waves and smooth solitons. Moreover, we provided some numerical simulations of these solutions.

  1. An Exact Interior Extension of a Static Solution for an Electric Charged Ball

    CERN Document Server

    Baranov, Alexandre M

    2011-01-01

    We use the model approach to the description of spherical gravitating static fluid ball with an electric charge in general relativity. The metric is written in Bondi's coordinates. The total energy-momentum tensor (EMT) is chosen as a sum of the EMT of a Pascal perfect fluid and that of the electromagnetic field. An exact solution of the Einstein-Maxwell equations is found, extending a similar solution with parabolic mass density distribution.

  2. Hilbert space for quantum mechanics on superspace

    CERN Document Server

    Coulembier, Kevin

    2011-01-01

    In superspace a realization of sl2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the sl2-representation is proven. Finally the Heisenberg uncertainty principle for the super Fourier transform is constructed.

  3. Hilbert space for quantum mechanics on superspace

    Science.gov (United States)

    Coulembier, K.; De Bie, H.

    2011-06-01

    In superspace a realization of {sl}_2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product was already defined for spaces of weighted polynomials (see [K. Coulembier, H. De Bie, and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, Proc. London Math. Soc. (accepted) arXiv:1002.1118]). In this article, it is proven that this inner product can be extended to the super Schwartz space, but not to the space of square integrable functions. Subsequently, the correct Hilbert space corresponding to this inner product is defined and studied. A complete basis of eigenfunctions for general orthosymplectically invariant quantum problems is constructed for this Hilbert space. Then the integrability of the {sl}_2-representation is proven. Finally, the Heisenberg uncertainty principle for the super Fourier transform is constructed.

  4. A geodesic model in conformal superspace

    CERN Document Server

    Gomes, Henrique de A

    2016-01-01

    In this paper, I look for the most general geometrodynamical symmetries compatible with spatial relational principles. I argue that they lead either to a completely static Universe, or one embodying spatial conformal diffeomorphisms. Demanding locality for an action compatible with these principles severely limits its form, both for the gravitational part as well as all matter couplings. The simplest and most natural choice for pure gravity has two propagating physical degrees of freedom (and no refoliation-invariance). The system has a geometric interpretation as a geodesic model in infinite dimensional conformal superspace. Conformal superspace is a stratified manifold, with different strata corresponding to different isometry groups. Choosing space to be (homeomorphic to) $S^3$, conformal superspace has a preferred stratum with maximal stabilizer group. This stratum consists of a single point -- corresponding to the conformal geometry of the round 3-sphere. This is the most homogeneous non-degenerate geome...

  5. Exactly complete solutions of the Coulomb potential plus a new ring-shaped potential

    Energy Technology Data Exchange (ETDEWEB)

    Chen Changyuan [Department of Physics, Yancheng Teachers College, Yancheng 224002 (China)]. E-mail: yctcccy@tom.com; Dong Shihai [Programa de Ingenieria Molecular, Instituto Mexicano del Petroleo, Lazaro Cardenas 152, 07730 Mexico, DF (Mexico)]. E-mail: dongsh2@yahoo.com

    2005-02-21

    A new exactly solvable ring-shaped potential is proposed. The energy eigenvalues and eigenfunctions of the bound states for the Schroedinger equation with this potential are presented analytically. The exact solutions of the continuous states of this quantum system are also obtained. The calculation formula of phase shifts is derived. Analytical properties of the scattering amplitude are discussed. We find that the energy of the particle and the radial wave functions of continuous states reduce to the energy eigenvalues and the radial wave functions of the bound states at the poles of the scattering amplitude.

  6. Exact solution of the Schrodinger equation with the spin-boson Hamiltonian

    CERN Document Server

    Gardas, Bartlomiej

    2011-01-01

    We address the problem of obtaining the exact reduced dynamics of the spin-half (qubit) immersed within the bosonic bath (enviroment). An exact solution of the Schrodinger equation with the paradigmatic spin-boson Hamiltonian is obtained. We believe that this result is a major step ahead and may ultimately contribute to the complete resolution of the problem in question. We also construct the constant of motion for the spin-boson system. In contrast to the standard techniques available within the framework of the open quantum systems theory, our analysis is based on the theory of block operator matrices.

  7. Unified Treatment of a Class of Spherically Symmetric Potentials: Quasi-Exact Solution

    Directory of Open Access Journals (Sweden)

    H. Panahi

    2016-01-01

    Full Text Available We investigate the Schrödinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all models give rise to the same basic differential equation, which is expressible as an element of the universal enveloping algebra of sl(2. Then, we obtain the general exact solutions of the problem by employing the representation theory of sl(2 Lie algebra.

  8. On exact solutions and numerics for cold, shallow, and thermocoupled ice sheets

    CERN Document Server

    Bueler, E; Brown, Jed; Bueler, Ed

    2006-01-01

    This three section report can be regarded as an extended appendix to (Bueler, Brown, and Lingle 2006). First we give the detailed construction of an exact solution to a standard continuum model of a cold, shallow, and thermocoupled ice sheet. The construction is by calculation of compensatory accumulation and heat source functions which make a chosen pair of functions for thickness and temperature into exact solutions of the coupled system. The solution we construct here is ``TestG'' in (Bueler and others, 2006) and the steady state solution ``Test F'' is a special case. In the second section we give a reference C implementation of these exact solutions. In the last section we give an error analysis of a finite difference scheme for the temperature equation in the thermocoupled model. The error analysis gives three results, first the correct form of the Courant-Friedrichs-Lewy (CFL) condition for stability of the advection scheme, second an equation for error growth which contributes to understanding the famo...

  9. Exact solution of the space-time fractional coupled EW and coupled MEW equations

    Science.gov (United States)

    Raslan, K. R.; S. EL-Danaf, Talaat; K. Ali, Khalid

    2017-07-01

    In this paper, we obtained a traveling wave solution by using the Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations, such as the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEWE), which are the important soliton equations. Both equations are reduced to ordinary differential equations by use of the fractional complex transform and of the properties of the modified Riemann-Liouville derivative. We plot the exact solutions for these equations at different time levels.

  10. Exact and numerical elastodynamic solutions for thick-walled functionally graded cylinders subjected to pressure shocks

    Energy Technology Data Exchange (ETDEWEB)

    Shariyat, M., E-mail: m_shariyat@yahoo.co [Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Pardis Street, Molla-Sadra Avenue, Vanak Square, P.O. Box: 19395-1999, Tehran 19991 43344 (Iran, Islamic Republic of); Nikkhah, M.; Kazemi, R. [Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Pardis Street, Molla-Sadra Avenue, Vanak Square, P.O. Box: 19395-1999, Tehran 19991 43344 (Iran, Islamic Republic of)

    2011-02-15

    In the present paper, analytical and numerical elastodynamic solutions are developed for long thick-walled functionally graded cylinders subjected to arbitrary dynamic and shock pressures. Both transient dynamic response and elastic wave propagation characteristics are studied in these non-homogeneous structures. Variations of the material properties across the thickness are described according to both polynomial and power law functions. A numerically consistent transfinite element formulation is presented for both functions whereas the exact solution is presented for the power law function. The FGM cylinder is not divided into isotropic sub-cylinders. An approach associated with dividing the dynamic radial displacement expression into quasi-static and dynamic parts and expansion of the transient wave functions in terms of a series of the eigenfunctions is employed to propose the exact solution. Results are obtained for various exponents of the functions of the material properties distributions, various radius ratios, and various dynamic and shock loads.

  11. Lie symmetry analysis and exact solutions of the quasigeostrophic two-layer problem

    Science.gov (United States)

    Bihlo, Alexander; Popovych, Roman O.

    2011-03-01

    The quasigeostrophic two-layer model is of superior interest in dynamic meteorology since it is one of the easiest ways to study baroclinic processes in geophysical fluid dynamics. The complete set of point symmetries of the two-layer equations is determined. An optimal set of one- and two-dimensional inequivalent subalgebras of the maximal Lie invariance algebra is constructed. On the basis of these subalgebras, we exhaustively carry out group-invariant reduction and compute various classes of exact solutions. Wherever possible, reference to the physical meaning of the exact solutions is given. In particular, the well-known baroclinic Rossby wave solutions in the two-layer model are rediscovered.

  12. On Exact Solutions of the Navier-Stokes Equations for Uni-directional Flows

    CERN Document Server

    Lam, F

    2015-01-01

    In the present note, we show that the uni-directional flows in a rectangular channel and in a circular pipe are exact spatio-temporal solutions of the Navier-Stokes equations over a short time interval. We assert that the classical plane Poiseuille-Couette flow and Hagen-Poiseuille flow are time-independent approximations of the exact solutions if an appropriate initial velocity distribution at starting location is specified. Conceptually, there do not exist absolute steady flows starting from unspecified initial data. The classic experimental measurements by Poiseuille can be explained in terms of the evolutional solutions. In particular, the pipe flow does not have a time-independent characteristic velocity. The orthodox notion that the parabolic profile exists for arbitrary Reynolds numbers is unwarranted.

  13. Exact Solutions in Modified Massive Gravity and Off-Diagonal Wormhole Deformations

    CERN Document Server

    Vacaru, Sergiu I

    2014-01-01

    There are explored off-diagonal deformations of "prime" metrics in Einstein gravity (for instance, for wormhole configurations) into "target" exact solutions in f(R,T)-modified and massive/ bi-metric gravity theories. The new classes of solutions may posses, or not, Killing symmetries and can be characterized by effective induced masses, anisotropic polarized interactions and cosmological constants. For nonholonomic deformations with (conformal) ellipsoid/ toroid and/or solitonic symmetries and, in particular, for small eccentricity rotoid configurations, we can generate wormholes like objects matching external black ellipsoid - de Sitter geometries. We conclude that there are nonholonomic transforms and/or non-trivial limits to exact solutions in general relativity when modified/ massive gravity effects are modeled by off-diagonal and/or nonholonomic parametric interactions.

  14. Peakons and new exact solitary wave solutions of extended quantum Zakharov-Kuznetsov equation

    Science.gov (United States)

    Zhang, Ben-gong; Li, Weibo; Li, Xiangpeng

    2017-06-01

    In this paper, the three dimensional extended quantum Zakharov-Kuznetsov equation, which arises in the dimensionless hydrodynamic equations describing the nonlinear propagation of the quantum ion-acoustic waves, is investigated by an auxiliary equation method. As a result, peakons and a series of new exact traveling wave solutions, including bell-shaped, kink-type solitary wave, shock wave, periodic wave, and Jacobi elliptic solutions, are obtained. We also analyze the three kinds of nonlinear structures of our results, i.e., blowup, peakons, and shock wave. These new exact solutions will enrich the previous results and help us to further understand the physical structures and analyze the nonlinear propagation of the quantum ion-acoustic waves.

  15. A modified thermodynamics method to generate exact solutions of the Einstein equations

    CERN Document Server

    Tan, Hong-Wei; He, Tang-Mei; Zhang, Jing-Yi

    2016-01-01

    We modify the method to generate the exact solutions of the Einstein equations basing on the laws of thermodynamics. Firstly, the Komar mass is used to take the place of the Misner-Sharp energy which is used in the original methods, and then several exact solutions of Einstein equations are obtained, including the black hole solution which surrounded by quintessence. Moreover, the geometry surface gravity defined by Komar mass is obtained. Secondly, we use both the Komar mass and the ADM mass to modify such method, and the similar results are obtained. Moreover, with some generalize added to the definition of the ADM mass, our method can be generalized to global monopole sapcetime.

  16. New exact solutions of hydrodynamics for rehadronizing fireballs with lattice QCD equation of state

    CERN Document Server

    Csörgő, T

    2016-01-01

    We describe fireballs that rehadronize from a perfectly fluid quark matter to a chemically frozen, multi-component hadron gas. In the hydrodynamics of these fireballs, we utilize the lattice QCD equation of state, however, we also apply non-relativistic kinematics for simplicity and clarity. Two new classes of exact, analytic solutions of fireball hydrodynamics are presented: the first class describes triaxially expanding, non-rotating ellipsoidal fireballs, while the second class of exact solutions corresponds to spheroidally symmetric, rotating fireballs. In both classes of solutions, we find evidence for a secondary explosion, that happens just after hadrochemical freeze-out. A realistic, linear mass scaling of the slope parameters of the single particle spectra of various hadronic species is obtained analytically, as well as an also realistic, linear mass scaling of the inverse of the squared HBT radius parameters of the Bose-Einstein correlation functions.

  17. Exact solutions to the geodesic equations of linear dilaton black holes

    CERN Document Server

    Hamo, A H H

    2015-01-01

    In this paper, we analyze the geodesics of the 4-dimensional ($4D$) linear dilaton black hole (LDBH) spacetime, which is an exact solution to the Einstein-Maxwell-Dilaton (EMD) theory. LDBHs have non-asymptotically flat (NAF) geometry, and their Hawking radiation is an isothermal process. The geodesics motions of the test particles are studied via the standard Lagrangian method. After obtaining the Euler-Lagrange (EL) equations, we show that exact analytical solutions to the radial and angular geodesic equations can be obtained. In particular, it is shown that one of the possible solutions for the radial trajectories can be given in terms of the WeierstrassP-function ($\\wp$-function), which is an elliptic-type special function.

  18. Exact solutions in modified massive gravity and off-diagonal wormhole deformations

    Energy Technology Data Exchange (ETDEWEB)

    Vacaru, Sergiu I. [Alexandru Ioan Cuza University, Rector' s Office, Iasi (Romania); CERN, Theory Division, Geneva 23 (Switzerland)

    2014-03-15

    We explore off-diagonal deformations of 'prime' metrics in Einstein gravity (for instance, for wormhole configurations) into 'target' exact solutions in f(R,T)-modified and massive/bi-metric gravity theories. The new classes of solutions may, or may not, possess Killing symmetries and can be characterized by effective induced masses, anisotropic polarized interactions, and cosmological constants. For nonholonomic deformations with (conformal) ellipsoid/ toroid and/or solitonic symmetries and, in particular, for small eccentricity rotoid configurations, we can generate wormhole-like objects matching an external black ellipsoid--de Sitter geometries. We conclude that there are nonholonomic transforms and/or non-trivial limits to exact solutions in general relativity when modified/massive gravity effects are modeled by off-diagonal and/or nonholonomic parametric interactions. (orig.)

  19. Fully developed MHD natural convection flow in a vertical annular microchannel: An exact solution

    Directory of Open Access Journals (Sweden)

    Basant K. Jha

    2015-07-01

    Full Text Available An exact solution of steady fully developed natural convection flow of viscous, incompressible, electrically conducting fluid in a vertical annular micro-channel with the effect of transverse magnetic field in the presence of velocity slip and temperature jump at the annular micro-channel surfaces is obtained. Exact solution is expressed in terms of modified Bessel function of the first and second kind. The solution obtained is graphically represented and the effects of radius ratio (η, Hartmann number (M, rarefaction parameter (βvKn, and fluid–wall interaction parameter (F on the flow are investigated. During the course of numerical computations, it is found that an increase in Hartmann number leads to a decrease in the fluid velocity, volume flow rate and skin friction. Furthermore, it is found that an increase in curvature radius ratio leads to an increase in the volume flow rate.

  20. Superspace Dynamics and Perturbations Around "Emptiness"

    CERN Document Server

    Soo, C P; Soo, Chopin; Chang, Lay Nam

    1994-01-01

    Superspace parametrized by gauge potentials instead of metric three-geometries is discussed in the context of the Ashtekar variables. Among other things, an "internal clock" for the full theory can be identified. Gauge-fixing conditions which lead to the natural geometrical separation of physical from gauge modes are derived with the use of the metric in connection-superspace. A perturbation scheme about an unconventional background which is inaccessible to conventional variables is presented. The resultant expansion retains much of the simplicity of Ashtekar's formulation of General Relativity.

  1. Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation

    Institute of Scientific and Technical Information of China (English)

    Zhang Liang; Zhang Li-Feng; Li Chong-Yin

    2008-01-01

    By using the modified mapping method,we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation.The solutions obtained in this paper include Jacobian elliptic function solutions,combined Jacobian elliptic function solutions,soliton solutions,triangular function solutions.

  2. Symbolic Computation and Construction of New Exact Travelling Wave Solutions to (3+1)-Dimensional KP Equation

    Institute of Scientific and Technical Information of China (English)

    ZHANG Xiao-Xian; WEN Xiao-Yong; SUN Ye-Peng

    2008-01-01

    With the aid of symbolic computation system Maple, many exact solutions for the (3+1)-dimensional KP equation axe constructed by introducing an auxiliary equation and using its new Jacobi elliptic function solutions, where the new solutions are also constructed. When the modulus m → 1 and m → 0, these solutions reduce to the corresponding solitary evolution solutions and trigonometric function solutions.

  3. New exact solutions of nonlinear Gross-Pitaevskii equation with weak bias magnetic and time-dependent laser fields

    Institute of Scientific and Technical Information of China (English)

    Li Hua-Mei

    2005-01-01

    By using the mapping method and an appropriate transformation, we find new exact solutions of nonlinear Gross-Pitaevskii equation with weak bias magnetic and time-dependent laser fields. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions , triangular function solutions, bright and dark solitons, and soliton-like solutions.

  4. A Series of Exact Solutions for a New (2+1)-Dimensional Calogero KdV Equation

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    An algebraic method is proposed to solve a new (2+1)-dimensional Calogero KdV equation and explicitly construct a series of exact solutions including rational solutions, triangular solutions, exponential solution, line soliton solutions, and doubly periodic wave solutions.

  5. New Exact Solutions for the Generalized (2+1)-dimensional Nonlinear Schr(o)dinger Equation with Variable Coefficients

    Institute of Scientific and Technical Information of China (English)

    JIANG Zhi-ping

    2012-01-01

    With the help of the variable-coefficient generalized projected Ricatti equation expansion method,we present exact solutions for the generalized (2+1)-dimensional nonlinear Schr(o)dinger equation with variable coefficients.These solutions include solitary wave solutions,soliton-like solutions and trigonometric function solutions.Among these solutions,some are found for the first time.

  6. Multi-Order Exact Solutions for a generalized shallow water wave equation and other nonlinear PDEs

    CERN Document Server

    Bagchi, Bijan; Ganguly, Asish

    2011-01-01

    We seek multi-order exact solutions of a generalized shallow water wave equation along with those corresponding to a class of nonlinear systems described by the KdV, modified KdV, Boussinesq, Klein-Gordon and modified Benjamin-Bona-Mahony equation. We employ a modified version of a generalized Lame equation and subject it to a perturbative treatment identifying the solutions order by order in terms of Jacobi elliptic functions. Our solutions are new and hold the key feature that they are expressible in terms of an auxiliary function f in a generic way. For appropriate choices of f we recover the previous results reported in the literature.

  7. Exact Solutions of the Klein-Gordon Equation with a New Anharmonic Oscillator Potential

    Institute of Scientific and Technical Information of China (English)

    ZHANG Min-Cang; WANG Zhen-Bang

    2005-01-01

    @@ We solve the Klein-Gordon equation with a new anharmonic oscillator potential and present the exact solutions.It is shown that under the condition of equal scalar and vector potentials, the Klein-Gordon equation could be separated into an angular equation and a radial equation. The angular solutions are the associated-Legendre polynomial and the radial solutions are expressed in terms of the confluent hypergeometric functions. Finally,the energy equation is obtained from the boundary condition satisfied by the radial wavefunctions.

  8. Nonequivalent Similarity Reductions and Exact Solutions for Coupled Burgers-Type Equations

    Science.gov (United States)

    M. H. M., Moussa; R. A. K., Omar; Rehab, M. El-Shiekh; H. R., El-Melegy

    2012-01-01

    Using the machinery of Lie group analysis, the nonlinear system of coupled Burgers-type equations is studied. Using the infinitesimal generators in the optimal system of subalgebra of the said Lie algebras, it leads to two nonequivalent similarity transformations by using it we obtain two reductions in the form of system of nonlinear ordinary differential equations. The search for solutions of these systems by using the G'/G-method has yielded certain exact solutions expressed by rational functions, hyperbolic functions, and trigonometric functions. Some figures are given to show the properties of the solutions.

  9. Renormalization of the fragmentation equation: exact self-similar solutions and turbulent cascades.

    Science.gov (United States)

    Saveliev, V L; Gorokhovski, M A

    2012-12-01

    Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.

  10. Nonequivalent Similarity Reductions and Exact Solutions for Coupled Burgers-Type Equations

    Institute of Scientific and Technical Information of China (English)

    M.H.M. Moussa; R.A.K. Omar; Rehab M. El-Shiekh; H.R. El-Melegy

    2012-01-01

    Using the machinery of Lie group analysis, the nonlinear system of coupled Burgers-type equations is studied. Using the infinitesimal generators in the optimal system of subalgebra of the said Lie algebras, it leads to two nonequivalent similarity transformations by using it we obtain two reductions in the form of system of nonlinear ordinary differential equations. The search for solutions of these systems by using the G/G-method has yielded certain exact solutions expressed by rational functions, hyperbolic functions, and trigonometric functions. Some figures are given to show the properties of the solutions.

  11. Electromagnetic fields radiated from a lightning return stroke - Application of an exact solution to Maxwell's equations

    Science.gov (United States)

    Le Vine, D. M.; Meneghini, R.

    1978-01-01

    A solution is presented for the electromagnetic fields radiated by an arbitrarily oriented current filament over a conducting ground plane in the case where the current propagates along the filament at the speed of light, and this solution is interpreted in terms of radiation from lightning return strokes. The solution is exact in the fullest sense; no mathematical approximations are made, and the governing differential equations and boundary conditions are satisfied. The solution has the additional attribute of being specified in closed form in terms of elementary functions. This solution is discussed from the point of view of deducing lightning current wave forms from measurements of the electromagnetic fields and understanding the effects of channel tortuosity on the radiated fields. In addition, it is compared with two approximate solutions, the traditional moment approximation and the Fraunhofer approximation, and a set of criteria describing their applicability are presented and interpreted.

  12. Self-interacting scalar field cosmologies: unified exact solutions and symmetries

    CERN Document Server

    Charters, T

    2009-01-01

    We investigate a mechanism that generates the exact solutions of scalar field cosmologies in a unified way. The procedure investigated here permits to recover allmost all known solutions, and allows one to derive new solutions as well. In particular, we derive and discuss one novel solution defined in terms of the Lambert function. The solutions are organized in a classification which depends on the choice of a generating function which we have denoted by $x(\\phi)$ that reflects the underlying thermodynamics of the model. We also analyse and discuss the existence of form invariances and dualities between solutions. A general way of defining the latter in an appropriate fashion for scalar fields is put forward.

  13. New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods

    Science.gov (United States)

    S Saha, Ray

    2016-04-01

    In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.

  14. Exact cosmological solutions of f(R theories via Hojman symmetry

    Directory of Open Access Journals (Sweden)

    Hao Wei

    2016-02-01

    Full Text Available Nowadays, f(R theory has been one of the leading modified gravity theories to explain the current accelerated expansion of the universe, without invoking dark energy. It is of interest to find the exact cosmological solutions of f(R theories. Besides other methods, symmetry has been proved as a powerful tool to find exact solutions. On the other hand, symmetry might hint the deep physical structure of a theory, and hence considering symmetry is also well motivated. As is well known, Noether symmetry has been extensively used in physics. Recently, the so-called Hojman symmetry was also considered in the literature. Hojman symmetry directly deals with the equations of motion, rather than Lagrangian or Hamiltonian, unlike Noether symmetry. In this work, we consider Hojman symmetry in f(R theories in both the metric and Palatini formalisms, and find the corresponding exact cosmological solutions of f(R theories via Hojman symmetry. There exist some new solutions significantly different from the ones obtained by using Noether symmetry in f(R theories. To our knowledge, they also have not been found previously in the literature. This work confirms that Hojman symmetry can bring new features to cosmology and gravity theories.

  15. Exact Solutions of a High-Order Nonlinear Wave Equation of Korteweg-de Vries Type under Newly Solvable Conditions

    Directory of Open Access Journals (Sweden)

    Weiguo Rui

    2014-01-01

    Full Text Available By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.

  16. Quantitative study on exact reconstruction sampling condition by verifying solution uniqueness in limited-view CT.

    Science.gov (United States)

    Yan, Bin; Zhang, Wenkun; Li, Lei; Zhang, Hanming; Wang, Linyuan

    2016-10-01

    In limited-view computed tomography reconstruction, iterative image reconstruction with sparsity-exploiting methods, such as total variation (TV) minimization, inspired by compressive sensing, potentially claims large reductions in sampling requirements. However, a quantitative notion of this claim is non-trivial because of the ill-defined reduction in sampling achieved by the sparsity-exploiting method. In this paper, exact reconstruction sampling condition for limited-view problem is studied by verifying the uniqueness of solution in TV minimization model. Uniqueness is tested by solving a convex optimization problem derived from the sufficient and necessary condition of solution uniqueness. Through this method, the sufficient sampling number of exact reconstruction is quantified for any fixed phantom and settled geometrical parameter in the limited-view problem. This paper provides a reference to quantify the sampling condition. Three phantoms are tested to study the sampling condition of limited view exact reconstruction in this paper. The experiment results show the quantified sampling number and indicate that an object would be accurately reconstructed as the scanning range becomes narrower by increasing sampling number. The increased samplings compensate for the deficiency of the projection angle. However, the lower bound of the scanning range corresponding to three different phantoms are presented, in which an exact reconstruction cannot be obtained once the projection angular is narrowed to this extent no matter how to increase sampling.

  17. Exact solutions of the one-dimensional generalized modified complex Ginzburg-Landau equation

    CERN Document Server

    Yomba, E

    2003-01-01

    The one-dimensional (1D) generalized modified complex Ginzburg-Landau (MCGL) equation for the traveling wave systems is analytically studied. Exact solutions of this equation are obtained using a method which combines the Painleve test for integrability in the formalism of Weiss-Tabor-Carnevale and Hirota technique of bilinearization. We show that pulses, fronts, periodic unbounded waves, sources, sinks and solution as collision between two fronts are the important coherent structures that organize much of the dynamical properties of these traveling wave systems. The degeneracies of the 1D generalized MCGL equation are examined as well as several of their solutions. These degeneracies include two important equations: the 1D generalized modified Schroedinger equation and the 1D generalized real modified Ginzburg-Landau equation. We obtain that the one parameter family of traveling localized source solutions called 'Nozaki-Bekki holes' become a subfamily of the dark soliton solutions in the 1D generalized modif...

  18. Exact solutions of SO(3) non-linear sigma model in a conic space background

    CERN Document Server

    Bezerra, V B; Romero, C

    2005-01-01

    We consider a nonlinear sigma model coupled to the metric of a conic space. We obtain restrictions for a nonlinear sigma model to be a source of the conic space. We then study nonlinear sigma model in the conic space background. We find coordinate transformations which reduce the chiral fields equations in the conic space background to field equations in Minkowski spacetime. This enables us to apply the same methods for obtaining exact solutions in Minkowski spacetime to the case of a conic spacetime. In the case the solutions depend on two spatial coordinates we employ Ivanov's geometrical ansatz. We give a general analysis and also present classes of solutions in which there is dependence on three and four coordinates. We discuss with special attention the intermediate instanton and meron solutions and their analogous in the conic space. We find differences in the total actions and topological charges of these solutions and discuss the role of the deficit angle.

  19. An exact smooth Gowdy-symmetric generalized Taub-NUT solution

    CERN Document Server

    Beyer, Florian

    2014-01-01

    In a recent paper (Beyer and Hennig, 2012 [9]), we have introduced a class of inhomogeneous cosmological models: the smooth Gowdy-symmetric generalized Taub-NUT solutions. Here we derive a three-parametric family of exact solutions within this class, which contains the two-parametric Taub solution as a special case. We also study properties of this solution. In particular, we show that for a special choice of the parameters, the spacetime contains a curvature singularity with directional behaviour that can be interpreted as a "true spike" in analogy to previously known Gowdy symmetric solutions with spatial T3-topology. For other parameter choices, the maximal globally hyperbolic region is singularity-free, but may contain "false spikes".

  20. Noether symmetries of a modified model in teleparallel gravity and a new approach for exact solutions

    Energy Technology Data Exchange (ETDEWEB)

    Tajahmad, Behzad [University of Tabriz, Faculty of Physics, Tabriz (Iran, Islamic Republic of)

    2017-04-15

    In this paper, we present the Noether symmetries of flat FRW spacetime in the context of a new action in teleparallel gravity which we construct based on the f(R) version. This modified action contains a coupling between the scalar field potential and magnetism. Also, we introduce an innovative approach, the beyond Noether symmetry (B.N.S.) approach, for exact solutions which carry more conserved currents than the Noether approach. By data analysis of the exact solutions, obtained from the Noether approach, late-time acceleration and phase crossing are realized, and some deep connections with observational data such as the age of the universe, the present value of the scale factor as well as the state and deceleration parameters are observed. In the B.N.S. approach, we consider the dark energy dominated era. (orig.)

  1. Ferrofluid patterns in Hele-Shaw cells: Exact, stable, stationary shape solutions

    Science.gov (United States)

    Lira, Sergio; Miranda, Jose

    2016-11-01

    We investigate a quasi-two-dimensional system composed by an initially circular ferrofluid droplet surrounded by a nonmagnetic fluid of higher density. These immiscible fluids flow in a rotating Hele-Shaw cell, under the influence of an in-plane radial magnetic field. We focus on the situation in which destabilizing bulk magnetic field effects are balanced by stabilizing centrifugal forces. In this framing, we consider the interplay of capillary and magnetic normal traction effects in determining the fluid-fluid interface morphology. By employing a vortex-sheet formalism we have been able to find a family of exact stationary N-fold polygonal shape solutions for the interface. A weakly nonlinear theory is then used to verify that such exact interfacial solutions are in fact stable. We thank CNPq (Brazilian Research Council) for financial support.

  2. Exact solutions to the supply chain equations for arbitrary, time-dependent demands

    DEFF Research Database (Denmark)

    Warburton, Roger D.H.; Hodgson, J.P.E.; Nielsen, Erland Hejn

    2014-01-01

    We study the impact on inventory of an unexpected, non-linear, time-dependent demand and present the exact solutions over time to the supply chain equations without requiring any approximations. We begin by imposing a boundary condition of stability at infinity, from which we derive expressions...... for the estimated demand and the target work in progress when the demand is time-dependent. The resulting inventory equation is solved in terms of the Lambert modes with all of the demand non-linearities confined to the pre-shape function. The series solution is exact, and all terms are reasonably easy to calculate......, so users can determine the inventory behavior to any desired precision. To illustrate, we solve the equations for a non-linear, quadratic time-dependence in the demand. For practical use, only a few terms in the series are required, a proposition illustrated by the For All Practical Purposes (FAPP...

  3. Exact solution to the Coulomb wave using the linearized phase-amplitude method

    Directory of Open Access Journals (Sweden)

    Shuji Kiyokawa

    2015-08-01

    Full Text Available The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation.

  4. Exact solutions to the supply chain equations for arbitrary, time-dependent demands

    DEFF Research Database (Denmark)

    Warburton, Roger D.H.; Hodgson, J.P.E.; Nielsen, Erland Hejn

    2014-01-01

    , so users can determine the inventory behavior to any desired precision. To illustrate, we solve the equations for a non-linear, quadratic time-dependence in the demand. For practical use, only a few terms in the series are required, a proposition illustrated by the For All Practical Purposes (FAPP......We study the impact on inventory of an unexpected, non-linear, time-dependent demand and present the exact solutions over time to the supply chain equations without requiring any approximations. We begin by imposing a boundary condition of stability at infinity, from which we derive expressions...... for the estimated demand and the target work in progress when the demand is time-dependent. The resulting inventory equation is solved in terms of the Lambert modes with all of the demand non-linearities confined to the pre-shape function. The series solution is exact, and all terms are reasonably easy to calculate...

  5. Exact solution of the 1D Riemann problem in Newtonian and relativistic hydrodynamics

    CERN Document Server

    Lora-Clavijo, F D; Guzman, F S; Gonzalez, J A

    2013-01-01

    Some of the most interesting scenarios that can be studied in astrophysics, contain fluids and plasma moving under the influence of strong gravitational fields. To study these problems it is required to implement numerical algorithms robust enough to deal with the equations describing such scenarios, which usually involve hydrodynamical shocks. It is traditional that the first problem a student willing to develop research in this area is to numerically solve the one dimensional Riemann problem, both Newtonian and relativistic. Even a more basic requirement is the construction of the exact solution to this problem in order to verify that the numerical implementations are correct. We describe in this paper the construction of the exact solution and a detailed procedure of its implementation.

  6. Exact Solution to Helmholtz Equation for Inhomogeneous Medium: Its Application in Optical Communication

    Institute of Scientific and Technical Information of China (English)

    WANG Gang; WU Shao-Quan; HOU Bang-Pin

    2005-01-01

    @@ In order to study the capability of amplifying the input optical signal of certain materials, we investigate the Helmholtz equation which describes a system of inhomogeneous media. After exploring its SU(1,1) algebraic structure, we obtain the exact solutions of this Helmholtz equation by means of the algebraic dynamical method.Based on the exact solutions, we analyse the capability of optical amplifiers, which is an important issue in modern optical communication. We take the wave number ko(z) and the expansion coefficient k2(z) to be the trigonometric functions, exponential functions and power functions of variable z, respectively. It is found that the material following the exponential functions is the best one for optical amplifiers.

  7. Experimental evaluation of apparent tissue surface tension based on the exact solution of the Laplace equation

    Science.gov (United States)

    Norotte, C.; Marga, F.; Neagu, A.; Kosztin, I.; Forgacs, G.

    2008-02-01

    The notion of apparent tissue surface tension offered a systematic way to interpret certain morphogenetic processes in early development. It also allowed deducing quantitative information on cellular and molecular parameters that is otherwise difficult to obtain. To accurately determine such tensions we combined novel experiments with the exact solution of the Laplace equation for the profile of a liquid drop under the employed experimental conditions and used the exact solution to evaluate data collected on tissues. Our results confirm that tissues composed of adhesive and motile cells indeed can be characterized in terms of well-defined apparent surface tension. Our experimental technique presents a way to measure liquid interfacial tensions under conditions when known methods fail.

  8. Localized light waves: Paraxial and exact solutions of the wave equation (a review)

    Science.gov (United States)

    Kiselev, A. P.

    2007-04-01

    Simple explicit localized solutions are systematized over the whole space of a linear wave equation, which models the propagation of optical radiation in a linear approximation. Much attention has been paid to exact solutions (which date back to the Bateman findings) that describe wave beams (including Bessel-Gauss beams) and wave packets with a Gaussian localization with respect to the spatial variables and time. Their asymptotics with respect to free parameters and at large distances are presented. A similarity between these exact solutions and harmonic in time fields obtained in the paraxial approximation based on the Leontovich-Fock parabolic equation has been studied. Higher-order modes are considered systematically using the separation of variables method. The application of the Bateman solutions of the wave equation to the construction of solutions to equations with dispersion and nonlinearity and their use in wavelet analysis, as well as the summation of Gaussian beams, are discussed. In addition, solutions localized at infinity known as the Moses-Prosser “acoustic bullets”, as well as their harmonic in time counterparts, “ X waves”, waves from complex sources, etc., have been considered. Everywhere possible, the most elementary mathematical formalism is used.

  9. Adinkras and the Dynamics of Superspace Prepotentials

    CERN Document Server

    Doran, C F; Gates, S J; Hübsch, T; Iga, K M; Landweber, G D

    2006-01-01

    We demonstrate a method for describing one-dimensional N-extended supermultiplets and building supersymmetric actions in terms of unconstrained prepotential superfields, explicitly working with the Scalar supermultiplet. The method uses intuitive manipulations of Adinkras and GR(d,N) algebras, a variant of Clifford algebras. In the process we clarify the relationship between Adinkras, GR(d,N) algebras, and superspace.

  10. Quaternionic (super) twistors extensions and general superspaces

    Science.gov (United States)

    Cirilo-Lombardo, Diego Julio; Pervushin, Victor N.

    2017-09-01

    In a attempt to treat a supergravity as a tensor representation, the four-dimensional N-extended quaternionic superspaces are constructed from the (diffeomorphyc) graded extension of the ordinary Penrose-twistor formulation, performed in a previous work of the authors [D. J. Cirilo-Lombardo and V. N. Pervushin, Int. J. Geom. Methods Mod. Phys., doi: http://dx.doi.org/10.1142/S0219887816501139.], with N = p + k. These quaternionic superspaces have 4 + k(N - k) even-quaternionic coordinates and 4N odd-quaternionic coordinates, where each coordinate is a quaternion composed by four ℂ-fields (bosons and fermions respectively). The fields content as the dimensionality (even and odd sectors) of these superspaces are given and exemplified by selected physical cases. In this case, the number of fields of the supergravity is determined by the number of components of the tensor representation of the four-dimensional N-extended quaternionic superspaces. The role of tensorial central charges for any N even USp(N) = Sp(N, ℍℂ) ∩ U(N, ℍℂ) is elucidated from this theoretical context.

  11. On some exact solutions of slightly variant forms of Yang's equations and their graphical representations

    Indian Academy of Sciences (India)

    Rupesh Kumar Sha; Pranab Krishna Chanda

    2008-05-01

    The equations obtained by Yang while discussing the condition of self-duality of (2) gauge fields on Euclidean four-dimensional space have been generalized. Exact solutions and their graphical representations for the generalized equation (for some particular values of the parameters) have been reported. They represent interesting physical characteristics like waves with spreading solitary profile, spreading wave packets, waves with pulsating solitary profile (between zero and a maximum), waves with oscillatory solitary profile and chaos.

  12. On exact solutions of the Dirac equation in a homogeneous magnetic field in the Lobachevsky space

    CERN Document Server

    Ovsiyuk, E M; Red'kov, V M

    2010-01-01

    There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue of the homogeneous magnetic field in the Minkowski space. A generalized formula for energy levels, describing quantization of the motion of the particle in magnetic field on the background of the Lobachevsky space geometry, has been obtained.

  13. Exact solutions for MHD flow of couple stress fluid with heat transfer

    Directory of Open Access Journals (Sweden)

    Najeeb Alam Khan

    2016-01-01

    Full Text Available This paper aims at presenting exact solutions for MHD flow of couple stress fluid with heat transfer. The governing partial differential equations (PDEs for an incompressible MHD flow of couple stress fluid are reduced to ordinary differential equations by employing wave parameter. The methodology is implemented for linearizing the flow equations without extra transformation and restrictive assumptions. Comparison is made with the result obtained previously.

  14. Exact Solutions of Fractional Burgers and Cahn-Hilliard Equations Using Extended Fractional Riccati Expansion Method

    Directory of Open Access Journals (Sweden)

    Wei Li

    2014-01-01

    Full Text Available Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.

  15. New exact solutions of the Einstein-Maxwell equations for magnetostatic fields

    Institute of Scientific and Technical Information of China (English)

    Nisha Goyal; R. K. Gupta

    2012-01-01

    The symmetry reduction method based on the Fréchet derivative of differential operators is applied to investigate symmetries of the Einstein-Maxwell field equations for magnetostatic fields,which is a coupled system of nonlinear partial differential equations of the second order.The technique yields invariant transformations that reduce the given system of partial differential equations to a system of nonlinear ordinary differential equations.Some of the reduced systems are further studied to obtain the exact solutions.

  16. Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential

    Energy Technology Data Exchange (ETDEWEB)

    Iacob, Felix, E-mail: felix@physics.uvt.ro [West University of Timişoara, V. Pârvan 4, Timişoara 300223 (Romania); Lute, Marina, E-mail: marina.lute@upt.ro [Politehnica University of Timişoara, Traian Lalescu 2, Timişoara 300223 (Romania)

    2015-12-15

    We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.

  17. Group Classification and Exact Solutions of a Class of Variable Coefficient Nonlinear Wave Equations

    Institute of Scientific and Technical Information of China (English)

    HUANG Ding-Jiang; MEI Jian-Qin; ZHANG Hong-Qing

    2009-01-01

    Complete group classification of a class of variable coefficient (1 + 1)-dimensional wave equations is performed.The possible additional equivalence transformations between equations from the class under consideration and the conditional equivalence groups are also investigated. These allow simplification of the results of the classification and further applications of them. The derived Lie symmetries are used to construct exact solutions of special forms of these equations via the classical Lie method. Nonclassical symmetries of the wave equations are discussed.

  18. An exact solution of the metric-affine gauge theory with dilation, shear, and spin charges

    CERN Document Server

    Obukhov, Yu N; Esser, W; Tresguerres, R; Hehl, F W

    1996-01-01

    The spacetime of the metric-affine gauge theory of gravity (MAG) encompasses {\\it nonmetricity} and {\\it torsion} as post-Riemannian structures. The sources of MAG are the conserved currents of energy-momentum and dilation, shear and spin. We present an exact static spherically symmetric vacuum solution of the theory describing the exterior of a lump of matter carrying mass and dilation, shear and spin charges.

  19. A procedure to construct exact solutions of nonlinear fractional differential equations.

    Science.gov (United States)

    Güner, Özkan; Cevikel, Adem C

    2014-01-01

    We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

  20. Exact solutions and maximal dimension of invariant subspaces of time fractional coupled nonlinear partial differential equations

    Science.gov (United States)

    Sahadevan, R.; Prakash, P.

    2017-01-01

    We show how invariant subspace method can be extended to time fractional coupled nonlinear partial differential equations and construct their exact solutions. Effectiveness of the method has been illustrated through time fractional Hunter-Saxton equation, time fractional coupled nonlinear diffusion system, time fractional coupled Boussinesq equation and time fractional Whitman-Broer-Kaup system. Also we explain how maximal dimension of the time fractional coupled nonlinear partial differential equations can be estimated.

  1. Exact Solutions of Nonlinear Dynamics Equation in a New Double-Chain Model of DNA

    Institute of Scientific and Technical Information of China (English)

    QIAN Xian-Min; LOU Sen-Yue

    2003-01-01

    The exact solutions of the general nonlinear dynamic system in a new double-chain model of DNA are studiedkink shape excitations can be found in both the Conte's truncation expansion and the Pickering's truncation expansion.Three types of new localized excitations, the asymmetric kink-kink excitations, the soliton-kink excitation, and thekink-soliton excitations, are found by using the Pickering's nonstandard truncation expansion.

  2. Exact solution of a generalized two-sites Bose-Hubbard model

    CERN Document Server

    Filho, Gilberto N Santos

    2016-01-01

    I introduce a new parametrization of a bosonic Lax operator for the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix and use it to present the exact solution of a generalized two-sites Bose-Hubbard model with asymmetric tunnelling. In the no interaction limit I show that the Bethe ansatz equations can be written as a $S^{N-1}$ sphere, where $N$ is the total number of atoms in the condensate.

  3. Exact Solution of the Markov Propagator for the Voter Model on the Complete Graph

    Science.gov (United States)

    2014-07-01

    Markov chains. It is known that the eigenvalues and eigenvectors of the transition matrix of the Markov chain have a vital role in the dy- namics of...B. Differential Eigenvalue Problem In this section, we will examine the eigenvectors in more detail. In particular, we wish to consider the ther...Models Exact solutions for the standard Voter model in terms of the spectrum and eigenvectors of the Markov propagator for macroststes are first obtained

  4. Exact travelling wave solutions for a class of nonlinear partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Xie Fuding E-mail: xiefd@sohu.com; Gao Xiaoshan

    2004-03-01

    In this paper, the tanh-method is improved by means of a proper rational transformation based upon a coupled projective Riccati equations. The ansatz can be applied to find more and new exact solutions of the partial differential equations with the aid of symbolic computation system, Maple. We choose an example, which includes phi{sup 4} equation, Klein-Gordon equation, Duffing equation, Landau-Ginburg-Higgs equation and Sine-Gordon equation, to illustrate the method.

  5. A new approach to exact solutions construction in scalar cosmology with a Gauss-Bonnet term

    Science.gov (United States)

    Fomin, I. V.; Chervon, S. V.

    2017-08-01

    We study the cosmological model based on Einstein-Gauss-Bonnet gravity with non-minimal coupling of a scalar field to a Gauss-Bonnet term in four-dimensional (4D) Friedmann universe. We show how constructing the exact solutions by the method based on a confrontation of the Hubble parameter in the model under consideration is achieved with that in a standard scalar field inflationary cosmology.

  6. An exact solution of the Jackiw-Rebbi equations for a fermion-monopole-Higgs system

    Science.gov (United States)

    Din, A. M.; Roy, S. M.

    1983-09-01

    We present an exact solution for arbitrary partial waves to the Jackiw-Rebbi equations for an isospinor fermion in the background of a non-abelian singular magnetic monopole and a Higgs field. The Higgs coupling produces a centrifugal barrier making the hamiltonian self-adjoint with ordinary boundary conditions at the origin. There are infinitely many bound states, each doubly degenerate. The scattering is charge conserving.

  7. Compressible Flow Produced by Distributed Sources of Mass: An Exact Solution

    OpenAIRE

    Clarke, J.F.

    1987-01-01

    The paper considers the case of a one-dimensional isentropic unsteady compressible flow that is driven entirely by a distribution of sources in the left-hand half space of an unbounded domain. The right-hand half-space contains no sources, so that source-strength drops discontinuously to zero as one crosses from left to right-hand space. Exact solutions are obtained for those parts of the flow that remain isentropic.

  8. Exact solution of rate equations for a two-spin-qubit system

    Energy Technology Data Exchange (ETDEWEB)

    Le Thi Ha Linh; Nguyen Bich Ha [Institute of Materials Science, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, Cau Giay District, Hanoi (Viet Nam)], E-mail: linhlth@ims.vast.ac.vn

    2009-09-01

    The quantum dynamics of a system of two interacting spin-qubits is studied for elaborating the physical mechanism of the quantum information transfer between them. A simple model with their Heisenberg XY exchange interaction is investigated. The rate equations are established. The analytical expressions of their solution are exactly derived. They explicitly demonstrate, how the quantum information encoded into a spin-qubit at the initial time t = 0 is transferred to other one at any time t > 0.

  9. Exact solutions to a class of nonlinear Schrödinger-type equations

    Indian Academy of Sciences (India)

    Jin-Liang Zhang; Ming-Liang Wing

    2006-12-01

    A class of nonlinear Schrödinger-type equations, including the Rangwala–Rao equation, the Gerdjikov–Ivanov equation, the Chen–Lee–Lin equation and the Ablowitz–Ramani–Segur equation are investigated, and the exact solutions are derived with the aid of the homogeneous balance principle, and a set of subsidiary higher order ordinary differential equations (sub-ODEs for short).

  10. Variable-coefficient nonisospectral Toda lattice hierarchy and its exact solutions

    Indian Academy of Sciences (India)

    Sheng Zhang; Di Wang

    2015-12-01

    In this paper, a hierarchy of nonisospectral equations with variable coefficients is derived from the compatibility condition of Toda spectral problem and its time evolution. In order to solve the derived Toda lattice hierarchy, the inverse scattering transformation is utilized. As a result, new and more general exact solutions are obtained. It is shown that the inverse scattering transformation can be generalized to solve some other nonisospectral lattice hierarchies with variable coefficients.

  11. Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain

    Energy Technology Data Exchange (ETDEWEB)

    Clark, S R; Jaksch, D [Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); Prior, J [Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU (United Kingdom); Hartmann, M J [Technische Universitaet Muenchen, Physik Department I, James Franck Strasse, 85748 Garching (Germany); Plenio, M B [Institute for Mathematical Sciences, Imperial College London, SW7 2PG (United Kingdom)], E-mail: s.clark@physics.ox.ac.uk

    2010-02-15

    In recent work, Hartmann et al (2009 Phys. Rev. Lett. 102 057202) demonstrated that the classical simulation of the dynamics of open 1D quantum systems with matrix product algorithms can often be dramatically improved by performing time evolution in the Heisenberg picture. For a closed system this was exemplified by an exact matrix product operator (MPO) solution of the time-evolved creation operator of a quadratic fermi chain with a matrix dimension of just two. In this work, we show that this exact solution can be significantly generalized to include the case of an open quadratic fermi chain subjected to master equation evolution with Lindblad operators that are linear in the fermionic operators. Remarkably even in this open system the time evolution of operators continues to be described by MPOs with the same fixed dimension as that required by the solution of a coherent quadratic fermi chain for all times. Through the use of matrix product algorithms the dynamical behaviour of operators in this non-equilibrium open quantum system can be computed with a cost that is linear in the system size. We present some simple numerical examples that highlight how useful this might be for the more detailed study of open system dynamics. Given that Heisenberg picture simulations have been demonstrated to offer significant accuracy improvements for other open systems that are not exactly solvable, our work also provides further insight into how and why this advantage arises.

  12. Some exact solutions to the Lighthill-Whitham-Richards-Payne traffic flow equations: II. Moderate congestion

    Science.gov (United States)

    Infeld, E.; Rowlands, G.; Skorupski, A. A.

    2014-10-01

    We find a further class of exact solutions to the Lighthill-Whitham- Richards-Payne (LWRP) traffic flow equations. As before, using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either obtain exact formulae for the dependence of the car density and velocity on x,t, or else, failing that, the same result in a parametric representation. The calculation always involves two possible factorizations of a consistency condition. Both must be considered. In physical terms, the lineup usually separates into two offshoots at different velocities. Each velocity soon becomes uniform. This outcome in many ways resembles not only that of Rowlands et al (2013 J. Phys. A: Math. Theor. 46 365202 (part I)) but also the two-soliton solution to the Korteweg-de Vries equation. This paper can be read independently of part I. This explains unavoidable repetitions. Possible uses of both papers in checking numerical codes are indicated. Since LWRP, numerous more elaborate models, including multiple lanes, traffic jams, tollgates, etc, abound in the literature. However, we present an exact solution. These are few and far between, other than found by inverse scattering. The literature for various models, including ours, is given. The methods used here and in part I may be useful in solving other problems, such as shallow water flow.

  13. A class of exact solutions for the incompressible viscous magnetohydrodynamic flow over a porous rotating disk

    Institute of Scientific and Technical Information of China (English)

    M. Turkyilmazoglu

    2012-01-01

    The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a constant angular speed.The three-dimensional hydromagnetic equations of motion are treated analytically to obtained exact solutions with the inclusion of suction and injection.The well-known thinning/thickening flow field effect of the suction/injection is better understood from the constructed closed form velocity equations.Making use of this solution,analytical formulas for the angular velocity components as well as for the permeable wall shear stresses are derived.Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation.The temperature field is shown to accord with the dissipation and the Joule heating.As a result,exact formulas are obtained for the temperature field which take different forms corresponding to the condition of suction or injection imposed on the wall.

  14. Exact vacuum solution of a (1+2)-dimensional Poincare gauge theory BTZ solution with torsion

    CERN Document Server

    Garcia, A A; Heinicke, C; Macías, A; Garcia, Alberto A.; Hehl, Friedrich W.; Heinicke, Christian; Macias, Alfredo

    2003-01-01

    In (1+2)-dimensional Poincar\\'e gauge gravity, we start from a Lagrangian depending on torsion and curvature which includes additionally {\\em translational} and {\\em Lorentzian} Chern-Simons terms. Limiting ourselves to to a specific subcase, the Mielke-Baekler (MB) model, we derive the corresponding field equations (of Einstein-Cartan-Chern-Simons type) and find the general vacuum solution. We determine the properties of this solution, in particular its mass and its angular momentum. For vanishing torsion, we recover the BTZ-solution. We also derive the general conformally flat vacuum solution with torsion. In this framework, we discuss {\\em Cartan's} (3-dimensional) {\\em spiral staircase} and find that it is not only a special case of our new vacuum solution, but can alternatively be understood as a solution of the 3-dimensional Einstein-Cartan theory with matter of constant pressure and constant torque. {\\em file 3dexact15.tex}

  15. Methods for constructing exact solutions of partial differential equations mathematical and analytical techniques with applications to engineering

    CERN Document Server

    Meleshko, Sergey V

    2005-01-01

    Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

  16. Exact solutions for the coupled Klein-Gordon-Schr(o)dinger equations using the extended F-expansion method

    Institute of Scientific and Technical Information of China (English)

    He Hong-Sheng; Chen Jiang; Yang Kong-Qing

    2005-01-01

    The extended F-expansion method or mapping method is used to construct exact solutions for the coupled Klein-Gordon Schr(o)dinger equations (K-G-S equations) by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.

  17. Exact solution of qubit decoherence models by a transfer matrix method

    CERN Document Server

    Nghiem, D; Joynt, Robert; Nghiem, Diu

    2005-01-01

    We present a new method for the solution of the behavior of an enesemble of qubits in a random time-dependent external field. The forward evolution in time is governed by a transfer matrix. The elements of this matrix determine the various decoherence times. The method provides an exact solution in cases where the noise is piecewise constant in time. We show that it applies, for example, to a realistic model of decoherence of electron spins in semiconductors. Results are obtained for the non-perturbative regimes of the models, and we see a transition from weak relaxation to overdamped behavior as a function of noise anisotropy.

  18. Exact two-body solutions and quantum defect theory of two-dimensional dipolar quantum gas

    Science.gov (United States)

    Jie, Jianwen; Qi, Ran

    2016-10-01

    In this paper, we provide the two-body exact solutions of the two-dimensional (2D) Schrödinger equation with isotropic +/- 1/{r}3 interactions. An analytic quantum defect theory is constructed based on these solutions and it is applied to investigate the scattering properties as well as two-body bound states of an ultracold polar molecules confined in a quasi-2D geometry. Interestingly, we find that for the attractive case, the scattering resonance happens simultaneously in all partial waves, which has not been observed in other systems. The effect of this feature on the scattering phase shift across such resonances is also illustrated.

  19. Q-Conditional Symmetries and Exact Solutions of Nonlinear Reaction–Diffusion Systems

    Directory of Open Access Journals (Sweden)

    Oleksii Pliukhin

    2015-10-01

    Full Text Available A wide range of reaction–diffusion systems with constant diffusivities that are invariant under Q-conditional operators is found. Using the symmetries obtained, the reductions of the corresponding systems to the systems of ODEs are conducted in order to find exact solutions. In particular, the solutions of some reaction–diffusion systems of the Lotka–Volterra type in an explicit form and satisfying Dirichlet boundary conditions are obtained. An biological interpretation is presented in order to show that two different types of interaction between biological species can be described.

  20. Construction of exact solutions to the modified forms of DP and CH equations by analytical methods

    Directory of Open Access Journals (Sweden)

    Jalil Manafian Heris

    2015-11-01

    Full Text Available In this work, we establish the exact solutions to the modified forms of Degasperis–Procesi (DP and Camassa–Holm (CH equations. The generalized (G’/G-expansion and generalized tanh-coth methods were used to construct solitary wave solutions of nonlinear evolution equations. The generalized (G’/G-expansion method presents a wider applicability for handling nonlinear wave equations. It is shown that the (G’/G-expansion method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.  

  1. Some exact anisotropic solutions via Noether symmetry in f(R) gravity

    Energy Technology Data Exchange (ETDEWEB)

    Sharif, M., E-mail: msharif.math@pu.edu.pk; Nawazish, I., E-mail: iqranawazish07@gmail.com [University of the Punjab, Department of Mathematics (Pakistan)

    2015-01-15

    We attempt to find exact solutions of the Bianchi I model in f(R) gravity using the Noether symmetry approach. For this purpose, we take a perfect fluid and formulate conserved quantities for the power-law f(R) model. We discuss some cosmological parameters for the resulting solution which are responsible for expanding behavior of the universe. We also explore Noether gauge symmetry and the corresponding conserved quantity. It is concluded that symmetry generators as well as conserved quantities exist in all cases and the behavior of cosmological parameters shows consistency with recent observational data.

  2. Exact Solutions for an MHD Generalized Burgers fluid: Stokes' Second Problem

    CERN Document Server

    Khan, Masood; Anjum, Asia

    2013-01-01

    This paper offers the exact analytical solutions for the magnetohydrodynamic (MHD) flow of an incompressible generalized Burgers fluid corresponding to the second problem of Stokes in the presence of the transverse magnetic field. Modified Darcy's law has been taken into account. The expression for the velocity field and associated tangential stress, presented as a sum of the steady-state and transient solutions, are obtained by means of the integral transforms. Moreover, several figures are plotted to investigate the effects of various emerging parameters on the velocity field. The obtained results show that the magnitude of the velocity and boundary layer thickness significantly reduce in the presence of magnetic field.

  3. Exact solutions of three dimensional black holes: Einstein gravity vs F(R) gravity

    CERN Document Server

    Hendi, S H; Saffari, R

    2014-01-01

    In this paper, we consider Einstein gravity in the presence of a class of nonlinear electrodynamics, called power Maxwell invariant (PMI). We take into account $(2+1)$-dimensional spacetime in Einstein-PMI gravity and obtain its black hole solutions. Then, we regard pure $F(R)$ gravity as well as $F(R)$-conformally invariant Maxwell theory to obtain exact solutions of the field equations with black hole interpretation. Finally, we investigate the conserved and thermodynamic quantities and discuss about the first law of thermodynamics for the mentioned gravitational models.

  4. Burgers方程的精确解%Exact solutions of Burgers equations

    Institute of Scientific and Technical Information of China (English)

    李伟

    2013-01-01

    借助于Cole-Hope变换,积分变换法和拟解的方法,获得Burgers方程,(2+1)维Burgers方程,(2+1)维高阶Burgers方程的新的精确解.这种方法可以解决一系列的偏微分方程.%With the help of cole - Hope transform, integral method and quasi solution method, some new exact solutions of Burgers equation, (2 +1) dimensional Burger equation and ( 2 + 1) dimensional higher - order Burgers equation were presented. This method could solve a series of partial differential equations.

  5. Exact solutions for the family of third order Korteweg de-Vries equations

    OpenAIRE

    2016-01-01

    In this work we apply an extended hyperbolic function method to solve the nonlinear family of third order Korteweg de-Vries (KdV) equations, namely, the KdV equation, the modified KdV (mKdV) equation, the potential KdV (pKdV) equation, the generalized KdV (gKdV) equation and gKdV with two power nonlinearities equation. New exact travelling wave solutions are obtained for the KdV, mKdV and pKdV equations. The solutions are expressed in terms of hyperbolic functions, trigonometric functions and...

  6. Some exact solutions for a unidimensional fokker-planck equation by using lie symmetries

    Directory of Open Access Journals (Sweden)

    Hugo Hernán Ortíz-Álvarez

    2015-01-01

    Full Text Available The Fokker Planck equation appears in the study of diffusion phenomena, stochastics processes and quantum and classical mechanics. A particular case fromthis equation, ut − uxx − xux − u=0, is examined by the Lie group method approach. From the invariant condition it was possible to obtain the infinitesimal generators or vectors associated to this equation, identifying the corresponding symmetry groups. Exact solution were found for each one of this generators and new solution were constructed by using symmetry properties.

  7. Stability of exact solutions describing two-layer flows with evaporation at the interface

    Science.gov (United States)

    Bekezhanova, V. B.; Goncharova, O. N.

    2016-12-01

    A new exact solution of the equations of free convection has been constructed in the framework of the Oberbeck-Boussinesq approximation of the Navier-Stokes equations. The solution describes the joint flow of an evaporating viscous heat-conducting liquid and gas-vapor mixture in a horizontal channel. In the gas phase the Dufour and Soret effects are taken into account. The consideration of the exact solution allows one to describe different classes of flows depending on the values of the problem parameters and boundary conditions for the vapor concentration. A classification of solutions and results of the solution analysis are presented. The effects of the external disturbing influences (of the liquid flow rates and longitudinal gradients of temperature on the channel walls) on the stability characteristics have been numerically studied for the system HFE7100-nitrogen in the common case, when the longitudinal temperature gradients on the boundaries of the channel are not equal. In the system both monotonic and oscillatory modes can be formed, which damp or grow depending on the values of the initial perturbations, flow rates and temperature gradients. Hydrodynamic perturbations are most dangerous under large gas flow rates. The increasing oscillatory perturbations are developed due to the thermocapillary effect under large longitudinal gradients of temperature. The typical forms of the disturbances are shown.

  8. New exact solutions for the discrete fourth Painlevé equation

    CERN Document Server

    Bassom, A P

    1994-01-01

    In this paper we derive a number of exact solutions of the discrete equation x_{n+1}x_{n-1}+x_n(x_{n+1}+x_{n-1})= {-2z_nx_n^3+(\\eta-3\\delta^{-2}-z_n^2)x_n^2+\\mu^2\\over (x_n+z_n+\\gamma)(x_n+z_n-\\gamma)},\\eqno(1) where z_n=n\\delta and \\eta, \\delta, \\mu and \\gamma are constants. In an appropriate limit (1) reduces to the fourth \\p\\ (PIV) equation {\\d^2w\\over\\d z^2} = {1\\over2w}\\left({\\d w\\over\\d z}\\right)^2+\\tfr32w^3 + 4zw^2 + 2(z^2-\\alpha)w +{\\beta\\over w},\\eqno(2) where \\alpha and \\beta are constants and (1) is commonly referred to as the discretised fourth Painlev\\'e equation. A suitable factorisation of (1) facilitates the identification of a number of solutions which take the form of ratios of two polynomials in the variable z_n. Limits of these solutions yield rational solutions of PIV (2). It is also known that there exist exact solutions of PIV (2) that are expressible in terms of the complementary error function and in this article we show that a discrete analogue of this function can be obtained by ana...

  9. New Exact Solutions for an Oldroyd-B Fluid in a Porous Medium

    Directory of Open Access Journals (Sweden)

    I. Khan

    2011-01-01

    Full Text Available New exact solutions for unsteady magnetohydrodynamic (MHD flows of an Oldroyd-B fluid have been derived. The Oldroyd-B fluid saturates the porous space. Two different flow cases have been considered. The analytical expressions for velocity and shear stress fields have been obtained by using Laplace transform technique. The corresponding solutions for hydrodynamic Oldroyd-B fluid in a nonporous space appeared as the limiting cases of the obtained solutions. Similar solutions for MHD Newtonian fluid passing through a porous space are also recovered. Graphs are sketched for the pertinent parameters. It is found that the MHD and porosity parameters have strong influence on velocity and shear stress fields.

  10. EXACT SOLUTIONS FOR NONLINEAR TRANSIENT FLOW MODEL INCLUDING A QUADRATIC GRADIENT TERM

    Institute of Scientific and Technical Information of China (English)

    曹绪龙; 同登科; 王瑞和

    2004-01-01

    The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented. The exact solution was given in real space for flow equation including quadratic gradiet term for both constant-rate and constant pressure production cases in an infinite system by using generalized Weber transform. Analytical solutions for flow equation including quadratic gradient term were also obtained by using the Hankel transform for a finite circular reservoir case. Both closed and constant pressure outer boundary conditions are considered. Moreover, both constant rate and constant pressure inner boundary conditions are considered. The difference between the nonlinear pressure solution and linear pressure solution is analyzed. The difference may be reached about 8% in the long time. The effect of the quadratic gradient term in the large time well test is considered.

  11. An Automated Algebraic Method for Finding a Series of Exact Travelling Wave Solutions of Nonlinear Evolution Equations

    Institute of Scientific and Technical Information of China (English)

    柳银萍; 李志斌

    2003-01-01

    Based on a 0 of elliptic equation, a new algebraic method to construct a series of exact solutions for nonlinear evolution equations is proposed, meanwhile, its complete implementation TRWS in Maple is presented. The TRWS can output a series of travelling wave solutions entirely automatically, which include polynomial solutions, exponential function solutions, triangular function solutions, hyperbolic function solutions, rational function solutions, Jacobi elliptic function solutions, and Weierstrass elliptic function solutions. The effectiveness of the package is illustrated by applying it to a variety of equations. Not only are previously known solutions recovered but also new solutions and more general form of solutions are obtained.

  12. Exact traveling wave solutions to the Klein-Gordon equation using the novel (G‧/G)-expansion method

    Science.gov (United States)

    Hafez, M. G.; Alam, Md. Nur; Akbar, M. Ali

    The novel (G‧/G)-expansion method is one of the powerful methods that appeared in recent times for establishing exact traveling wave solutions of nonlinear partial differential equations. Exact traveling wave solutions in terms of hyperbolic, trigonometric and rational functions to the cubic nonlinear Klein-Gordon equation via this method are obtained in this article. The efficiency of this method for finding exact solutions and traveling wave solutions has been demonstrated. It is shown that the novel (G‧/G)-expansion method is a simple and valuable mathematical tool for solving nonlinear evolution equations (NLEEs) in applied mathematics, mathematical physics and engineering.

  13. Exact traveling wave solutions to the Klein–Gordon equation using the novel (G′/G-expansion method

    Directory of Open Access Journals (Sweden)

    M.G. Hafez

    2014-01-01

    Full Text Available The novel (G′/G-expansion method is one of the powerful methods that appeared in recent times for establishing exact traveling wave solutions of nonlinear partial differential equations. Exact traveling wave solutions in terms of hyperbolic, trigonometric and rational functions to the cubic nonlinear Klein–Gordon equation via this method are obtained in this article. The efficiency of this method for finding exact solutions and traveling wave solutions has been demonstrated. It is shown that the novel (G′/G-expansion method is a simple and valuable mathematical tool for solving nonlinear evolution equations (NLEEs in applied mathematics, mathematical physics and engineering.

  14. AUTO-BÄCKLUND Transformation and New Exact Solutions of the (2 + 1)-DIMENSIONAL Nizhnik-Novikov Equation

    Science.gov (United States)

    Wang, Dengshan; Zhang, Hong-Qing

    In this paper, making use of the truncated Laurent series expansion method and symbolic computation we get the auto-Bäcklund transformation of the (2 + 1)-dimensional Nizhnik-Novikov-Veselov equation. As a result, single soliton solution, single soliton-like solution, multi-soliton solution, multi-soliton-like solution, the rational solution and other exact solutions of the (2 + 1)-dimensional Nizhnik-Novikov-Veselov equation are found. These solutions may be useful to explain some physical phenomena.

  15. Exact solutions for the populations of the n-level ion

    CERN Document Server

    Taylor, Michael

    2007-01-01

    We present a matrix solution to the full equations of statistical equilibrium that give the energy level populations of collisionally-excited ions in photoionised gaseous nebulae. The rationale for such a calculation is to maintain a parity between improvements in the quantum-mechanically evaluated values for collision strengths and transition probabilities from the Iron and Opacity Projects on the one hand, and 3D photoionisation codes such as MOCASSIN and astrophysical software for producing nebular diagnostics such as the Nebular package for IRAF, on the other. We have taken advantage of the fact that mathematics programs such as MATLAB and Mathematica have proven to be very adept at symbolic manipulation providing a route to exact solutions for the n-level ion. In particular, we have avoided the substitution of estimated values. We provide the matrix solution for the 5-level ion as an example and show how the equations faithfully reduce to the exact solution for the 3-level ion. Through the forbidden line...

  16. Exact solution of planar and nonplanar weak shock wave problem in gasdynamics

    Energy Technology Data Exchange (ETDEWEB)

    Singh, L.P. [Department of Applied Mathematics, Institute of Technology, Bananas Hindu University, Varanasi 221 005 (India); Ram, S.D., E-mail: sram.rs.apm@itbhu.ac.in [Department of Applied Mathematics, Institute of Technology, Bananas Hindu University, Varanasi 221 005 (India); Singh, D.B. [Department of Applied Mathematics, Institute of Technology, Bananas Hindu University, Varanasi 221 005 (India)

    2011-11-15

    Highlights: > An exact solution is derived for a problem of weak shock wave in adiabatic gas dynamics. > The density ahead of the shock is taken as a power of the position from the origin of the shock wave. > For a planar and non-planar motion, the total energy carried by the wave varies with respect to time. > The solution obtained for the planer, and cylindrically symmetric flow is new one. > The results obtained are also presented graphically for different Mach numbers. - Abstract: In the present paper, an analytical approach is used to determine a new exact solution of the problem of one dimensional unsteady adiabatic flow of planer and non-planer weak shock waves in an inviscid ideal fluid. Here it is assumed that the density ahead of the shock front varies according to the power law of the distance from the source of disturbance. The solution of the problem is presented in the form of a power in the distance and the time.

  17. Discretization error estimation and exact solution generation using the method of nearby problems.

    Energy Technology Data Exchange (ETDEWEB)

    Sinclair, Andrew J. (Auburn University Auburn, AL); Raju, Anil (Auburn University Auburn, AL); Kurzen, Matthew J. (Virginia Tech Blacksburg, VA); Roy, Christopher John (Virginia Tech Blacksburg, VA); Phillips, Tyrone S. (Virginia Tech Blacksburg, VA)

    2011-10-01

    The Method of Nearby Problems (MNP), a form of defect correction, is examined as a method for generating exact solutions to partial differential equations and as a discretization error estimator. For generating exact solutions, four-dimensional spline fitting procedures were developed and implemented into a MATLAB code for generating spline fits on structured domains with arbitrary levels of continuity between spline zones. For discretization error estimation, MNP/defect correction only requires a single additional numerical solution on the same grid (as compared to Richardson extrapolation which requires additional numerical solutions on systematically-refined grids). When used for error estimation, it was found that continuity between spline zones was not required. A number of cases were examined including 1D and 2D Burgers equation, the 2D compressible Euler equations, and the 2D incompressible Navier-Stokes equations. The discretization error estimation results compared favorably to Richardson extrapolation and had the advantage of only requiring a single grid to be generated.

  18. Hamiltonian formulation and exact solutions of the Bianchi type I space-time in conformal gravity

    CERN Document Server

    Demaret, J; Scheen, C

    1999-01-01

    We develop a Hamiltonian formulation of the Bianchi type I space-time in conformal gravity, i.e. the theory described by a Lagrangian that is defined by the contracted quadratic product of the Weyl tensor, in a four-dimensional space-time. We derive the explicit forms of the super-Hamiltonian and of the constraint expressing the conformal invariance of the theory and we write down the system of canonical equations. To seek out exact solutions of this system we add extra constraints on the canonical variables and we go through a global involution algorithm which eventually leads to the closure of the constraint algebra. The Painleve approach provides us with a proof of non-integrability, as a consequence of the presence of movable logarithms in the general solution of the problem. We extract all possible particular solutions that may be written in closed analytical form. This enables us to demonstrate that the global involution algorithm has brought forth the complete list of exact solutions that may be writte...

  19. The Bäcklund Transformations and Abundant Exact Explicit Solutions for a General Nonintegrable Nonlinear Convection-Diffusion Equation

    Directory of Open Access Journals (Sweden)

    Yong Huang

    2012-01-01

    Full Text Available The Bäcklund transformations and abundant exact explicit solutions for a class of nonlinear wave equation are obtained by the extended homogeneous balance method. These solutions include the solitary wave solution of rational function, the solitary wave solutions, singular solutions, and the periodic wave solutions of triangle function type. In addition to rederiving some known solutions, some entirely new exact solutions are also established. Explicit and exact particular solutions of many well-known nonlinear evolution equations which are of important physical significance, such as Kolmogorov-Petrovskii-Piskunov equation, FitzHugh-Nagumo equation, Burgers-Huxley equation, Chaffee-Infante reaction diffusion equation, Newell-Whitehead equation, Fisher equation, Fisher-Burgers equation, and an isothermal autocatalytic system, are obtained as special cases.

  20. Exact and heuristic solutions to the Double TSP with Multiple Stacks

    DEFF Research Database (Denmark)

    Petersen, Hanne Løhmann; Archetti, Claudia; Madsen, Oli B.G.;

    The double travelling salesman problem with multiple stacks (DTSPMS) is a pickup and delivery problem where pickups and deliveries are separated, such that all pickup operations are performed before the first delivery takes place. All operations are carried out by one vehicle and no reloading...... is allowed. The vehicle provides several separated (horizontal) stacks/rows for the transportation of the orders, such that each stack is accessed using a LIFO principle, independently of the other stacks. In a real-life setting the dimensions of the problem is 33 orders each consisting of one euro......-pallet, which can be loaded in 3 stacks in a standard 40 foot container. Different exact and heuristic solution approaches to the DTSPMS have been implemented and tested. The exact approaches are based on different mathematical formulations of the problem which are solved using branch-and-cut. One formulation...

  1. EDISON-WMW: Exact Dynamic Programing Solution of the Wilcoxon–Mann–Whitney Test

    Directory of Open Access Journals (Sweden)

    Alexander Marx

    2016-02-01

    Full Text Available In many research disciplines, hypothesis tests are applied to evaluate whether findings are statistically significant or could be explained by chance. The Wilcoxon–Mann–Whitney (WMW test is among the most popular hypothesis tests in medicine and life science to analyze if two groups of samples are equally distributed. This nonparametric statistical homogeneity test is commonly applied in molecular diagnosis. Generally, the solution of the WMW test takes a high combinatorial effort for large sample cohorts containing a significant number of ties. Hence, P value is frequently approximated by a normal distribution. We developed EDISON-WMW, a new approach to calculate the exact permutation of the two-tailed unpaired WMW test without any corrections required and allowing for ties. The method relies on dynamic programing to solve the combinatorial problem of the WMW test efficiently. Beyond a straightforward implementation of the algorithm, we presented different optimization strategies and developed a parallel solution. Using our program, the exact P value for large cohorts containing more than 1000 samples with ties can be calculated within minutes. We demonstrate the performance of this novel approach on randomly-generated data, benchmark it against 13 other commonly-applied approaches and moreover evaluate molecular biomarkers for lung carcinoma and chronic obstructive pulmonary disease (COPD. We found that approximated P values were generally higher than the exact solution provided by EDISON-WMW. Importantly, the algorithm can also be applied to high-throughput omics datasets, where hundreds or thousands of features are included. To provide easy access to the multi-threaded version of EDISON-WMW, a web-based solution of our algorithm is freely available at http://www.ccb.uni-saarland.de/software/wtest/.

  2. EDISON-WMW:Exact Dynamic Programing Solution of the Wilcoxon-Mann-Whitney Test

    Institute of Scientific and Technical Information of China (English)

    Alexander Marx; Christina Backes; Eckart Meese; Hans-Peter Lenhof; Andreas Keller

    2016-01-01

    In many research disciplines, hypothesis tests are applied to evaluate whether findings are statistically significant or could be explained by chance. The Wilcoxon–Mann–Whitney (WMW) test is among the most popular hypothesis tests in medicine and life science to analyze if two groups of samples are equally distributed. This nonparametric statistical homogeneity test is commonly applied in molecular diagnosis. Generally, the solution of the WMW test takes a high combinatorial effort for large sample cohorts containing a significant number of ties. Hence, P value is frequently approximated by a normal distribution. We developed EDISON-WMW, a new approach to calcu-late the exact permutation of the two-tailed unpaired WMW test without any corrections required and allowing for ties. The method relies on dynamic programing to solve the combinatorial problem of the WMW test efficiently. Beyond a straightforward implementation of the algorithm, we pre-sented different optimization strategies and developed a parallel solution. Using our program, the exact P value for large cohorts containing more than 1000 samples with ties can be calculated within minutes. We demonstrate the performance of this novel approach on randomly-generated data, benchmark it against 13 other commonly-applied approaches and moreover evaluate molec-ular biomarkers for lung carcinoma and chronic obstructive pulmonary disease (COPD). We found that approximated P values were generally higher than the exact solution provided by EDISONWMW. Importantly, the algorithm can also be applied to high-throughput omics datasets, where hundreds or thousands of features are included. To provide easy access to the multi-threaded version of EDISON-WMW, a web-based solution of our algorithm is freely available at http:// www.ccb.uni-saarland.de/software/wtest/.

  3. EDISON-WMW: Exact Dynamic Programing Solution of the Wilcoxon-Mann-Whitney Test.

    Science.gov (United States)

    Marx, Alexander; Backes, Christina; Meese, Eckart; Lenhof, Hans-Peter; Keller, Andreas

    2016-02-01

    In many research disciplines, hypothesis tests are applied to evaluate whether findings are statistically significant or could be explained by chance. The Wilcoxon-Mann-Whitney (WMW) test is among the most popular hypothesis tests in medicine and life science to analyze if two groups of samples are equally distributed. This nonparametric statistical homogeneity test is commonly applied in molecular diagnosis. Generally, the solution of the WMW test takes a high combinatorial effort for large sample cohorts containing a significant number of ties. Hence, P value is frequently approximated by a normal distribution. We developed EDISON-WMW, a new approach to calculate the exact permutation of the two-tailed unpaired WMW test without any corrections required and allowing for ties. The method relies on dynamic programing to solve the combinatorial problem of the WMW test efficiently. Beyond a straightforward implementation of the algorithm, we presented different optimization strategies and developed a parallel solution. Using our program, the exact P value for large cohorts containing more than 1000 samples with ties can be calculated within minutes. We demonstrate the performance of this novel approach on randomly-generated data, benchmark it against 13 other commonly-applied approaches and moreover evaluate molecular biomarkers for lung carcinoma and chronic obstructive pulmonary disease (COPD). We found that approximated P values were generally higher than the exact solution provided by EDISON-WMW. Importantly, the algorithm can also be applied to high-throughput omics datasets, where hundreds or thousands of features are included. To provide easy access to the multi-threaded version of EDISON-WMW, a web-based solution of our algorithm is freely available at http://www.ccb.uni-saarland.de/software/wtest/.

  4. Exact traveling wave solutions and L1 stability for the shallow water wave model of moderate amplitude

    Science.gov (United States)

    Wang, Ying; Guo, Yunxi

    2017-09-01

    In this paper, we developed, for the first time, the exact expressions of several periodic travelling wave solutions and a solitary wave solution for a shallow water wave model of moderate amplitude. Then, we present the existence theorem of the global weak solutions. Finally, we prove the stability of solution in L1(R) space for the Cauchy problem of the equation.

  5. Some Exact Solutions of Variable Coefficient Cubic-Quintic Nonlinear Schr(o)dinger Equation with an External Potential

    Institute of Scientific and Technical Information of China (English)

    ZHU Jia-Min; LIU Yu-Lu

    2009-01-01

    By constructing appropriate transformations and an extended elliptic sub-equation approach, we find some exact solutions of variable coefficient cubic-qulntic nonlinear Schrodinger equation with an external potential, which include bell and kink profile solitary wave solutions, singular solutions, triangular periodic wave solutions and so on.

  6. Exact traveling wave solutions and L1 stability for the shallow water wave model of moderate amplitude

    Science.gov (United States)

    Wang, Ying; Guo, Yunxi

    2016-07-01

    In this paper, we developed, for the first time, the exact expressions of several periodic travelling wave solutions and a solitary wave solution for a shallow water wave model of moderate amplitude. Then, we present the existence theorem of the global weak solutions. Finally, we prove the stability of solution in L1(R) space for the Cauchy problem of the equation.

  7. Exact analytical solutions for the Poiseuille and Couette-Poiseuille flow of third grade fluid between parallel plates

    Science.gov (United States)

    Danish, Mohammad; Kumar, Shashi; Kumar, Surendra

    2012-03-01

    Exact analytical solutions for the velocity profiles and flow rates have been obtained in explicit forms for the Poiseuille and Couette-Poiseuille flow of a third grade fluid between two parallel plates. These exact solutions match well with their numerical counter parts and are better than the recently developed approximate analytical solutions. Besides, effects of various parameters on the velocity profile and flow rate have been studied.

  8. Exact behavior of singular solutions to Protter's problem with lower order terms

    Directory of Open Access Journals (Sweden)

    Aleksey Nikolov

    2012-08-01

    Full Text Available For the (2+1-D wave equation Protter formulated (1952 some boundary value problems which are three-dimensional analogues of the Darboux problems on the plane. Protter studied these problems in a 3-D domain, bounded by two characteristic cones and by a planar region. Now it is well known that, for an infinite number of smooth functions in the right-hand side, these problems do not have classical solutions, because of the strong power-type singularity which appears in the generalized solution. In the present paper we consider the wave equation involving lower order terms and obtain new a priori estimates describing the exact behavior of singular solutions of the third boundary value problem. According to the new estimates their singularity is of the same order as in case of the wave equation without lower order terms.

  9. Exact solution of Schroedinger equation in the case of reduction to Riccati type of ODE

    CERN Document Server

    Ershkov, Sergey V

    2011-01-01

    Here is presented a new type of exact solution of Schroedinger equation in the case of it's reduction to Riccati type of ordinary differential equations. Due to a very special character of Riccati's type equation, it's general solution is proved to have a proper gap of components of the particle wavefunction (which is known to be determining a proper quantum state of the particle). It means a possibility of sudden transformation or transmutation of quantum state of the particle (from one meaning of wavefunction to another), at definite moment of parametrical time. Besides, in the case of spherical symmetry of particle potential V in position space, as well as spherical symmetry of quantum system E total energy, such a solution is proved to be a multiplying of Bessel function (for radial component) & Legendre spherical function (for angle component), in spherical coordinate system.

  10. Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.

    Science.gov (United States)

    Islam, S M Rayhanul; Khan, Kamruzzaman; Akbar, M Ali

    2015-01-01

    In this paper, we implement the exp(-Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We obtained four types of explicit function solutions, namely hyperbolic, trigonometric, exponential and rational function solutions of the variables in the considered equations. It has shown that the applied method is quite efficient and is practically well suited for the aforementioned problems and so for the other NLEEs those arise in mathematical physics and engineering fields. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fq.

  11. Exact travelling solutions for some nonlinear physical models by (′/)-expansion method

    Indian Academy of Sciences (India)

    B Salim Bahrami; H Abdollahzadeh; I M Berijani; D D Ganji; M Abdollahzadeh

    2011-08-01

    In this paper, we establish exact solutions for some special nonlinear partial differential equations. The (′/)-expansion method is used to construct travelling wave solutions of the twodimensional sine-Gordon equation, Dodd–Bullough–Mikhailov and Schrödinger–KdV equations, which appear in many fields such as, solid-state physics, nonlinear optics, fluid dynamics, fluid flow, quantum field theory, electromagnetic waves and so on. In this method we take the advantage of general solutions of second-order linear ordinary differential equation (LODE) to solve many nonlinear evolution equations effectively. The (′/)-expansion method is direct, concise and elementary and can be used with a wider applicability for handling many nonlinear wave equations.

  12. Exact vacuum solutions of 4-dimensional metric-affine gauge theories of gravitation

    Energy Technology Data Exchange (ETDEWEB)

    Tresguerres, R. (Koeln Univ. (Germany). Inst. fuer Theoretische Physik)

    1995-01-01

    We present two exact spherically symmetric vacuum solutions of gauge theories of gravity on a space-time with non metric-compatible connection. One of them is defined on a Weyl-Cartan spacetime and the other on a general metric-affine space. We consider Lagrangians which include terms quadratic in the irreducible parts of the curvature, the torsion, and the nonmetricity. The metric part of both solutions is of the Reissner-Nordstroem type and includes a contribution of an effective dilatation charge. A nontrivial Weyl 1-form is also common to both solutions. It resembles a Coulomb potential originating from the dilatation charge. The torsion is closely related to the nonmetricity. (orig.)

  13. New type of exact solutions of nonlinear evolution equations via the new Sine-Poisson equation expansion method

    Energy Technology Data Exchange (ETDEWEB)

    Yao Yuqin [College of Sciences, Shanghai University, Shanghai 200436 (China)] e-mail: yyqinw@126.com

    2005-11-01

    In this paper, based on the well-known Sine-Poisson equation, a new Sine-Poisson equation expansion method with constant coefficients or variable coefficients is presented, which can be used to construct more new exact solutions of nonlinear evolution equations in mathematical physics. The KdV-mKdV equation and the typical breaking soliton equation are chosen to illustrate our method such that many types of new exact solutions are obtained, which include exponential solutions, kink-shaped solutions, singular solutions and soliton-like solutions.

  14. Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis

    Directory of Open Access Journals (Sweden)

    Roman Cherniha

    2016-06-01

    Full Text Available The nonlinear mathematical model for solute and fluid transport induced by the osmotic pressure of glucose and albumin with the dependence of several parameters on the hydrostatic pressure is described. In particular, the fractional space available for macromolecules (albumin was used as a typical example and fractional fluid void volume were assumed to be different functions of hydrostatic pressure. In order to find non-uniform steady-state solutions analytically, some mathematical restrictions on the model parameters were applied. Exact formulae (involving hypergeometric functions for the density of fluid flux from blood to tissue and the fluid flux across tissues were constructed. In order to justify the applicability of the analytical results obtained, a wide range of numerical simulations were performed. It was found that the analytical formulae can describe with good approximation the fluid and solute transport (especially the rate of ultrafiltration for a wide range of values of the model parameters.

  15. Exact solution for the vibrations of cylindrical nanoshells considering surface energy effect

    Directory of Open Access Journals (Sweden)

    Hessam Rouhi

    2015-12-01

    Full Text Available It has been revealed that the surface stress effect plays an important role in the mechanical behavior ofstructures (such as bending, buckling and vibration when their dimensions are on the order ofnanometer. In addition, recent advances in nanotechnology have proposed several applications fornanoscale shells in different fields. Hence, in the present article, within the framework of surfaceelasticity theory, the free vibration behavior of simply-supported cylindrical nanoshells with theconsideration of the aforementioned effect is studied using an exact solution method. To this end, first,the governing equations of motion and boundary conditions are obtained by an energy-basedapproach. The surface stress influence is incorporated into the formulation according to the Gurtin-Murdoch theory. The nanoshell is modeled according to the first-order shear deformation shell theory.After that, the free vibration problem is solved through an exact solution approach. To this end, thedimensionless form of governing equations is derived and then solved under the simply-supportedboundary conditions using a Navier-type solution method. Selected numerical results are presentedabout the effects of surface stress and surface material properties on the natural frequencies ofnanoshells with different radii and lengths. The results show that the surface energies significantlyaffect the vibrational behavior of nanoshells with small magnitudes of thickness. Also, it is indicatedthat the natural frequency of the nanoshell is dependent of the surface material properties.

  16. Exact, E = 0, classical and quantum solutions for general power-law oscillators

    Science.gov (United States)

    Nieto, Michael Martin; Daboul, Jamil

    1995-01-01

    For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.

  17. A (1 + 2-Dimensional Simplified Keller–Segel Model: Lie Symmetry and Exact Solutions. II

    Directory of Open Access Journals (Sweden)

    Roman Cherniha

    2017-01-01

    Full Text Available A simplified Keller–Segel model is studied by means of Lie symmetry based approaches. It is shown that a (1 + 2-dimensional Keller–Segel type system, together with the correctly-specified boundary and/or initial conditions, is invariant with respect to infinite-dimensional Lie algebras. A Lie symmetry classification of the Cauchy problem depending on the initial profile form is presented. The Lie symmetries obtained are used for reduction of the Cauchy problem to that of (1 + 1-dimensional. Exact solutions of some (1 + 1-dimensional problems are constructed. In particular, we have proved that the Cauchy problem for the (1 + 1-dimensional simplified Keller–Segel system can be linearized and solved in an explicit form. Moreover, additional biologically motivated restrictions were established in order to obtain a unique solution. The Lie symmetry classification of the (1 + 2-dimensional Neumann problem for the simplified Keller–Segel system is derived. Because Lie symmetry of boundary-value problems depends essentially on geometry of the domain, which the problem is formulated for, all realistic (from applicability point of view domains were examined. Reduction of the the Neumann problem on a strip is derived using the symmetries obtained. As a result, an exact solution of a nonlinear two-dimensional Neumann problem on a finite interval was found.

  18. Exact Analytical Solutions in Three-Body Problems and Model of Neutrino Generator

    Directory of Open Access Journals (Sweden)

    Takibayev N.Zh.

    2010-04-01

    Full Text Available Exact analytic solutions are obtained in three-body problem for the scattering of light particle on the subsystem of two fixed centers in the case when pair potentials have a separable form. Solutions show an appearance of new resonance states and dependence of resonance energy and width on distance between two fixed centers. The approach of exact analytical solutions is expanded to the cases when two-body scattering amplitudes have the Breit-Wigner’s form and employed for description of neutron resonance scattering on subsystem of two heavy nuclei fixed in nodes of crystalline lattice. It is shown that some resonance states have widths close to zero at the certain values of distance between two heavy scatterer centers, this gives the possibility of transitions between states. One of these transitions between three-body resonance states could be connected with process of electron capture by proton with formation of neutron and emission of neutrino. This exoenergic process leading to the cooling of star without nuclear reactions is discussed.

  19. On exact solution of topological CFT models based on Kazama-Suzuki cosets

    Science.gov (United States)

    Belavin, Alexander; Belavin, Vladimir

    2016-10-01

    We compute the flat coordinates on the Frobenius manifolds arising on the deformation space of Gepner \\widehat{{SU}}{(3)}k chiral rings. The explicit form of the flat coordinates is important for exact solutions of models of topological CFT and 2D Liouville gravity. We describe the case k = 3, which is of particular interest because apart from the relevant chiral fields it contains a marginal one. Whereas marginal perturbations are relevant in different contexts, their analysis requires additional care compared to the relevant perturbations.

  20. On exact solution of topological CFT models based on Kazama-Suzuki cosets

    CERN Document Server

    Belavin, Alexander

    2016-01-01

    We compute the flat coordinates on the Frobenius manifolds arising on the deformation space of Gepner $\\hat{SU}(3)_k$ chiral rings. The explicit form of the flat coordinates is important for exact solutions of models of topological CFT and 2d Liouville gravity. We describe the case k=3, which is of particular interest because apart from the relevant chiral fields it contains a marginal one. Whereas marginal perturbations are relevant in different contexts, their analysis requires additional care compared to the relevant perturbations.