Chaotic oscillations of the Klein-Gordon equation with distributed energy pumping and van der Pol boundary regulation and distributed time-varying coefficients

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Bo Sun

2014-09-01

Full Text Available Consider the Klein-Gordon equation with variable coefficients, a van der Pol cubic nonlinearity in one of the boundary conditions and a spatially distributed antidamping term, we use a variable-substitution technique together with the analogy with the 1-dimensional wave equation to prove that for the Klein-Gordon equation chaos occurs for a class of equations and boundary conditions when system parameters enter a certain regime. Chaotic and nonchaotic profiles of solutions are illustrated by computer graphics.

Klein-Gordon oscillators in noncommutative phase space

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Wang Jianhua

2008-01-01

We study the Klein-Gordon oscillators in non-commutative (NC) phase space. We find that the Klein-Gordon oscillators in NC space and NC phase-space have a similar behaviour to the dynamics of a particle in commutative space moving in a uniform magnetic field. By solving the Klein-Gordon equation in NC phase space, we obtain the energy levels of the Klein-Gordon oscillators, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly. (authors)

Scattering states of the Klein-Gordon equation with Coulomb-like scalar plus vector potentials in arbitrary dimension

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Chen Changyuan; Sun Dongsheng; Lu Falin

2004-01-01

Properties of scattering states of the Klein-Gordon equation with Coulomb-like scalar plus vector potentials are investigated in an arbitrary dimension. Exact results of normalized wave functions of scattering states in the 'k/2π scale' and formula of phase shifts are presented

Superstatistics of the Klein-Gordon equation in deformed formalism for modified Dirac delta distribution

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Sargolzaeipor, S.; Hassanabadi, H.; Chung, W. S.

2018-04-01

The Klein-Gordon equation is extended in the presence of an Aharonov-Bohm magnetic field for the Cornell potential and the corresponding wave functions as well as the spectra are obtained. After introducing the superstatistics in the statistical mechanics, we first derived the effective Boltzmann factor in the deformed formalism with modified Dirac delta distribution. We then use the concepts of the superstatistics to calculate the thermodynamics properties of the system. The well-known results are recovered by the vanishing of deformation parameter and some graphs are plotted for the clarity of our results.

On the stationary Einstein-Maxwell-Klein-Gordon equations

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Gegenberg, J.D.

1981-05-01

The stationary Einstein-Maxwell-Klein-Gordon (EMKG) equations for interacting gravitational, electromagnetic and meson fields are examined. The theory is cast into the formalism of principal fiber bundles with a connection, wherein its relationship to current trends in theoretical physics is made manifest. The EMKG equations are shown to admit a Higgs-like mechanism for giving mass to the gauge field. A theorem specifying sufficient conditions for the stationarity of the spacetime metric to imply stationarity of the other fields is proved. By imposing additional constraints and symmetries, the EMKG equations are considerably simplified. An attempt is made to apply a solution-generation technique, and this meets with only partial success. Finally, a stationary but non-static solution is found, and the geometric and physical properties are discussed

Perron-Frobenius operators and the Klein-Gordon equation

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Canto-Martin, Francisco; Hedenmalm, Haakan; Montes-Rodriguez, Alfonso

2012-01-01

For a smooth curve Γ and a set Λ in the plane R2, let AC(Γ; Λ) be the space of finite Borel measures in the plane supported on Γ, absolutely continuous with respect to the arc length and whose Fourier transform vanishes on Λ. Following [12], we say that (Γ, Λ) is a Heisenberg uniqueness pair if AC(Γ; Λ) = {0}. In the context of a hyperbola Γ, the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets Λ of a collection of solutions to the Klein-Gordon equation. In t...

Bound State Solutions of the Klein-Gordon Equation for the Mathews-Lakshmanan Oscillator

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Schulze-Halberg, Axel; Wang, Jie

2014-01-01

We study a boundary-value problem for the Klein-Gordon equation that is inspired by the well-known Mathews-Lakshmanan oscillator model. By establishing a link to the spheroidal equation, we show that our problem admits an infinite number of discrete energies, together with associated solutions that form an orthogonal set in a weighted L 2 -Hilbert space. (author)

Separable coordinates and particle creation I: the klein-Gordon equation

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Costa, Isaias

1987-01-01

A very simple derivation of the 10 orthogonal coordinate systems where the Klein-Gordon equation separates is presented. It is based on the conformal structure of the two dimensional Minkowski space. Horizons, proper time and acceleration of abserves that follow the time coordinate line, as well as other physical properties of the systems, are obtained. The relevance of these coordinates is discussed, specially in the context of quantum field theory in curved space. (author) [pt

Quadratic algebras and noncommutative integration of Klein-Gordon equations in non-steckel Riemann spaces

International Nuclear Information System (INIS)

Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.; Shirokov, I.V.

1995-01-01

The method of noncommutative integration of linear partial differential equations is used to solve the Klein-Gordon equations in Riemann space, in the case when the set of noncommutating symmetry operators of this equation for a quadratic algebra consists of one second-order operator and several first-order operators. Solutions that do not permit variable separation are presented

Non-existence of global solutions to generalized dissipative Klein-Gordon equations with positive energy

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Maxim Olegovich Korpusov

2012-07-01

Full Text Available In this article the initial-boundary-value problem for generalized dissipative high-order equation of Klein-Gordon type is considered. We continue our study of nonlinear hyperbolic equations and systems with arbitrary positive energy. The modified concavity method by Levine is used for proving blow-up of solutions.

Realization of a unique time evolution unitary operator in Klein Gordon theory

International Nuclear Information System (INIS)

Balasubramanian, T.S.; Bhatia, S.Kr.

1986-01-01

The scattering theory for the Klein Gordon equation, with time-dependent potential and in a non-static space-time, is considered. Using the Klein Gordon equation formulated in the Hilbert space L 2 (R 3 ) and the Einstein's relativistic equation in the space L 2 (R 3 ,dx) and establishing the equivalence of the vacuum states of their linearized forms in the Hilbert space L 2 (R 3 ) with the help of unique symmetric symplectic operator, the time evolution unitary operator U(t) has been fixed for the Klein Gordon eqution, incorporating either the positive or negative frequencies, in the infinite dimensional Hilbert space L 2 (R 3 ). (author)

The Klein-Gordon Operator on Möbius Strip Domains and the Klein Bottle in ℝn

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Kraußhar, Rolf Sören

2013-01-01

In this paper we present explicit formulas for the fundamental solution to the Klein-Gordon operator on some higher dimensional generalizations of the Möbius strip and the Klein bottle with values in distinct pinor bundles. The fundamental solution is described in terms of generalizations of the Weierstrass ℘ -function that are adapted to the context of these geometries. The explicit formulas for the kernel then allow us to express all solutions to the homogeneous and inhomogeneous Klein-Gordon problem with given boundary data in the context of these manifolds. In the case of the Klein bottle we are able to describe all null solutions of the Klein-Gordon equation in terms of finite linear combinations of the fundamental solution and its partial derivatives

Some Exact Solutions for a Klein Gordon Equation Algunas soluciones exactas para una ecuación de Klein Gordon

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H H Ortíz Álvarez

2012-12-01

Full Text Available In solving practical problems in science and engineering arises as a direct consequence differential equations that explains the dynamics of the phenomena.Finding exact solutions to this equations provides importan informationabout the behavior of physical systems. The Lie symmetry method allows tofind invariant solutions under certain groups of transformations for differentialequations.This method not very well known and used is of great importance inthe scientific community. By this approach it was possible to find several exactinvariant solutions for the Klein Gordon Equation uxx − utt = k(u. A particularcase, The Kolmogorov equation uxx − utt = k1u + k2un was considered.These equations appear in the study of relativistic and quantum physics. Thegeneral solutions found, could be used for future explorations on the study forother specific K(u functions. En la solución de problemas prácticos de las ciencias y la ingeniería surgen como consecuencia directa ecuaciones diferenciales que dan razón de la dinámica de los fenómenos. El encontrar soluciones exactas a estas ecuaciones proporciona información importante sobre el comportamiento de sistemas físicos. El método de las simetrías de Lie permite encontrar soluciones invariantes bajo ciertos grupos de transformaciones para ecuaciones diferenciales. Mediante este método fue posible encontrar familias de soluciones exactas invariantes para la ecuación de Klein Gordon uxx- utt = k(u: En particular, se consideró la ecuación de Kolmogorov uxx - utt = k1u + k2u n. Estas ecuaciones aparecen en el estudio de la física relativista y cuántica. Las soluciones generales encontradas podrían emplearse en futuros desarrollos en el estudio para otro tipo de funciones k(u.

Operational Solution to the Nonlinear Klein-Gordon Equation

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Bengochea, G.; Verde-Star, L.; Ortigueira, M.

2018-05-01

We obtain solutions of the nonlinear Klein-Gordon equation using a novel operational method combined with the Adomian polynomial expansion of nonlinear functions. Our operational method does not use any integral transforms nor integration processes. We illustrate the application of our method by solving several examples and present numerical results that show the accuracy of the truncated series approximations to the solutions. Supported by Grant SEP-CONACYT 220603, the first author was supported by SEP-PRODEP through the project UAM-PTC-630, the third author was supported by Portuguese National Funds through the FCT Foundation for Science and Technology under the project PEst-UID/EEA/00066/2013

Quadratic algebras applied to noncommutative integration of the Klein-Gordon equation: Four-dimensional quadratic algebras containing three-dimensional nilpotent lie algebras

International Nuclear Information System (INIS)

Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.

1995-01-01

The study is continued on noncommutative integration of linear partial differential equations in application to the exact integration of quantum-mechanical equations in a Riemann space. That method gives solutions to the Klein-Gordon equation when the set of noncommutative symmetry operations for that equation forms a quadratic algebra consisting of one second-order operator and of first-order operators forming a Lie algebra. The paper is a continuation of, where a single nontrivial example is used to demonstrate noncommutative integration of the Klein-Gordon equation in a Riemann space not permitting variable separation

Geon-type solutions of the non-linear Heisenberg-Klein-Gordon equation

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Mielke, E.W.; Scherzer, R.

1980-10-01

As a model for a ''unitary'' field theory of extended particles we consider the non-linear Klein-Gordon equation - associated with a ''squared'' Heisenberg-Pauli-Weyl non-linear spinor equation - coupled to strong gravity. Using a stationary spherical ansatz for the complex scalar field as well as for the background metric generated via Einstein's field equation, we are able to study the effects of the scalar self-interaction as well as of the classical tensor forces. By numerical integration we obtain a continuous spectrum of localized, gravitational solitons resembling the geons previously constructed for the Einstein-Maxwell system by Wheeler. A self-generated curvature potential originating from the curved background partially confines the Schroedinger type wave functions within the ''scalar geon''. For zero angular momentum states and normalized scalar charge the spectrum for the total gravitational energy of these solitons exhibits a branching with respect to the number of nodes appearing in the radial part of the scalar field. Preliminary studies for higher values of the corresponding ''principal quantum number'' reveal that a kind of fine splitting of the energy levels occurs, which may indicate a rich, particle-like structure of these ''quantized geons''. (author)

Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets

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Ai-Min Yang

2014-01-01

Full Text Available We use the local fractional series expansion method to solve the Klein-Gordon equations on Cantor sets within the local fractional derivatives. The analytical solutions within the nondifferential terms are discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems of the liner differential equations on Cantor sets.

On classical solutions of the relativistic Vlasov-Klein-Gordon system

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Michael Kunzinger

2005-01-01

Full Text Available We consider a collisionless ensemble of classical particles coupled with a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. We also show that classical solutions are global in time in the one-dimensional case.

SOLVING NONLINEAR KLEIN-GORDON EQUATION WITH A QUADRATIC NONLINEAR TERM USING HOMOTOPY ANALYSIS METHOD

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H. Jafari

2010-07-01

Full Text Available In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM.Comparisons are made between the Adomian decomposition method (ADM, the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.

Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations

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Liu, Changying; Iserles, Arieh; Wu, Xinyuan

2018-03-01

The Klein-Gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering. Its computation represents a major challenge. The main theme of this paper is the construction of symmetric and arbitrarily high-order time integrators for the nonlinear Klein-Gordon equation by integrating Birkhoff-Hermite interpolation polynomials. To this end, under the assumption of periodic boundary conditions, we begin with the formulation of the nonlinear Klein-Gordon equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula. We then derive a symmetric and arbitrarily high-order Birkhoff-Hermite time integration formula for the nonlinear abstract ODE. Accordingly, the stability, convergence and long-time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix, subject to suitable temporal and spatial smoothness. A remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for PDEs in the literature. Numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches.

The general Klein-Gordon-Schroedinger system: modulational instability and exact solutions

International Nuclear Information System (INIS)

Tang Xiaoyan; Ding Wei

2008-01-01

The general Klein-Gordon-Schroedinger (gKGS) system is studied where the cubic auto-interactions are introduced in both the nonlinear Schroedinger and the nonlinear Klein-Gordon fields. We first investigate the modulational instability (MI) of the system, and thus derive the general dispersion relation between the frequency and wavenumber of the modulating perturbations, which demonstrates many possibilities for the MI regions. Using the travelling wave reduction, the gKGS system is greatly simplified. Via a simple function expansion method, we obtain some exact travelling wave solutions. Under some special parameter values, some representative wave structures are graphically displayed including the kink, anti-kink, bright, dark, grey and periodic solitons

Construction of wave operator for two-dimensional Klein-Gordon-Schrodinger systems with Yukawa coupling

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Kai Tsuruta

2013-05-01

Full Text Available We prove the existence of the wave operator for the Klein-Gordon-Schrodinger system with Yukawa coupling. This non-linearity type is below Strichartz scaling, and therefore classic perturbation methods will fail in any Strichartz space. Instead, we follow the "first iteration method" to handle these critical non-linearities.

New quasi-periodic waves of the (2+1)-dimensional sine-Gordon system

International Nuclear Information System (INIS)

Hu, H.C.; Lou, S.Y.

2005-01-01

New exact solutions of the well-known (2+1)-dimensional sine-Gordon system are studied by introducing the modified mapping relations between the cubic nonlinear Klein-Gordon and sine-Gordon equations. Two arbitrary functions are included into the Jacobi elliptic function solutions. By proper selections of the arbitrary functions, new quasi-periodic wave solutions are obtained and displayed graphically

Unstable Mode Solutions to the Klein-Gordon Equation in Kerr-anti-de Sitter Spacetimes

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Dold, Dominic

2017-03-01

For any cosmological constant {Λ = -3/ℓ2 r+2 > |a|ℓ}. We obtain an analogous result for Neumann boundary conditions if {5/4 < α < 9/4}. Moreover, in the Dirichlet case, one can prove that, for any Kerr-AdS spacetime violating the Hawking-Reall bound, there exists an open family of masses {α} such that the corresponding Klein-Gordon equation permits exponentially growing mode solutions. Our result adopts methods of Shlapentokh-Rothman developed in (Commun. Math. Phys. 329:859-891, 2014) and provides the first rigorous construction of a superradiant instability for negative cosmological constant.

A new auxiliary equation and exact travelling wave solutions of nonlinear equations

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Sirendaoreji

2006-01-01

A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients

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Nauman Raza

2016-01-01

Full Text Available The nonlinear Klein-Gordon equation (KGE models many nonlinear phenomena. In this paper, we propose a scheme for numerical approximation of solutions of the one-dimensional nonlinear KGE. A common approach to find a solution of a nonlinear system is to first linearize the equations by successive substitution or the Newton iteration method and then solve a linear least squares problem. Here, we show that it can be advantageous to form a sum of squared residuals of the nonlinear problem and then find a zero of the gradient. Our scheme is based on the Sobolev gradient method for solving a nonlinear least square problem directly. The numerical results are compared with Lattice Boltzmann Method (LBM. The L2, L∞, and Root-Mean-Square (RMS values indicate better accuracy of the proposed method with less computational effort.

Quantum cybernetics: a new perspective for Nelson's stochastic theory, nonlocality, and the Klein-Gordon equation

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Grössing, Gerhard

2002-04-01

The Klein-Gordon equation is shown to be equivalent to coupled partial differential equations for a sub-quantum Brownian movement of a “particle”, which is both passively affected by, and actively affecting, a diffusion process of its generally nonlocal environment. This indicates circularly causal, or “cybernetic”, relationships between “particles” and their surroundings. Moreover, in the relativistic domain, the original stochastic theory of Nelson is shown to hold as a limiting case only, i.e., for a vanishing quantum potential.

Klein-Gordon oscillator with position-dependent mass in the rotating cosmic string spacetime

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Wang, Bing-Qian; Long, Zheng-Wen; Long, Chao-Yun; Wu, Shu-Rui

2018-02-01

A spinless particle coupled covariantly to a uniform magnetic field parallel to the string in the background of the rotating cosmic string is studied. The energy levels of the electrically charged particle subject to the Klein-Gordon oscillator are analyzed. Afterwards, we consider the case of the position-dependent mass and show how these energy levels depend on the parameters in the problem. Remarkably, it shows that for the special case, the Klein-Gordon oscillator coupled covariantly to a homogeneous magnetic field with the position-dependent mass in the rotating cosmic string background has the similar behaviors to the Klein-Gordon equation with a Coulomb-type configuration in a rotating cosmic string background in the presence of an external magnetic field.

Exact solution of the Klein-Gordon equation for the PT-symmetric generalized Woods-Saxon potential by the Nikiforov-Uvarov method

International Nuclear Information System (INIS)

Ikhdair, S.M.; Sever, R.

2007-01-01

The exact solution of the one-dimensional Klein-Gordon equation of the PT-symmetric generalized Woods-Saxon potential is obtained. The exact energy eigenvalues and wavefunctions are derived analytically by using the Nikiforov and Uvarov method. In addition, the positive and negative exact bound states of the s-states are also investigated for different types of complex generalized Woods-Saxon potentials. (Abstract Copyright [2007], Wiley Periodicals, Inc.)

Relativistic particle in a box: Klein-Gordon versus Dirac equations

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Alberto, Pedro; Das, Saurya; Vagenas, Elias C.

2018-03-01

The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein-Gordon equation in the Feshbach-Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.

The solitary wave solution of coupled Klein-Gordon-Zakharov equations via two different numerical methods

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Dehghan, Mehdi; Nikpour, Ahmad

2013-09-01

In this research, we propose two different methods to solve the coupled Klein-Gordon-Zakharov (KGZ) equations: the Differential Quadrature (DQ) and Globally Radial Basis Functions (GRBFs) methods. In the DQ method, the derivative value of a function with respect to a point is directly approximated by a linear combination of all functional values in the global domain. The principal work in this method is the determination of weight coefficients. We use two ways for obtaining these coefficients: cosine expansion (CDQ) and radial basis functions (RBFs-DQ), the former is a mesh-based method and the latter categorizes in the set of meshless methods. Unlike the DQ method, the GRBF method directly substitutes the expression of the function approximation by RBFs into the partial differential equation. The main problem in the GRBFs method is ill-conditioning of the interpolation matrix. Avoiding this problem, we study the bases introduced in Pazouki and Schaback (2011) [44]. Some examples are presented to compare the accuracy and easy implementation of the proposed methods. In numerical examples, we concentrate on Inverse Multiquadric (IMQ) and second-order Thin Plate Spline (TPS) radial basis functions. The variable shape parameter (exponentially and random) strategies are applied in the IMQ function and the results are compared with the constant shape parameter.

Exact Solution of Klein-Gordon and Dirac Equations with Snyder-de Sitter Algebra

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Merad, M.; Hadj Moussa, M.

2018-01-01

In this paper, we present the exact solution of the (1+1)-dimensional relativistic Klein-Gordon and Dirac equations with linear vector and scalar potentials in the framework of deformed Snyder-de Sitter model. We introduce some changes of variables, we show that a one-dimensional linear potential for the relativistic system in a space deformed can be equivalent to the trigonometric Rosen-Morse potential in a regular space. In both cases, we determine explicitly the energy eigenvalues and their corresponding eigenfunctions expressed in terms of Romonovski polynomials. The limiting cases are analyzed for α 1 and α 2 → 0 and are compared with those of literature.

A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2008-01-01

With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to two types of NLPDEs. First, we present new family of solutions to a nonlinear Klein-Gordon equation, by using this auxiliary equation method including a new first-order nonlinear ODE with six-degree nonlinear term proposed by Sirendaoreji. Then, we apply an indirect F-function method very close to the F-expansion method to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage of the new first-order nonlinear ODE with six degree nonlinear term, this indirect F-function method is used to map the solutions of C(l,n,p) equations to those of that nonlinear ODE. As a result, we can successfully obtain in a unified way, many exact solutions

Global existence and uniform stabilization of a generalized dissipative Klein-Gordon equation type with boundary damping

International Nuclear Information System (INIS)

Zhang Zaiyun; Miao Xiujin; Chen Yuezhong; Liu Zhenhai

2011-01-01

In this paper, we prove the existence, uniqueness, and uniform stability of strong and weak solutions of the nonlinear generalized Klein-Gordon equation (1.1) 1 (see Sec. I) in bounded domains with nonlinear damped boundary conditions given by (1.1) 3 (see Sec. I) with some restrictions on function f(u), h(∇u), g(u t ), and b(x), we prove the existence and uniqueness by means of nonlinear semigroup method and obtain the uniform stabilization by using the multiplier technique.

Hunting the ghosts of a 'strictly quantum field': the Klein-Gordon equation

International Nuclear Information System (INIS)

Bertozzi, Eugenio

2010-01-01

This paper aims to identify and tackle some problems related to teaching quantum field theory (QFT) at university level. In particular, problems arising from the canonical quantization are addressed by focusing on the Klein-Gordon equation (KGE). After a brief description of the status of the KGE in teaching as it emerges from an analysis of a selected sample of university textbooks, an analysis of the applications of the KGE in contexts different from the QFT is presented. The results of the analysis show that, while in the real case the solutions of the equation can be easily interpreted from a physical point of view, in the complex case the coherence with relativistic quantum mechanics and the electrodynamics framework brings to light interpretative problems related to the classical complex KG field. The comparison between the classical cases investigated and the QFT framework, where the equation finds a coherent particle interpretation, leads to share Ryder's statement asserting that the KG field is a 'strictly quantum field'. Implications of the results in terms of remarks about the canonical procedure currently utilized for teaching are underlined.

A new sub-equation method applied to obtain exact travelling wave solutions of some complex nonlinear equations

International Nuclear Information System (INIS)

Zhang Huiqun

2009-01-01

By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.

The relativistic electron wave equation

International Nuclear Information System (INIS)

Dirac, P.A.M.

1977-08-01

The paper was presented at the European Conference on Particle Physics held in Budapest between the 4th and 9th July of 1977. A short review is given on the birth of the relativistic electron wave equation. After Schroedinger has shown the equivalence of his wave mechanics and the matrix mechanics of Heisenberg, a general transformation theory was developed by the author. This theory required a relativistic wave equation linear in delta/delta t. As the Klein--Gordon equation available at this time did not satisfy this condition the development of a new equation became necessary. The equation which was found gave the value of the electron spin and magnetic moment automatically. (D.P.)

Mode solutions for a Klein-Gordon field in anti-de Sitter spacetime with dynamical boundary conditions of Wentzell type

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Dappiaggi, Claudio; Ferreira, Hugo R. C.; Juárez-Aubry, Benito A.

2018-04-01

We study a real, massive Klein-Gordon field in the Poincaré fundamental domain of the (d +1 )-dimensional anti-de Sitter (AdS) spacetime, subject to a particular choice of dynamical boundary conditions of generalized Wentzell type, whereby the boundary data solves a nonhomogeneous, boundary Klein-Gordon equation, with the source term fixed by the normal derivative of the scalar field at the boundary. This naturally defines a field in the conformal boundary of the Poincaré fundamental domain of AdS. We completely solve the equations for the bulk and boundary fields and investigate the existence of bound state solutions, motivated by the analogous problem with Robin boundary conditions, which are recovered as a limiting case. Finally, we argue that both Robin and generalized Wentzell boundary conditions are distinguished in the sense that they are invariant under the action of the isometry group of the AdS conformal boundary, a condition which ensures in addition that the total flux of energy across the boundary vanishes.

Smooth manifolds for certain dynamical systems and periodic solitons for nonlinear Klein-Gordon equations on R2

International Nuclear Information System (INIS)

Vuillermot, P.A.

1988-01-01

We present and discuss three new theorems concerning the existence of smooth manifolds associated with certain infinite-dimensional dynamical systems defined from nonlinear Klein-Gordon equations of the form u tt (x, t) = u xx (x, t)-g(u(x, t)), where g: R → R is analytic and where (x, t) ε R 2 . In particular, we prove the nonexistence of small amplitude soliton bound state solutions in the classical Φ 4 -theory, a fact recently brought about by the perturbative analysis of Kruskal and Segur [fr

Experimental verification of the relativistic fine-structure term of the Klein-Gordon equation in pionic titanium atoms

International Nuclear Information System (INIS)

Delker, L.; Dugan, G.; Wu, C.S.; Lu, D.C.; Caffrey, A.J.; Cheng, Y.T.; Lee, Y.K.

1979-01-01

A newly designed, large-aperture and high-resolution bent-crystal spectrometer has been used to observe high-intensity sources of pionic x rays. The pionic x-ray source was a target of natural titanium which was placed adjacent to a copper pion-production target in the external beam of the Nevis synchrocyclotron. The energy difference between the 5g → 4f and 5f → 4d transitions in pionic titanium was measured to be 87.6 +- 1.8 eV. Comparison with the prediction of the Klein-Gordon equation is made

Hadamard States for the Klein-Gordon Equation on Lorentzian Manifolds of Bounded Geometry

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Gérard, Christian; Oulghazi, Omar; Wrochna, Michał

2017-06-01

We consider the Klein-Gordon equation on a class of Lorentzian manifolds with Cauchy surface of bounded geometry, which is shown to include examples such as exterior Kerr, Kerr-de Sitter spacetime and the maximal globally hyperbolic extension of the Kerr outer region. In this setup, we give an approximate diagonalization and a microlocal decomposition of the Cauchy evolution using a time-dependent version of the pseudodifferential calculus on Riemannian manifolds of bounded geometry. We apply this result to construct all pure regular Hadamard states (and associated Feynman inverses), where regular refers to the state's two-point function having Cauchy data given by pseudodifferential operators. This allows us to conclude that there is a one-parameter family of elliptic pseudodifferential operators that encodes both the choice of (pure, regular) Hadamard state and the underlying spacetime metric.

Generalised master equations for wave equation separation in a Kerr or Kerr-Newman black hole background

International Nuclear Information System (INIS)

Carter, B.; McLenaghan, R.G.

1982-01-01

It is shown how previous general formulae for the separated radial and angular parts of the massive, charged scalar (Klein, Gordon) wave equation on one hand, and of the zero mass, neutral, but higher spin (neutrino, electromagnetic and gravitational) wave equations on the other hand may be combined in a more general formula which also covers the case of the full massive charged Dirac equation in a Kerr or Kerr-Newman background space. (Auth.)

On the prolongation structure and Backlund transformation for new non-linear Klein-Gordon equations

International Nuclear Information System (INIS)

Roy Chowdhury, A.; Mukherjee, J.

1986-07-01

We have considered the complete integrability of two nonlinear equations which are some kind of extensions of usual Sine-Gordon and Sinh-Gordon equations. The first one is of non-autonomous version of Sinh-Gordon system and the second is closely related to the usual Sine-Gordon theory. The first problem indicates how (x,t) dependent non-linear equations can be treated in the prolongation theory and how a Backlund map can be constructed. The second one is a variation of the usual Sine-Gordon equation and suggests that there may be other equations (similar to Sine-Gordon) which are completely integrable. In both cases we have been able to construct the Lax pair. We then construct an auto-Backlund map by following the idea of Konno and Wadati, for the generation of multisolution states. (author)

Equation with the many fathers

DEFF Research Database (Denmark)

Kragh, Helge

1984-01-01

In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...... as electrodynamics. Although this ambitious attempt attracted some interest in 1926, its impact on the mainstream of development in quantum mechanics was virtually nil....... of the usual Schrödinger equation. In most of the early versions the Klein-Gordon equation was connected with the general theory of relativity. Klein and some other physicists attempted to express quantum mechanics within a five-dimensional unified theory, embracing general relativity as well...

Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations

International Nuclear Information System (INIS)

Esteban, M.J.; Georgiev, V.; Sere, E.

1995-01-01

The Maxwell-Dirac system describes the interaction of an electron with its own electromagnetic field. We prove the existence of soliton-like solutions of Maxwell-Dirac in (3+1)-Minkowski space-time. The solutions obtained are regular, stationary in time, and localized in space. They are found by a variational method, as critical points of an energy functional. This functional is strongly indefinite and presents a lack of compactness. We also find soliton-like solutions for the Klein-Gordon-Dirac system, arising in the Yukawa model. (author). 32 refs

Spaces of positive and negative frequency solutions of field equations in curved space--times. I. The Klein--Gordon equation in stationary space--times

International Nuclear Information System (INIS)

Moreno, C.

1977-01-01

In stationary space--times V/sub n/ x R with compact space-section manifold without boundary V/sub n/, the Klein--Gordon equation is solved by the one-parameter group of unitary operators generated by the energy operator i -1 T -1 in the Sobolev spaces H/sup l/(V/sub n/) x H/sup l/(V/sub n/). The canonical symplectic and complex structures of the associated dynamical system are calculated. The existence and the uniqueness of the Lichnerowicz kernel are established. The Hilbert spaces of positive and negative frequency-part solutions defined by means of this kernel are constructed

Partial Internal Control Recovery on 1-D Klein-Gordon Systems

Directory of Open Access Journals (Sweden)

Iwan Pranoto

2010-03-01

Full Text Available In this exposition, a technique to recover internal control on a distributed parameter system is reported. The system is described by 1-D Klein-Gordon partial differential equation with a time-varying parameter. We would like to recover the internal control applied to the system if we know some limited information about the output. We use a method called sentinel method to recover the internal control. It involves some construction of a linear functional, and we show that this construction relates closely to the exact controllability problem.

Extended sine-Gordon Equation Method and Its Application to Maccari's System

International Nuclear Information System (INIS)

Song Lina; Zhang Hongqing

2005-01-01

An extended sine-Gordon equation method is proposed to construct exact travelling wave solutions to Maccari's equation based upon a generalized sine-Gordon equation. It is shown that more new travelling wave solutions can be found by this new method, which include bell-shaped soliton solutions, kink-shaped soliton solutions, periodic wave solution, and new travelling waves.

Relativistic wave equations and compton scattering

International Nuclear Information System (INIS)

Sutanto, S.H.; Robson, B.A.

1998-01-01

Full text: Recently an eight-component relativistic wave equation for spin-1/2 particles was proposed.This equation was obtained from a four-component spin-1/2 wave equation (the KG1/2 equation), which contains second-order derivatives in both space and time, by a procedure involving a linearisation of the time derivative analogous to that introduced by Feshbach and Villars for the Klein-Gordon equation. This new eight-component equation gives the same bound-state energy eigenvalue spectra for hydrogenic atoms as the Dirac equation but has been shown to predict different radiative transition probabilities for the fine structure of both the Balmer and Lyman a-lines. Since it has been shown that the new theory does not always give the same results as the Dirac theory, it is important to consider the validity of the new equation in the case of other physical problems. One of the early crucial tests of the Dirac theory was its application to the scattering of a photon by a free electron: the so-called Compton scattering problem. In this paper we apply the new theory to the calculation of Compton scattering to order e 2 . It will be shown that in spite of the considerable difference in the structure of the new theory and that of Dirac the cross section is given by the Klein-Nishina formula

Combined Sinh-Cosh-Gordon equation: Symmetry reductions, exact ...

African Journals Online (AJOL)

Combined Sinh-Cosh-Gordon equation: Symmetry reductions, exact solutions and conservation laws. ... In this paper we study the combined sinh-cosh-Gordon equation, which arises in mathematical physics and has a wide range of scientific applications that range from chemical reactions to water surface gravity waves.

Near-Integrability of Low-Dimensional Periodic Klein-Gordon Lattices

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Ognyan Christov

2018-01-01

Full Text Available The low-dimensional periodic Klein-Gordon lattices are studied for integrability. We prove that the periodic lattice with two particles and certain nonlinear potential is nonintegrable. However, in the cases of up to six particles, we prove that their Birkhoff-Gustavson normal forms are integrable, which allows us to apply KAM theory in most cases.

New exact travelling wave solutions of generalised sinh- Gordon and (2 + 1-dimensional ZK-BBM equations

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Sachin Kumar

2012-10-01

Full Text Available Exact travelling wave solutions have been established for generalised sinh-Gordon andgeneralised (2+1 dimensional ZK-BBM equations by using GG      expansion method whereG  G( satisfies a second-order linear ordinary differential equation. The travelling wave solutionsare expressed by hyperbolic, trigonometric and rational functions.

Axisymmetric black holes allowing for separation of variables in the Klein-Gordon and Hamilton-Jacobi equations

Science.gov (United States)

Konoplya, R. A.; Stuchlík, Z.; Zhidenko, A.

2018-04-01

We determine the class of axisymmetric and asymptotically flat black-hole spacetimes for which the test Klein-Gordon and Hamilton-Jacobi equations allow for the separation of variables. The known Kerr, Kerr-Newman, Kerr-Sen and some other black-hole metrics in various theories of gravity are within the class of spacetimes described here. It is shown that although the black-hole metric in the Einstein-dilaton-Gauss-Bonnet theory does not allow for the separation of variables (at least in the considered coordinates), for a number of applications it can be effectively approximated by a metric within the above class. This gives us some hope that the class of spacetimes described here may be not only generic for the known solutions allowing for the separation of variables, but also a good approximation for a broader class of metrics, which does not admit such separation. Finally, the generic form of the axisymmetric metric is expanded in the radial direction in terms of the continued fractions and the connection with other black-hole parametrizations is discussed.

An interpolation between the wave and diffusion equations through the fractional evolution equations Dirac like

International Nuclear Information System (INIS)

Pierantozzi, T.; Vazquez, L.

2005-01-01

Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case

New exact solutions of the Dirac equation. 11

International Nuclear Information System (INIS)

Bagrov, V.G.; Noskov, M.D.

1984-01-01

Investigations into determining new exact solutions of relativistic wave equations started in another paper were continued. Exact solutions of the Dirac, Klein-Gordon equations and classical relativistic equations of motion in four new types of external electromagnetic fields were found

Nuclearity, split-property and duality for the Klein-Gordon field in curved spacetime

International Nuclear Information System (INIS)

Verch, R.

1993-05-01

Nuclearity, Split-Property and Duality are establihed for the nets of von Neumann algebras associated with the representations of distinguished states of the massive Klein-Gordon field propagating in particular classes of curved spacetimes. (orig.)

Uniform decay for a local dissipative Klein-Gordon-Schrodinger type system

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Marilena N. Poulou

2012-10-01

Full Text Available In this article, we consider a nonlinear Klein-Gordon-Schrodinger type system in $mathbb{R}^n$, where the nonlinear term exists and the damping term is effective. We prove the existence and uniqueness of a global solution and its exponential decay. The result is achieved by using the multiplier technique.

Exact solutions to sine-Gordon-type equations

International Nuclear Information System (INIS)

Liu Shikuo; Fu Zuntao; Liu Shida

2006-01-01

In this Letter, sine-Gordon-type equations, including single sine-Gordon equation, double sine-Gordon equation and triple sine-Gordon equation, are systematically solved by Jacobi elliptic function expansion method. It is shown that different transformations for these three sine-Gordon-type equations play different roles in obtaining exact solutions, some transformations may not work for a specific sine-Gordon equation, while work for other sine-Gordon equations

Exact explicit travelling wave solutions for (n + 1)-dimensional Klein-Gordon-Zakharov equations

International Nuclear Information System (INIS)

Li Jibin

2007-01-01

Using the methods of dynamical systems for the (n + 1)-dimensional KGS nonlinear wave equations, five classes of exact explicit parametric representations of the bounded travelling solutions are obtained. To guarantee the existence of the above solutions, all parameter conditions are given

On some classes of breather lattice solutions to the sinh-Gordon equation

International Nuclear Information System (INIS)

Fu Zuntao; Liu Shikuo

2007-01-01

In this paper, dependent and independent variable transformations are introduced to solve the sinh-Gordon equation by using the knowledge of the elliptic equation and Jacobian elliptic functions. It is shown that different kinds of solutions can be obtained to the sinh-Gordon equation, including breather lattice solutions and periodic wave solutions. (orig.)

Exact, multiple soliton solutions of the double sine Gordon equation

International Nuclear Information System (INIS)

Burt, P.B.

1978-01-01

Exact, particular solutions of the double sine Gordon equation in n dimensional space are constructed. Under certain restrictions these solutions are N solitons, where N <= 2q - 1 and q is the dimensionality of space-time. The method of solution, known as the base equation technique, relates solutions of nonlinear partial differential equations to solutions of linear partial differential equations. This method is reviewed and its applicability to the double sine Gordon equation shown explicitly. The N soliton solutions have the remarkable property that they collapse to a single soliton when the wave vectors are parallel. (author)

Nonlinear scalar field equations. Pt. 1

International Nuclear Information System (INIS)

Berestycki, H.; Lions, P.L.

1983-01-01

This paper as well as a subsequent one is concerned with the existence of nontrivial solutions for some semi-linear elliptic equations in Rsup(N). Such problems are motivated in particular by the search for certain kinds of solitary waves (stationary states) in nonlinear equations of the Klein-Gordon or Schroedinger type. (orig./HSI)

A new sine-Gordon equation expansion algorithm to investigate some special nonlinear differential equations

International Nuclear Information System (INIS)

Yan Zhenya

2005-01-01

A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gordon equation, the Magma equation and the generalized Pochhammer-Chree (PC) equation to illustrate the method. As a result, many types of new doubly periodic solutions are obtained. Moreover when using the method to these special nonlinear differential equations, some transformations are firstly needed. The method can be also extended to other nonlinear differential equations

New exact solutions of (2 + 1)-dimensional Gardner equation via the new sine-Gordon equation expansion method

International Nuclear Information System (INIS)

Chen Yong; Yan Zhenya

2005-01-01

In this paper (2 + 1)-dimensional Gardner equation is investigated using a sine-Gordon equation expansion method, which was presented via a generalized sine-Gordon reduction equation and a new transformation. As a consequence, it is shown that the method is more powerful to obtain many types of new doubly periodic solutions of (2 + 1)-dimensional Gardner equation. In particular, solitary wave solutions are also given as simple limits of doubly periodic solutions

Entanglement between smeared field operators in the Klein-Gordon vacuum

International Nuclear Information System (INIS)

Zych, Magdalena; Costa, Fabio; Kofler, Johannes; Brukner, Caslav

2010-01-01

Quantum field theory is the application of quantum physics to fields. It provides a theoretical framework widely used in particle physics and condensed matter physics. One of the most distinct features of quantum physics with respect to classical physics is entanglement or the existence of strong correlations between subsystems that can even be spacelike separated. In quantum fields, observables restricted to a region of space define a subsystem. While there are proofs on the existence of local observables that would allow a violation of Bell's inequalities in the vacuum states of quantum fields as well as some explicit but technically demanding schemes requiring an extreme fine-tuning of the interaction between the fields and detectors, an experimentally accessible entanglement witness for quantum fields is still missing. Here we introduce smeared field operators which allow reducing the vacuum to a system of two effective bosonic modes. The introduction of such collective observables is motivated by the fact that no physical probe has access to fields in single spatial (mathematical) points but rather smeared over finite volumes. We first give explicit collective observables whose correlations reveal vacuum entanglement in the Klein-Gordon field. We then show that the critical distance between the two regions of space above which two effective bosonic modes become separable is of the order of the Compton wavelength of the particle corresponding to the massive Klein-Gordon field.

Rotationally symmetric numerical solutions to the sine-Gordon equation

DEFF Research Database (Denmark)

Olsen, O. H.; Samuelsen, Mogens Rugholm

1981-01-01

We examine numerically the properties of solutions to the spherically symmetric sine-Gordon equation given an initial profile which coincides with the one-dimensional breather solution and refer to such solutions as ring waves. Expanding ring waves either exhibit a return effect or expand towards...

Antiparticle in Light of Einstein-Podolsky-Rosen Paradox and Klein Paradox

OpenAIRE

Ni, Guang-jiong; Guan, Hong; Zhou, Weimin; Yan, Jun

2000-01-01

The original version of Einstein-Podolsky-Rosen (EPR) paradox and the Klein paradox of Klein-Gordon (KG) equation are discussed to show the necessity of existence of antiparticle with its wavefunction being fixed unambiguously. No concept of "hole" is needed.

A novel SUSY energy bound-states treatment of the Klein-Gordon equation with PT-symmetric and q-deformed parameter Hulthén potential

Science.gov (United States)

Aktas, M.

2018-01-01

In this study, we focus on investigating the exact relativistic bound-state spectra for supersymmetric, PT-supersymmetric and non-Hermitian versions of the q-deformed parameter Hulthén potential. The Hamiltonian hierarchy mechanism, namely the factorization method, is adopted within the framework of SUSYQM. This algebraic approach is used in solving the Klein-Gordon equation with the potential cases. The results obtained analytically by executing the straightforward calculations are in consistent forms for certain values of q. Achieving the results may have a particular interest for such applications. That is, they can be involved in determining the quantum structural properties of molecules for ro-vibrational states, and optical spectra characteristics of semiconductor devices with regard to the lattice dynamics. They are also employed to construct the broken or unbroken case of the supersymmetric particle model concerning the interaction between the elementary particles.

Ultradiscrete sine-Gordon Equation over Symmetrized Max-Plus Algebra, and Noncommutative Discrete and Ultradiscrete sine-Gordon Equations

Directory of Open Access Journals (Sweden)

Kenichi Kondo

2013-11-01

Full Text Available Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sine-Gordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sine-Gordon equation and its 1-soliton and 2-soliton solutions, using the symmetrized max-plus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sine-Gordon equations.

Continuity relations and quantum wave equations

International Nuclear Information System (INIS)

Goedecke, G.H.; Davis, B.T.

2010-01-01

We investigate the mathematical synthesis of the Schroedinger, Klein-Gordon, Pauli-Schroedinger, and Dirac equations starting from probability continuity relations. We utilize methods similar to those employed by R. E. Collins (Lett. Nuovo Cimento, 18 (1977) 581) in his construction of the Schroedinger equation from the position probability continuity relation for a single particle. Our new results include the mathematical construction of the Pauli-Schroedinger and Dirac equations from the position probability continuity relations for a particle that can transition between two states or among four states, respectively.

KLEIN: Coulomb functions for real lambda and positive energy to high accuracy

International Nuclear Information System (INIS)

Barnett, A.R.

1981-01-01

KLEIN computes relativistic Schroedinger (Klein-Gordon) equation solutions, i.e. Coulomb functions for real lambda > - 1, Fsub(lambda)(eta,x), Gsub(lambda)(eta,x), F'sub(lambda)(eta,x) and G'sub(lambda)(eta,x) for real kappa > 0 and real eta, - 10 4 4 . Hence it is also suitable for Bessel and spherical Bessel functions. Accuracies are in the range 10 -14 -10 -16 in oscillating region, and approx. equal to 10 -30 on an extended precision compiler. The program is suitable for generating Klein-Gordon wavefunctions for matching in pion and kaon physics. (orig.)

Exact solutions for nonlinear evolution equations using Exp-function method

International Nuclear Information System (INIS)

Bekir, Ahmet; Boz, Ahmet

2008-01-01

In this Letter, the Exp-function method is used to construct solitary and soliton solutions of nonlinear evolution equations. The Klein-Gordon, Burger-Fisher and Sharma-Tasso-Olver equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations

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

International Nuclear Information System (INIS)

Dai Chaoqing; Zhang Jiefang

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.

Solutions of the lattice sine–Gordon equation and the solitons of its cellular automaton

International Nuclear Information System (INIS)

Willox, R; Ramani, A; Grammaticos, B

2014-01-01

We analyse the solutions of the cellular automaton sine–Gordon equation and link them to solutions of the discrete, lattice, sine–Gordon. We show that while the ultradiscretizable, positive definite, solutions of the latter behave dispersively, certain parts of these dispersive waves nonetheless survive in the ultradiscrete limit, giving rise to the solutions of the cellular automaton. We examine the ultradiscrete solutions in the case of a generalized cellular automaton in which the dependent variable can assume non-integer values and we show that the collision of two solitary waves is inelastic, leading to the creation of a ‘bridge’ of constant height that links two outgoing structures. Based on the ultradiscrete form of the sine–Gordon equation we explain the appearance of this bridging region and we describe its interaction with a solitary wave. (paper)

Topological symmetry breaking of self-interacting fractional Klein-Gordon field theories on toroidal spacetime

International Nuclear Information System (INIS)

Lim, S C; Teo, L P

2008-01-01

Quartic self-interacting fractional Klein-Gordon scalar massive and massless field theories on toroidal spacetime are studied. The effective potential and topologically generated mass are determined using zeta-function regularization technique. Renormalization of these quantities are derived. Conditions for symmetry breaking are obtained analytically. Simulations are carried out to illustrate regions or values of compactified dimensions where symmetry-breaking mechanisms appear

Quantum mechanics of Klein-Gordon-type fields and quantum cosmology

International Nuclear Information System (INIS)

Mostafazadeh, Ali

2004-01-01

With a view to address some of the basic problems of quantum cosmology, we formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (∂ t 2 +D)ψ(t)=0, where t is an element of R and D is a positive-definite operator acting in a Hilbert space H-tilde. In particular, we determine all the positive-definite inner products on the space H of the solutions of such an equation and establish their physical equivalence. This specifies the Hilbert space structure of H uniquely. We use a simple realization of the latter to construct the observables of the theory explicitly. The field equation does not fix the choice of a Hamiltonian operator unless it is supplemented by an underlying classical system and a quantization scheme supported by a correspondence principle. In general, there are infinitely many choices for the Hamiltonian each leading to a different notion of time-evolution in H. Among these is a particular choice that generates t-translations in H and identifies t with time whenever D is t-independent. For a t-dependent D, we show that regardless of the choice of the inner product the t-translations do not correspond to unitary evolutions in H, and t cannot be identified with time. We apply these ideas to develop a formulation of quantum cosmology based on the Wheeler-DeWitt equation for a Friedman-Robertson-Walker model coupled to a real scalar field with an arbitrary positive confining potential. In particular, we offer a complete solution of the Hilbert space problem, construct the observables, use a position-like observable to introduce the wave functions of the universe (which differ from the Wheeler-DeWitt fields), reformulate the corresponding quantum theory in terms of the latter, reduce the problem of the identification of time to the determination of a Hamiltonian operator acting in L 2 R+L 2 R, show that the factor-ordering problem is irrelevant for the kinematics of the quantum theory, and propose a formulation of the

Quantum mechanics of Klein-Gordon-type fields and quantum cosmology

Science.gov (United States)

Mostafazadeh, Ali

2004-01-01

With a view to address some of the basic problems of quantum cosmology, we formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (∂t2+D)ψ(t)=0, where t∈R and D is a positive-definite operator acting in a Hilbert space H~. In particular, we determine all the positive-definite inner products on the space H of the solutions of such an equation and establish their physical equivalence. This specifies the Hilbert space structure of H uniquely. We use a simple realization of the latter to construct the observables of the theory explicitly. The field equation does not fix the choice of a Hamiltonian operator unless it is supplemented by an underlying classical system and a quantization scheme supported by a correspondence principle. In general, there are infinitely many choices for the Hamiltonian each leading to a different notion of time-evolution in H. Among these is a particular choice that generates t-translations in H and identifies t with time whenever D is t-independent. For a t-dependent D, we show that regardless of the choice of the inner product the t-translations do not correspond to unitary evolutions in H, and t cannot be identified with time. We apply these ideas to develop a formulation of quantum cosmology based on the Wheeler-DeWitt equation for a Friedman-Robertson-Walker model coupled to a real scalar field with an arbitrary positive confining potential. In particular, we offer a complete solution of the Hilbert space problem, construct the observables, use a position-like observable to introduce the wave functions of the universe (which differ from the Wheeler-DeWitt fields), reformulate the corresponding quantum theory in terms of the latter, reduce the problem of the identification of time to the determination of a Hamiltonian operator acting in L2(R)⊕L2(R), show that the factor-ordering problem is irrelevant for the kinematics of the quantum theory, and propose a formulation of the dynamics. Our method is

Approximate damped oscillatory solutions and error estimates for the perturbed Klein–Gordon equation

International Nuclear Information System (INIS)

Ye, Caier; Zhang, Weiguo

2015-01-01

Highlights: • Analyze the dynamical behavior of the planar dynamical system corresponding to the perturbed Klein–Gordon equation. • Present the relations between the properties of traveling wave solutions and the perturbation coefficient. • Obtain all explicit expressions of approximate damped oscillatory solutions. • Investigate error estimates between exact damped oscillatory solutions and the approximate solutions and give some numerical simulations. - Abstract: The influence of perturbation on traveling wave solutions of the perturbed Klein–Gordon equation is studied by applying the bifurcation method and qualitative theory of dynamical systems. All possible approximate damped oscillatory solutions for this equation are obtained by using undetermined coefficient method. Error estimates indicate that the approximate solutions are meaningful. The results of numerical simulations also establish our analysis

Sinh-Gordon, cosh-Gordon, and Liouville equations for strings and multistrings in constant curvature spacetimes

International Nuclear Information System (INIS)

Larsen, A.L.; Sanchez, N.

1996-01-01

We find that the fundamental quadratic form of classical string propagation in (2+1)-dimensional constant curvature spacetimes solves the sinh-Gordon equation, the cosh-Gordon equation, or the Liouville equation. We show that in both de Sitter and anti endash de Sitter spacetimes (as well as in the 2+1 black hole anti endash de Sitter spacetime), all three equations must be included to cover the generic string dynamics. The generic properties of the string dynamics are directly extracted from the properties of these three equations and their associated potentials (irrespective of any solution). These results complete and generalize earlier discussions on this topic (until now, only the sinh-Gordon sector in de Sitter spacetime was known). We also construct new classes of multistring solutions, in terms of elliptic functions, to all three equations in both de Sitter and anti endash de Sitter spacetimes. Our results can be straightforwardly generalized to constant curvature spacetimes of arbitrary dimension, by replacing the sinh-Gordon equation, the cosh-Gordon equation, and the Liouville equation by their higher dimensional generalizations. copyright 1996 The American Physical Society

Mathieu functions describing particles evolving in electromagnetic waves

Science.gov (United States)

Mihu, Denisa-Andreea; Dariescu, Marina-Aura

2017-12-01

Solutions of Klein-Gordon equation for particles moving in a standing wave configuration bring into attention an intricate and complicated category of special functions, namely the Mathieu functions. The stability of the solutions governed by the intercorrelation between Mathieu equation' parameters is discussed. For specific intervals of the wave number, the instability regime installs, pointing out the tendency of exponential growth for the oscillatory wave functions, as a consequence of parametric resonance phenomenon. The expression of the wave function allows the computation of the four-dimensional conserved current density components.

Nonlinear interactions of counter-travelling waves

International Nuclear Information System (INIS)

Matsuuchi, Kazuo

1980-01-01

Nonlinear interactions between two waves travelling in opposite directions are investigated. When a nonlinear Klein-Gordon equation is adopted as a model equation, it is shown that such a wave system is governed by a simple set of equations for their complex amplitudes. Steady progressive waves governed by this set are investigated for various cases classified according to the signs of the coefficients. It is then found that one wave travelling in one direction appears from a certain point and the other travelling in the opposite direction has a constant amplitude from that point. This phenomenon may be regarded as a sort of reflection in spite of no rigid boundary. (author)

Properties of the DKP [Duffin-Kemmer-Petiau] equation

International Nuclear Information System (INIS)

Nieto, M.M.

1988-01-01

After recalling the development of relativistic quantum mechanics, I elucidating the properties of the Duffin-Kemmer-Petiau first-order wave equation for spin-0 and -1 mesons. The DKP equation is formally compared to the Dirac equation, and physically compared to the Klein-Gordon second-order equation for mesons. I point out where the DKP and KG equations predict the same results, and where their predictions are different. I conclude with an example of where these differences might interest people studying quark models of nuclei. 9 refs

Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in 2D

OpenAIRE

Kinoshita, Shinya

2016-01-01

This paper is concerned with the Cauchy problem of $2$D Klein-Gordon-Zakharov system with very low regularity initial data. We prove the bilinear estimates which are crucial to get the local in time well-posedness. The estimates are established by the Fourier restriction norm method. We utilize the bilinear Strichartz estimates and the nonlinear version of the classical Loomis-Whitney inequality which was applied to Zakharov system.

Pramana – Journal of Physics | Indian Academy of Sciences

Indian Academy of Sciences (India)

In the framework of Bohmian quantum mechanics, the Klein--Gordon equation can be seen as representing a particle with mass m which is guided by a guiding wave ϕ ( x ) in a causal manner. Here a relevant question is whether Bohmian quantum mechanics is applicable to a non-linear Klein--Gordon equation?

Three-dimensional Einstein-Klein-Gordon system in characteristic numerical relativity

International Nuclear Information System (INIS)

Barreto, W.; Silva, A. da; Lehner, L.; Gomez, R.; Rosales, L.; Winicour, J.

2005-01-01

We incorporate a massless scalar field into a three-dimensional code for the characteristic evolution of the gravitational field. The extended three-dimensional code for the Einstein-Klein-Gordon system is calibrated to be second-order convergent. It provides an accurate calculation of the gravitational and scalar radiation at infinity. As an application, we simulate the fully nonlinear evolution of an asymmetric scalar pulse of ingoing radiation propagating toward an interior Schwarzschild black hole and compute the backscattered scalar and gravitational outgoing radiation patterns. The amplitudes of the scalar and gravitational outgoing radiation modes exhibit the predicted power law scaling with respect to the amplitude of the initial data. For the scattering of an axisymmetric scalar field, the final ring down matches the complex frequency calculated perturbatively for the l=2 quasinormal mode

Abundant Interaction Solutions of Sine-Gordon Equation

Directory of Open Access Journals (Sweden)

DaZhao Lü

2012-01-01

Full Text Available With the help of computer symbolic computation software (e.g., Maple, abundant interaction solutions of sine-Gordon equation are obtained by means of a constructed Wronskian form expansion method. The method is based upon the forms and structures of Wronskian solutions of sine-Gordon equation, and the functions used in the Wronskian determinants do not satisfy linear partial differential equations. Such interaction solutions are difficultly obtained via other methods. And the method can be automatically carried out in computer.

Moving discrete breathers in a Klein-Gordon chain with an impurity

International Nuclear Information System (INIS)

Cuevas, J; Palmero, F; Archilla, J F R; Romero, F R

2002-01-01

We analyse the influence of an impurity in the evolution of moving discrete breathers in a Klein-Gordon chain with non-weak nonlinearity. Three different types of behaviour can be observed when moving breathers interact with the impurity: they pass through the impurity continuing their direction of movement; they are reflected by the impurity; they are trapped by the impurity, giving rise to chaotic breathers, as their Fourier power spectra show. Resonance with a breather centred at the impurity site is conjectured to be a necessary condition for the appearance of the trapping phenomenon. This paper establishes a difference between the resonance condition of the non-weak nonlinearity approach and the resonance condition with the linear impurity mode in the case of weak nonlinearity

On the stability of solitary waves for classical scalar fields

International Nuclear Information System (INIS)

Blanchard, P.; Stubbe, J.; Vazquez, L.

1986-01-01

We study the stability for the bound states of lowest action of certain nonlinear Klein-Gordon and Schroedinger equations by applying the Shatah-Strauss formalism. We extend the range of application of this formalism by using a recent existence theorem for minimum action solutions to a large class of equations including logarithmic Klein-Gordon equation and logarithmic Schroedinger equation and scalar fields with fractional non-linearities. Furthermore we discuss the relation between different stability criteria considered in the literature. (orig.)

Relativistic two-body equation for one Dirac and one Duffin-Kemmer particle

International Nuclear Information System (INIS)

Krolikowski, W.

1983-01-01

A new relativistic two-body wave equation is proposed for one spin-1/2 and one spin-0 or spin-1 particle which, if isolated from each other, are described by the Dirac and the Duffin-Kemmer equation, respectively. For a static mutual interaction this equation splits into two equations: a two-body wave equation for one Dirac and one Klein-Gordon particle (which was introduced by the author previously) and a new two-body wave equation for one Dirac and one Proca particle. The proposed equation may be applied in particular to the quark-diquark system. In Appendix, however, an alternative approach is sketched, where the diquark is described as the point limit of a very close Breit system rather than a Duffin-Kemmer particle. (Author)

Klein paradox in the Breit equation

International Nuclear Information System (INIS)

Krolikowski, W.; Turski, A.; Rzewuski, J.

1979-01-01

We demonstrate that in the Breit equation with a central potential V(r) having the property V(r 0 )=E there appears a Klein paradox at r=r 0 . This phenomenon, besides the previously found Klein paradox at r→infinite appearing if V(r)→infinite at r→infinite, seems to indicate that in the Breit equation valid in the single-particle theory the sea of particle-antiparticle pairs is not well separated from the considered two-body configuration. We conjecture that both phenomena should be absent from the Salpeter equation which is consistent with the hole theory. We prove this conjecture in the limit of m( 1 )→infinite and m( 2 )→infinite, where we neglect the terms approx. 1/m( 1 ) and 1/m( 2 ). (orig./WL) [de

Nonlinear steady-state coupling of LH waves

International Nuclear Information System (INIS)

Ko, K.; Krapchev, V.B.

1981-02-01

The coupling of lower hybrid waves at the plasma edge by a two waveguide array with self-consistent density modulation is solved numerically. For a linear density profile, the governing nonlinear Klein-Gordon equation for the electric field can be written as a system of nonlinearly modified Airy equations in Fourier k/sub z/-space. Numerical solutions to the nonlinear system satisfying radiation condition are obtained. Spectra broadening and modifications to resonance cone trajectories are observed with increase of incident power

A fractional Dirac equation and its solution

International Nuclear Information System (INIS)

Muslih, Sami I; Agrawal, Om P; Baleanu, Dumitru

2010-01-01

This paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit α → 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics.

Nonlinear wave equation with intrinsic wave particle dualism

International Nuclear Information System (INIS)

Klein, J.J.

1976-01-01

A nonlinear wave equation derived from the sine-Gordon equation is shown to possess a variety of solutions, the most interesting of which is a solution that describes a wave packet travelling with velocity usub(e) modulating a carrier wave travelling with velocity usub(c). The envelop and carrier wave speeds agree precisely with the group and phase velocities found by de Broglie for matter waves. No spreading is exhibited by the soliton, so that it behaves exactly like a particle in classical mechanics. Moreover, the classically computed energy E of the disturbance turns out to be exactly equal to the frequency ω of the carrier wave, so that the Planck relation is automatically satisfied without postulating a particle-wave dualism. (author)

New correct solutions of the Dirac equation. 5

International Nuclear Information System (INIS)

Bagrov, V.G.; Byzov, N.N.; Gitman, D.M.; Klimenko, Yu.I.; Meshkov, A.G.; Shapovalov, V.N.; Shakhmatov, V.M.

1975-01-01

Some exact solutions for the Dirac equation, Klein-Gordon equation and classical relativistic equations of motion of an electron in external electromagnetic fields of a special type are considered. When fields E vector and H vector are related by the expression H vector=[n vector E vector]+n vector H 3 , where n vector is a constant unit vector, it turns out that among fields permitting the separation of variables in the Klein-Gordon equation more than half satisfy this relationship. For such fields the solution of the Dirac equation may be simplified considerably. Four specific kinds of fields are examined. The character of electron motion in such fields is peculiar but in the mathematical aspect, part of the problem is reduced to those considered previously

Sine-Gordon Equation in (1+2 and (1+3 dimensions: Existence and Classification of Traveling-Wave Solutions.

Directory of Open Access Journals (Sweden)

Yair Zarmi

Full Text Available The (1+1-dimensional Sine-Gordon equation passes integrability tests commonly applied to nonlinear evolution equations. Its kink solutions (one-dimensional fronts are obtained by a Hirota algorithm. In higher space-dimensions, the equation does not pass these tests. Although it has been derived over the years for quite a few physical systems that have nothing to do with Special Relativity, the Sine-Gordon equation emerges as a non-linear relativistic wave equation. This opens the way for exploiting the tools of the Theory of Special Relativity. Using no more than the relativistic kinematics of tachyonic momentum vectors, from which the solutions are constructed through the Hirota algorithm, the existence and classification of N-moving-front solutions of the (1+2- and (1+3-dimensional equations for all N ≥ 1 are presented. In (1+2 dimensions, each multi-front solution propagates rigidly at one velocity. The solutions are divided into two subsets: Solutions whose velocities are lower than a limiting speed, c = 1, or are greater than or equal to c. To connect with concepts of the Theory of Special Relativity, c will be called "the speed of light." In (1+3-dimensions, multi-front solutions are characterized by spatial structure and by velocity composition. The spatial structure is either planar (rotated (1+2-dimensional solutions, or genuinely three-dimensional--branes. Planar solutions, propagate rigidly at one velocity, which is lower than, equal to, or higher than c. Branes must contain clusters of fronts whose speed exceeds c = 1. Some branes are "hybrids": different clusters of fronts propagate at different velocities. Some velocities may be lower than c but some must be equal to, or exceed, c. Finally, the speed of light cannot be approached from within the subset of slower-than-light solutions in both (1+2 and (1+3 dimensions.

Ring-shaped quasi-soliton solutions to the two-and three-dimensional Sine-Gordon equation

International Nuclear Information System (INIS)

Christiansen, P.L.; Olsen, O.H.

1979-01-01

Ring-shaped solitary wave solutions to the Sine-Gordon equation in two and three spatial dimensions are investigated by numerical computation. Each expanding wave exhibits a return effect. The reflection of the shrinking wave at the singularity at the center of the wave is investigated in a particular case. Collision experiments in numero for expanding and shrinking concentric ring waves show that the solutions possess quasisoliton properties. A Baecklund transformation for the non-symmetric three-dimensional case is given. (Auth.)

Sine-Gordon equation and its application to tectonic stress transfer

Science.gov (United States)

Bykov, Victor G.

2014-07-01

An overview is given on remarkable progress that has been made in theoretical studies of solitons and other nonlinear wave patterns, excited during the deformation of fault block (fragmented) geological media. The models that are compliant with the classical and perturbed sine-Gordon equations have only been chosen. In these mathematical models, the rotation angle of blocks (fragments) and their translatory displacement of the medium are used as dynamic variables. A brief description of the known models and their geophysical and geodynamic applications is given. These models reproduce the kinematic and dynamic features of the traveling deformation front (kink, soliton) generated in the fragmented media. It is demonstrated that the sine-Gordon equation is applicable to the description of series of the observed seismic data, modeling of strain waves, as well as the features related to fault dynamics and the subduction slab, including slow earthquakes, periodicity of episodic tremor and slow slip (ETS) events, and migration pattern of tremors. The study shows that simple heuristic models and analytical and numerical computations can explain triggering of seismicity by transient processes, such as stress changes associated with solitary strain waves in crustal faults. The need to develop the above-mentioned new (nonlinear) mathematical models of the deformed fault and fragmented media was caused by the reason that it is impossible to explain a lot of the observed effects, particularly, slow redistribution and migration of stresses in the lithosphere, within the framework of the linear elasticity theory.

Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

Science.gov (United States)

Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar

2018-05-01

The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.

A novel singular pattern in the sine-Gordon equation

International Nuclear Information System (INIS)

Huang, Debin

2003-01-01

By the scatter problem and the Backlund transformation of the sine-Gordon equation, we find a novel solution with the singularity of jumping phenomenon, which displays pattern structure similar respectively to soliton, kink, anti-kink and double pole solution with the different choice of the purely imaginary spectrum of the sine-Gordon equation

Coherence and chaos in the driven damped sine-Gordon equation: Measurement of the soliton spectrum

Energy Technology Data Exchange (ETDEWEB)

Overman, II, E A; McLaughlin, D W; Bishop, A R; Los Alamos National Lab., NM

1986-02-01

A numerical procedure is developed which measures the sine-Gordon soliton and radiation content of any field (PHI, PHIsub(t)) which is periodic in space. The procedure is applied to the field generated by a damped, driven sine-Gordon equation. This field can be either temporally periodic (locked to the driver) or chaotic. In either case the numerical measurement shows that the spatial structure can be described by only a few spatially localized (soliton wave-train) modes. The numerical procedure quantitatively identifies the presence, number and properties of these soliton wave-trains. For example, an increase of spatial symmetry is accompanied by the injection of additional solitons into the field. (orig.).

The Poisson equation on Klein surfaces

Directory of Open Access Journals (Sweden)

Monica Rosiu

2016-04-01

Full Text Available We obtain a formula for the solution of the Poisson equation with Dirichlet boundary condition on a region of a Klein surface. This formula reveals the symmetric character of the solution.

Integrable discretizations of the (2+1)-dimensional sinh-Gordon equation

International Nuclear Information System (INIS)

Hu, Xing-Biao; Yu, Guo-Fu

2007-01-01

In this paper, we propose two semi-discrete equations and one fully discrete equation and study them by Hirota's bilinear method. These equations have continuum limits into a system which admits the (2+1)-dimensional generalization of the sinh-Gordon equation. As a result, two integrable semi-discrete versions and one fully discrete version for the sinh-Gordon equation are found. Baecklund transformations, nonlinear superposition formulae, determinant solution and Lax pairs for these discrete versions are presented

The symmetries and conservation laws of some Gordon-type

Indian Academy of Sciences (India)

Conservation laws; Milne space-time; Gordon-type equations. Abstract. In this letter, the Lie point symmetries of a class of Gordon-type wave equations that arise in the Milne space-time are presented ... Pramana – Journal of Physics | News.

Relativistic Treatment of Spinless Particles Subject to a Tietz-Wei Oscillator

Institute of Scientific and Technical Information of China (English)

孙国华; 董世海

2012-01-01

The bound state solutions of the relativistic Klein-Gordon equation with the Tietz-Wei diatomic molecular potential are presented for the s wave. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived.

New exact solutions of the Dirac equation. 8

International Nuclear Information System (INIS)

Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Sukhomlin, N.B.; Shapovalov, V.N.

1978-01-01

The paper continues the investigation into the exact solutions of the Dirac, Klein-Gordon, and Lorentz equations for a charge in an external electromagnetic field. The fields studied do not allow for separation of variables in the Dirac equation, but solutions to the Dirac equation are obtained

Thermodynamic quantities for the Klein–Gordon equation

Indian Academy of Sciences (India)

We study some thermodynamic quantities for the Klein–Gordon equation with a linear plus inverselinear, scalar potential. We obtain the energy eigenvalues with the help of the quantization rule from the biconfluent Heun's equation.We use a method based on the Euler–MacLaurin formula to analytically compute thethermal ...

Invariant solutions of the supersymmetric sine-Gordon equation

International Nuclear Information System (INIS)

Grundland, A M; Hariton, A J; Snobl, L

2009-01-01

A comprehensive symmetry analysis of the N=1 supersymmetric sine-Gordon equation is performed. Two different forms of the supersymmetric system are considered. We begin by studying a system of partial differential equations corresponding to the coefficients of the various powers of the anticommuting independent variables. Next, we consider the super-sine-Gordon equation expressed in terms of a bosonic superfield involving anticommuting independent variables. In each case, a Lie (super)algebra of symmetries is determined and a classification of all subgroups having generic orbits of codimension 1 in the space of independent variables is performed. The method of symmetry reduction is systematically applied in order to derive invariant solutions of the supersymmetric model. Several types of algebraic, hyperbolic and doubly periodic solutions are obtained in explicit form.

Group-theoretical aspects of the discrete sine-Gordon equation

International Nuclear Information System (INIS)

Orfanidis, S.J.

1980-01-01

The group-theoretical interpretation of the sine-Gordon equation in terms of connection forms on fiber bundles is extended to the discrete case. Solutions of the discrete sine-Gordon equation induce surfaces on a lattice in the SU(2) group space. The inverse scattering representation, expressing the parallel transport of fibers, is implemented by means of finite rotations. Discrete Baecklund transformations are realized as gauge transformations. The three-dimensional inverse scattering representation is used to derive a discrete nonlinear sigma model, and the corresponding Baecklund transformation and Pohlmeyer's R transformation are constructed

A two-component wave equation for particles of spin 1/2 and non-zero rest mass

International Nuclear Information System (INIS)

Srivastava, T.

1981-11-01

We have discussed here the qualifications of the equation (delta 0 +sigmasup(k)deltasub(k))psi = -kappaTpsi, where deltasub(μ) is identical to delta/deltaxsup(μ), sigmasup(k) are the Pauli spin matrices, T is the linear operator which changes the sign of t, kappa=m 0 c/(h/2π) and psi a function with two components, as a suitable wave equation for a spin 1/2 particle with non-zero rest mass. We have established that both components of all its solutions satisfy the Klein-Gordon equation and that a 1-1 correspondence can be set up between its solutions and the positive energy solutions of the Dirac equation which preserves inner products (suitably defined for our case). We have then gone on to show covariance under transformations of the proper Lorentz group as also under space and time inversions and translations. Eigenfunctions of energy-momentum and spin have been explicitly found and it is shown that causality is preserved and a Green's function exists. A list appears, at the end, of points to be discussed in Part II of this paper, points which, it is hoped, will complete the acceptability of the theory. (author)

Noether's theorem and Steudel's conserved currents for the sine-Gordon equation

International Nuclear Information System (INIS)

Shadwick, W.F.

1980-01-01

A version of Noether's theorem appropriate for the extended Hamilton-Cartan formalism for regular first-order Lagrangians is proposed. Steudel's derivation of an infinite collection of conserved currents for the sine-Gordon equation is presented in this context and it is demonstrated that, as a consequence of the commutativity of the sine-Gordon Baecklund transformations, the conserved charges corresponding to these currents are in involution with respect to the natural Poisson bracket provided by the formalism. Thus one obtains the formal 'complete integrability' of the sine-Gordon equation as a consequence of the properties of the Baecklund transformation. (orig.)

On completeness and orthogonality of solutions of relativistic wave equations on zero plane

International Nuclear Information System (INIS)

Gitman, D.M.; Shakhmatov, V.M.; Shvartsman, Sh.M.

1975-01-01

The work considers the possible redeterminations of the scalar product for the relativistic wave fields, such as the Klein-Gordon and Dirac ones. It has been shown that a whole class of new exact solutions, for which the usual scalar product on the plane x 0 =const. could not be previously determinated, allows a correct scalar product on the zero plane x 0 -x 3 =const. The relations of orthogonality and completeness with respect to the above scalar product have been proved. Possible applications of the obtained results are discussed

Finite temperature Casimir effect for a massless fractional Klein-Gordon field with fractional Neumann conditions

International Nuclear Information System (INIS)

Eab, C. H.; Lim, S. C.; Teo, L. P.

2007-01-01

This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the field is introduced. The fractional Neumann condition allows the interpolation of Dirichlet and Neumann conditions imposed on the two plates. There exists a transition value in the difference between the orders of the fractional Neumann conditions for which the Casimir force changes from attractive to repulsive. Low and high temperature limits of Casimir energy and pressure are obtained. For sufficiently high temperature, these quantities are dominated by terms independent of the boundary conditions. Finally, validity of the temperature inversion symmetry for various boundary conditions is discussed

Solutions of the finite type of Sine-Gordon equation

International Nuclear Information System (INIS)

Zhao Guosong

1998-01-01

We use the technique of differential geometry to prove that the solutions of finite type of the sine-Gordon equation φ xx - φ yy = sin φ cosφ can be obtained from a system of ordinary differential equations

Lectures on nonlinear evolution equations initial value problems

CERN Document Server

Racke, Reinhard

2015-01-01

This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...

Asymptotic study and numerical simulation of laser wave propagation in an inhomogeneous medium; Etude asymptotique et simulation numerique de la propagation laser en milieu inhomogene

Energy Technology Data Exchange (ETDEWEB)

Doumic, M

2005-05-15

To simulate the propagation of a monochromatic laser beam in a medium, we use the paraxial approximation of the Klein-Gordon (in the time-varying problem) and of the Maxwell (in the non time-depending case) equations. In a first part, we make an asymptotic analysis of the Klein-Gordon equation. We obtain approximated problems, either of Schroedinger or of transport-Schroedinger type. We prove the existence and uniqueness of a solution for these problems, and estimate the difference between it and the exact solution of the Klein-Gordon equation. In a second part, we study the boundary problem for the advection Schroedinger equation, and show what the boundary condition must be so that the problem on our domain should be the restriction of the problem in the whole space: such a condition is called a transparent or an absorbing boundary condition. In a third part, we use the preceding results to build a numerical resolution method, for which we prove stability and show some simulations. (author)

Exact solutions to some modified sine-Gordon equations

International Nuclear Information System (INIS)

Saermark, K.

1983-01-01

Exact, translational solutions to a number of modified sine-Gordon equations are presented. In deriving the equations and the solutions use is made of results from the theory of ordinary differential equations without moving critical points as given by Ince. It is found that kink-like solutions exist also in cases where the coefficients of the trigonometric terms are space- and time-dependent. (Auth.)

Heun equation in a 5D sine-Gordon brane-world model with dilaton

International Nuclear Information System (INIS)

Cunha, M.S.; Christiansen, H.

2011-01-01

Full text: In a brane-world scenario we find the propagation modes of the gauge field in a five-dimensional space-time. We adopt warping factors of the Randall-Sundrum type which are appropriate to regularize the hierarchy problem without imposing finite compactified extra dimensions. The existence and localization of gauge particles in the ordinary four-dimensional world is studied in detail on a thick brane derived out from the equations of motion of an action with a sine-Gordon potential contribution. Maxwell zero modes together with torsion effective fields are then obtained in a gravity-dilaton background inspired in close string theories. The dilaton plays a crucial role in order that the gauge field gets localized in a conformally invariant context. Kaluza-Klein massive states are also computed and, depending on certain parameters like dilaton coupling constant and asymptotic curvature, we are able to do it fully analytically. In a general approach we find that the solutions are of the Heun type. In some specific cases we can show that the Heun general solutions can be transformed into hypergeometric functions. In others, confluent Heun solutions can be transformed into simpler functions like Mathieu functions. Exact mass spectra are found in several cases. In others, we performed numerical calculations that show a well behaved phenomenology as well. In all the cases, Kaluza-Klein modes are strongly suppressed on the brane in the effective four-dimensional theory. (author)

The elliptic sine-Gordon equation in a half plane

International Nuclear Information System (INIS)

Pelloni, B; Pinotsis, D A

2010-01-01

We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane y > 0. This problem was considered in Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) using the classical inverse scattering transform approach. Given the limitations of this approach, the results obtained rely on a nonlinear constraint on the spectral data derived heuristically by analogy with the linearized case. We revisit the analysis of such problems using a recent generalization of the inverse scattering transform known as the Fokas method, and show that the nonlinear constraint of Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) is a consequence of the so-called global relation. We also show that this relation implies a stronger constraint on the spectral data, and in particular that no choice of boundary conditions can be associated with a decaying (possibly mod 2π) solution analogous to the pure soliton solutions of the usual, time-dependent sine-Gordon equation. We also briefly indicate how, in contrast to the evolutionary case, the elliptic sine-Gordon equation posed in the half plane does not admit linearisable boundary conditions

Nonlinear de Broglie waves and the relation between relativistic and nonrelativistic solitons

International Nuclear Information System (INIS)

Barut, A.O.; Baby, B.V.

1988-07-01

It is shown that the well-known envelope soliton and kink solutions of the nonlinear Schroedinger equation are the nonrelativistic limit of the corresponding solutions of the nonlinear Klein-Gordon equation. 34 refs

Supergroup extensions: from central charges to quantization through relativistic wave equations

International Nuclear Information System (INIS)

Aldaya, V.; Azcarraga, J.A. de.

1982-07-01

We give in this paper the finite group law of a family of supergroups including the U(1)-extended N=2 super-Poincare group. From this family of supergroups, and by means of a canonical procedure, we are able to derive the Klein-Gordon and Dirac equations for the fields contained in the superfield. In the process, the physical content of the central charge as the mass parameter and the role of covariant derivatives are shown to come out canonically from the group structure, and the U(1)-extended supersymmetry is seen as necessary for the geometric quantization of the relativistic elementary systems. (author)

Numerical search for a Phi4 breather mode and study of the Phi4, sine-Gordon, and Kdv equations with adibatic coefficients

International Nuclear Information System (INIS)

Wingate, C.A.

1978-01-01

Two major problems are studied in this thesis. The first is a numerical search for a stable oscillating mode in the Phi4 equation similar to the one that is known for the sine-Gordon equation. Starting with a widely separated soliton and anti-soliton traveling toward each other, it is observed, after a long period of time (t = 2800), that the solitons form a quasistable oscillating state. An interesting, previously unknown structure in the interaction depending on the initial velocity and initial separation is found and studied in detail. The second topic covered here is a study of the phi4, KdV and sine-Gordon equations when the coefficients vary slowly with time. A general first order solution is found for the wave equation with a non-linear potential and is applied to the phi4 and sine-Gordon potentials. In doing this it is found that the conservation of momentum is equivalent order by order to the secular conditions. Deficiencies in existing calculations for the KdV equation are pointed out through the use of adiabatic invariants and numerical calculations

Stability and Instability of the Sub-extremal Reissner-Nordström Black Hole Interior for the Einstein-Maxwell-Klein-Gordon Equations in Spherical Symmetry

Science.gov (United States)

Van de Moortel, Maxime

2018-05-01

We show non-linear stability and instability results in spherical symmetry for the interior of a charged black hole—approaching a sub-extremal Reissner-Nordström background fast enough—in presence of a massive and charged scalar field, motivated by the strong cosmic censorship conjecture in that setting: 1. Stability We prove that spherically symmetric characteristic initial data to the Einstein-Maxwell-Klein-Gordon equations approaching a Reissner-Nordström background with a sufficiently decaying polynomial decay rate on the event horizon gives rise to a space-time possessing a Cauchy horizon in a neighbourhood of time-like infinity. Moreover, if the decay is even stronger, we prove that the space-time metric admits a continuous extension to the Cauchy horizon. This generalizes the celebrated stability result of Dafermos for Einstein-Maxwell-real-scalar-field in spherical symmetry. 2. Instability We prove that for the class of space-times considered in the stability part, whose scalar field in addition obeys a polynomial averaged- L 2 (consistent) lower bound on the event horizon, the scalar field obeys an integrated lower bound transversally to the Cauchy horizon. As a consequence we prove that the non-degenerate energy is infinite on any null surface crossing the Cauchy horizon and the curvature of a geodesic vector field blows up at the Cauchy horizon near time-like infinity. This generalizes an instability result due to Luk and Oh for Einstein-Maxwell-real-scalar-field in spherical symmetry. This instability of the black hole interior can also be viewed as a step towards the resolution of the C 2 strong cosmic censorship conjecture for one-ended asymptotically flat initial data.

Thermodynamic quantities for the Klein–Gordon equation with a ...

Indian Academy of Sciences (India)

2017-02-01

Feb 1, 2017 ... Abstract. We study some thermodynamic quantities for the Klein–Gordon equation with a linear plus inverse- linear, scalar potential. We obtain the energy eigenvalues with the help of the quantization rule from the biconfluent Heun's equation. We use a method based on the Euler–MacLaurin formula to ...

Generalized nonlinear Proca equation and its free-particle solutions

Energy Technology Data Exchange (ETDEWEB)

Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)

2016-06-15

We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)

TBA equations for excited states in the sine-Gordon model

International Nuclear Information System (INIS)

Balog, Janos; Hegedus, Arpad

2004-01-01

We propose thermodynamic Bethe ansatz (TBA) integral equations for multi-particle soliton (fermion) states in the sine-Gordon (massive Thirring) model. This is based on T-system and Y-system equations, which follow from the Bethe ansatz solution in the light-cone lattice formulation of the model. Even and odd charge sectors are treated on an equal footing, corresponding to periodic and twisted boundary conditions, respectively. The analytic properties of the Y-system functions are conjectured on the basis of the large volume solution of the system, which we find explicitly. A simple relation between the TBA Y-functions and the counting function variable of the alternative non-linear integral equation (Destri-de Vega equation) description of the model is given. At the special value β 2 = 6π of the sine-Gordon coupling, exact expressions for energy and momentum eigenvalues of one-particle states are found

Semiclassical approach to the quantization of the periodic solutions of the sine-Gordon equation

International Nuclear Information System (INIS)

Ghika, G.; Visinescu, M.

1978-01-01

The periodic solutions of the sine-Gordon equation are proved to be singular. For the semiclassical quantization of the periodic solutions we calculate the fluctuations around them and we use the path integrals in the Gaussian approximation in order to obtain the bound states of the sine-Gordon field equation. (author)

A note on the three dimensional sine--Gordon equation

OpenAIRE

Shariati, Ahmad

1996-01-01

Using a simple ansatz for the solutions of the three dimensional generalization of the sine--Gordon and Toda model introduced by Konopelchenko and Rogers, a class of solutions is found by elementary methods. It is also shown that these equations are not evolution equations in the sense that solution to the initial value problem is not unique.

New exact solutions of the Dirac equation

International Nuclear Information System (INIS)

Bagrov, V.G.; Gitman, D.M.; Zadorozhnyj, V.N.; Lavrov, P.M.; Shapovalov, V.N.

1980-01-01

Search for new exact solutions of the Dirac and Klein-Gordon equations are in progress. Considered are general properties of the Dirac equation solutions for an electron in a purely magnetic field, in combination with a longitudinal magnetic and transverse electric fields. New solutions for the equations of charge motion in an electromagnetic field of axial symmetry and in a nonstationary field of a special form have been found for potentials selected concretely

Separation Transformation and New Exact Solutions of the (N + 1)-dimensional Dispersive Double sine-Gordon Equation

International Nuclear Information System (INIS)

Tian Ye; Chen Jing; Zhang Zhifei

2012-01-01

In this paper, the separation transformation approach is extended to the (N + 1)-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of 3 He superfluid. This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation. Then the general solutions of the set of partial differential equations are obtained and the nonlinear ordinary differential equation is solved by F-expansion method. Finally, many new exact solutions of the (N + 1)-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation. For the case of N > 2, there is an arbitrary function in the exact solutions, which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.

Rotationally symmetric breather-like solutions to the sine-Gordon equation

International Nuclear Information System (INIS)

Olsen, O.H.; Samuelsen, M.R.

1980-01-01

Breather-like solutions to the spherically symmetric sine-Gordon equation are examined numerically. Depending on the initial conditions they either exhibit a return effect or expand towards infinity. (orig.)

Perturbation analysis of a parametrically changed sine-Gordon equation

DEFF Research Database (Denmark)

Sakai, S.; Samuelsen, Mogens Rugholm; Olsen, O. H.

1987-01-01

A long Josephson junction with a spatially varying inductance is a physical manifestation of a modified sine-Gordon equation with parametric perturbation. Soliton propagation in such Josephson junctions is discussed. First, for an adiabatic model where the inductance changes smoothly compared...

Low-mode truncation methods in the sine-Gordon equation

International Nuclear Information System (INIS)

Xiong Chuyu.

1991-01-01

In this dissertation, the author studies the chaotic and coherent motions (i.e., low-dimensional chaotic attractor) in some near integrable partial differential equations, particularly the sine-Gordon equation and the nonlinear Schroedinger equation. In order to study the motions, he uses low mode truncation methods to reduce these partial differential equations to some truncated models (low-dimensional ordinary differential equations). By applying many methods available to low-dimensional ordinary differential equations, he can understand the low-dimensional chaotic attractor of PDE's much better. However, there are two important questions one needs to answer: (1) How many modes is good enough for the low mode truncated models to capture the dynamics uniformly? (2) Is the chaotic attractor in a low mode truncated model close to the chaotic attractor in the original PDE? And how close is? He has developed two groups of powerful methods to help to answer these two questions. They are the computation methods of continuation and local bifurcation, and local Lyapunov exponents and Lyapunov exponents. Using these methods, he concludes that the 2N-nls ODE is a good model for the sine-Gordon equation and the nonlinear Schroedinger equation provided one chooses a 'good' basis and uses 'enough' modes (where 'enough' depends on the parameters of the system but is small for the parameter studied here). Therefore, one can use 2N-nls ODE to study the chaos of PDE's in more depth

Relativistic quantum mechanics and introduction to field theory

Energy Technology Data Exchange (ETDEWEB)

Yndurain, F.J. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica

1996-12-01

The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources.

Relativistic quantum mechanics and introduction to field theory

International Nuclear Information System (INIS)

Yndurain, F.J.

1996-01-01

The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources

Continuous dimensions and evanescent couplings

International Nuclear Information System (INIS)

Bollini, C.G.; Giambiagi, J.J.

1975-01-01

Analytical solutions for the wave equation in many dimensional calculation, are given. The difference for even or odd number of dimensions is shown. The simplest cases of the lowest order divergent diagrams (self-energy, vacuum polarization) are discussed. Causal solution of Klein-Gordon equation is used [pt

On Darboux transformation of the supersymmetric sine-Gordon equation

International Nuclear Information System (INIS)

Siddiq, M; Hassan, M; Saleem, U

2006-01-01

Darboux transformation is constructed for superfields of the super sine-Gordon equation and the superfields of the associated linear problem. The Darboux transformation is shown to be related to the super Baecklund transformation and is further used to obtain N super soliton solutions

Homoclinic tubes and chaos in perturbed sine-Gordon equation

International Nuclear Information System (INIS)

Li, Y. Charles

2004-01-01

Sine-Gordon equation under a quasi-periodic perturbation or a chaotic perturbation is studied. Existence of a homoclinic tube is proved. Established are chaos associated with the homoclinic tube, and 'chaos cascade' referring to the embeddings of smaller scale chaos in larger scale chaos

Darboux Transformations for Energy-Dependent Potentials and the Klein–Gordon Equation

International Nuclear Information System (INIS)

Schulze-Halberg, Axel

2013-01-01

We construct explicit Darboux transformations for a generalized Schrödinger-type equation with energy-dependent potential, a special case of which is the stationary Klein–Gordon equation. Our results complement and generalize former findings (Lin et al., Phys Lett A 362:212–214, 2007).

Sine-Gordon equation as a model of a nonlinear scalar field in the Duffin-Kemmer formalism

International Nuclear Information System (INIS)

Getmanov, B.S.

1980-01-01

The nonlinear self-interaction of a scalar field is studied in the Minkowski space-time of an arbitrary dimension. It is shown that the sine-Gordon equation can be considered as a model of the nonlinear scalar field in the Duffin-Kemmer formalism with a specific kind of nonlinearity. The ''V-A'' type interaction is found to be equivalent to the ''complex sine-Gordon'' model. Such a new formation of the sine-Gordon equation might be useful for search for its integrable generalizations

Exact Solutions to a Combined sinh-cosh-Gordon Equation

International Nuclear Information System (INIS)

Wei Long

2010-01-01

Based on a transformed Painleve property and the variable separated ODE method, a function transformation method is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleve property and reduce the given PDEs to a variable-coefficient ordinary differential equations, then we seek for solutions to the resulting equations by some methods. As an application, exact solutions for the combined sinh-cosh-Gordon equation are formally derived. (general)

The (2+1)-dimensional axial universes—solutions to the Einstein equations, dimensional reduction points and Klein–Fock–Gordon waves

International Nuclear Information System (INIS)

Fiziev, P P; Shirkov, D V

2012-01-01

The paper presents a generalization and further development of our recent publications, where solutions of the Klein–Fock–Gordon equation defined on a few particular D = (2 + 1)-dimensional static spacetime manifolds were considered. The latter involve toy models of two-dimensional spaces with axial symmetry, including dimensional reduction to the one-dimensional space as a singular limiting case. Here, the non-static models of space geometry with axial symmetry are under consideration. To make these models closer to physical reality, we define a set of ‘admissible’ shape functions ρ(t, z) as the (2 + 1)-dimensional Einstein equation solutions in the vacuum spacetime, in the presence of the Λ-term and for the spacetime filled with the standard ‘dust’. It is curious that in the last case the Einstein equations reduce to the well-known Monge–Ampère equation, thus enabling one to obtain the general solution of the Cauchy problem, as well as a set of other specific solutions involving one arbitrary function. A few explicit solutions of the Klein–Fock–Gordon equation in this set are given. An interesting qualitative feature of these solutions relates to the dimensional reduction points, their classification and time behavior. In particular, these new entities could provide us with novel insight into the nature of P- and T-violations and of the Big Bang. A short comparison with other attempts to utilize the dimensional reduction of the spacetime is given. (paper)

Higher order field equations. II

International Nuclear Information System (INIS)

Tolhoek, H.A.

1977-01-01

In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for mod(M)→infinity the Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) approach the Green's functions Δsub(R)(x) and Δsub(A)(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) is the same as of Δsub(R)(x) and Δsub(A)(x)-and also the same as for Dsub(R)(x) and Dsub(A)(x) for t→+-infinity;, where Dsub(R) and Dsub(A) are the Green's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense. (Auth.)

Generalized sine-Gordon solitons

International Nuclear Information System (INIS)

Santos, C dos; Rubiera-Garcia, D

2011-01-01

In this paper, we construct analytical self-dual soliton solutions in (1+1) dimensions for two families of models which can be seen as generalizations of the sine-Gordon system but where the kinetic term is non-canonical. For that purpose we use a projection method applied to the sine-Gordon soliton. We focus our attention on the wall and lump-like soliton solutions of these k-field models. These solutions and their potentials reduce to those of the Klein-Gordon kink and the standard lump for the case of a canonical kinetic term. As we increase the nonlinearity on the kinetic term the corresponding potentials get modified and the nature of the soliton may change, in particular, undergoing a topology modification. The procedure constructed here is shown to be a sort of generalization of the deformation method for a specific class of k-field models. (paper)

Effective evolution equations from quantum mechanics

OpenAIRE

Leopold, Nikolai

2018-01-01

The goal of this thesis is to provide a mathematical rigorous derivation of the Schrödinger-Klein-Gordon equations, the Maxwell-Schrödinger equations and the defocusing cubic nonlinear Schrödinger equation in two dimensions. We study the time evolution of the Nelson model (with ultraviolet cutoff) in a limit where the number N of charged particles gets large while the coupling of each particle to the radiation field is of order N^{−1/2}. At time zero it is assumed that almost all charges a...

The gravitational Schwinger effect and attenuation of gravitational waves

Science.gov (United States)

McDougall, Patrick Guarneri

This paper will discuss the possible production of photons from gravitational waves. This process is shown to be possible by examining Feynman diagrams, the Schwinger Effect, and Hawking Radiation. The end goal of this project is to find the decay length of a gravitational wave and assert that this decay is due to photons being created at the expense of the gravitational wave. To do this, we first find the state function using the Klein Gordon equation, then find the current due to this state function. We then take the current to be directly proportional to the production rate per volume. This is then used to find the decay length that this kind of production would produce, gives a prediction of how this effect will change the distance an event creating a gravitational wave will be located, and shows that this effect is small but can be significant near the source of a gravitational wave.

Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method

Directory of Open Access Journals (Sweden)

A. A. Hemeda

2013-01-01

Full Text Available An extension of the so-called new iterative method (NIM has been used to handle linear and nonlinear fractional partial differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation, and fractional Boussinesq-like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with those obtained by both Adomian decomposition method (ADM and the variational iteration method (VIM reveals that the NIM is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus.

Multiphase averaging of periodic soliton equations

International Nuclear Information System (INIS)

Forest, M.G.

1979-01-01

The multiphase averaging of periodic soliton equations is considered. Particular attention is given to the periodic sine-Gordon and Korteweg-deVries (KdV) equations. The periodic sine-Gordon equation and its associated inverse spectral theory are analyzed, including a discussion of the spectral representations of exact, N-phase sine-Gordon solutions. The emphasis is on physical characteristics of the periodic waves, with a motivation from the well-known whole-line solitons. A canonical Hamiltonian approach for the modulational theory of N-phase waves is prescribed. A concrete illustration of this averaging method is provided with the periodic sine-Gordon equation; explicit averaging results are given only for the N = 1 case, laying a foundation for a more thorough treatment of the general N-phase problem. For the KdV equation, very general results are given for multiphase averaging of the N-phase waves. The single-phase results of Whitham are extended to general N phases, and more importantly, an invariant representation in terms of Abelian differentials on a Riemann surface is provided. Several consequences of this invariant representation are deduced, including strong evidence for the Hamiltonian structure of N-phase modulational equations

Alternatives to the Dirac equation

International Nuclear Information System (INIS)

Girvin, S.M.; Brownstein, K.R.

1975-01-01

Recent work by Biedenharn, Han, and van Dam (BHvD) has questioned the uniqueness of the Dirac equation. BHvD have obtained a two-component equation as an alternate to the Dirac equation. Although they later show their alternative to be unitarily equivalent to the Dirac equation, certain physical differences were claimed. BHvD attribute the existence of this alternate equation to the fact that their factorizing matrices were position-dependent. To investigate this, we factor the Klein-Gordon equation in spherical coordinates allowing the factorizing matrices to depend arbitrarily upon theta and phi. It is shown that despite this additional freedom, and without involving any relativistic covariance, the conventional four-component Dirac equation is the only possibility

Nonminimally coupled scalar fields may not curve spacetime

International Nuclear Information System (INIS)

Ayon-Beato, Eloy; Martinez, Cristian; Troncoso, Ricardo; Zanelli, Jorge

2005-01-01

It is shown that flat spacetime can be dressed with a real scalar field that satisfies the nonlinear Klein-Gordon equation without curving spacetime. Surprisingly, this possibility arises from the nonminimal coupling of the scalar field with the curvature, since a footprint of the coupling remains in the energy-momentum tensor even when gravity is switched off. Requiring the existence of solutions with vanishing energy-momentum tensor fixes the self-interaction potential as a local function of the scalar field depending on two coupling constants. The solutions describe shock waves and, in the Euclidean continuation, instanton configurations in any dimension. As a consequence of this effect, the tachyonic solutions of the free massive Klein-Gordon equation become part of the vacuum

Logical inference approach to relativistic quantum mechanics: Derivation of the Klein–Gordon equation

International Nuclear Information System (INIS)

Donker, H.C.; Katsnelson, M.I.; De Raedt, H.; Michielsen, K.

2016-01-01

The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein–Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space–time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds. - Highlights: • Logical inference applied to relativistic, massive, charged, and spinless particle experiments leads to the Klein–Gordon equation. • The relativistic Hamilton–Jacobi is scrutinized by employing a field description for the four-velocity. • Logical inference allows analysis of experiments with uncertainty in detection events and experimental conditions.

Generating Solutions to Discrete sine-Gordon Equation from Modified Baecklund Transformation

International Nuclear Information System (INIS)

Kou Xin; Zhang Dajun; Shi Ying; Zhao Songlin

2011-01-01

We modify the bilinear Baecklund transformation for the discrete sine-Gordon equation and derive variety, of solutions by freely choosing parameters from the modified Baecklund transformation. Dynamics of solutions and continuum limits are also discussed. (general)

Correlations between chaos in a perturbed sine-Gordon equation and a truncated model system

International Nuclear Information System (INIS)

Bishop, A.R.; Flesch, R.; Forests, M.G.; Overman, E.A.

1990-01-01

The purpose of this paper is to present a first step toward providing coordinates and associated dynamics for low-dimensional attractors in nearly integrable partial differential equations (pdes), in particular, where the truncated system reflects salient geometric properties of the pde. This is achieved by correlating: (1) numerical results on the bifurcations to temporal chaos with spatial coherence of the damped, periodically forced sine-Gordon equation with periodic boundary conditions; (2) an interpretation of the spatial and temporal bifurcation structures of this perturbed integrable system with regard to the exact structure of the sine-Gordon phase space; (3) a model dynamical systems problem, which is itself a perturbed integrable Hamiltonian system, derived from the perturbed sine-Gordon equation by a finite mode Fourier truncation in the nonlinear Schroedinger limit; and (4) the bifurcations to chaos in the truncated phase space. In particular, a potential source of chaos in both the pde and the model ordinary differential equation systems is focused on: the existence of homoclinic orbits in the unperturbed integrable phase space and their continuation in the perturbed problem. The evidence presented here supports the thesis that the chaotic attractors of the weakly perturbed periodic sine-Gordon system consists of low-dimensional metastable attacking states together with intermediate states that are O(1) unstable and correspond to homoclinic states in the integrable phase space. It is surmised that the chaotic dynamics on these attractors is due to the perturbation of these homocline integrable configurations

Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with a soft on-site potential.

Science.gov (United States)

Yang, Linlin; Li, Nianbei; Li, Baowen

2014-12-01

The temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential (soft-KG) are investigated systematically. Similarly to the previously studied hard-KG lattices, the existence of renormalized phonons is also confirmed in soft-KG lattices. In particular, the temperature dependence of the renormalized phonon frequency predicted by a classical field theory is verified by detailed numerical simulations. However, the thermal conductivities of soft-KG lattices exhibit the opposite trend in temperature dependence in comparison with those of hard-KG lattices. The interesting thing is that the temperature-dependent thermal conductivities of both soft- and hard-KG lattices can be interpreted in the same framework of effective phonon theory. According to the effective phonon theory, the exponents of the power-law dependence of the thermal conductivities as a function of temperature are only determined by the exponents of the soft or hard on-site potentials. These theoretical predictions are consistently verified very well by extensive numerical simulations.

Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with a soft on-site potential

Science.gov (United States)

Yang, Linlin; Li, Nianbei; Li, Baowen

2014-12-01

The temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential (soft-KG) are investigated systematically. Similarly to the previously studied hard-KG lattices, the existence of renormalized phonons is also confirmed in soft-KG lattices. In particular, the temperature dependence of the renormalized phonon frequency predicted by a classical field theory is verified by detailed numerical simulations. However, the thermal conductivities of soft-KG lattices exhibit the opposite trend in temperature dependence in comparison with those of hard-KG lattices. The interesting thing is that the temperature-dependent thermal conductivities of both soft- and hard-KG lattices can be interpreted in the same framework of effective phonon theory. According to the effective phonon theory, the exponents of the power-law dependence of the thermal conductivities as a function of temperature are only determined by the exponents of the soft or hard on-site potentials. These theoretical predictions are consistently verified very well by extensive numerical simulations.

The wave properties of matter and the zeropoint radiation field

International Nuclear Information System (INIS)

Pena, L. de la; Cetto, A.M.

1994-01-01

The origin of the wave properties of matter is discussed from the point of view of stochastic electrodynamics. A nonrelativistic model of a changed particle with an effective structure embedded in the random zeropoint radiation field reveals that the field induces a high-frequency vibration on the particle; internal consistency of the theory fixes the frequency of this jittering at mc 2 /h. The particle is therefore assumed to interact intensely with stationary zeropoint waves of this frequency as seen from its proper frame of reference; such waves, identified here as de Broglie's phase waves, give rise to a modulated wave in the laboratory frame, with de Broglie's wavelength and phase velocity equal to the particle velocity. The time-independent equation that describes this modulated wave is shown to be the stationary Schroedinger equation (or the Klein-Gordon equation in the relativistic version). In a heuristic analysis applied to simple periodic cases, the quantization rules are recovered from the assumption that for a particle in a stationary state there must correspond a stationary modulation. Along an independent and complementary line of reasoning, an equation for the probability amplitude in configuration space for a particle under a general potential V(x) is constructed, and it is shown that under conditions derived from stochastic electrodynamics it reduces to Schroedinger's equation. This equation reflects therefore the dual nature of the quantum particles, by describing simultaneously the corresponding modulated wave and the ensemble of particles

Exact eigenstates and open-quotes trivialityclose quotes of λ(var-phi *var-phi)2 theory in the Feshbach-Villars formulation

International Nuclear Information System (INIS)

Darewych, J.W.

1997-01-01

The complex scalar (Klein-Gordon) quantum field theory (QFT) with a λ(var-phi * var-phi) 2 interaction is considered in the Feshbach-Villars formulation. It is shown that exact few-particle eigenstates of the QFT Hamiltonian can be obtained. The resulting relativistic few-body equations correspond to Klein-Gordon particles interacting via delta-function, or open-quotes contact,close quotes potentials. Momentum-space solutions of the two-body equation yield a open-quotes trivialclose quotes unity S matrix. copyright 1997 The American Physical Society

EPR and Klein Paradoxes in Complex Hamiltonian Dynamics and Krein Space Quantization

International Nuclear Information System (INIS)

Payandeh, Farrin

2015-01-01

Negative energy states are applied in Krein space quantization approach to achieve a naturally renormalized theory. For example, this theory by taking the full set of Dirac solutions, could be able to remove the propagator Green function's divergences and automatically without any normal ordering, to vanish the expected value for vacuum state energy. However, since it is a purely mathematical theory, the results are under debate and some efforts are devoted to include more physics in the concept. Whereas Krein quantization is a pure mathematical approach, complex quantum Hamiltonian dynamics is based on strong foundations of Hamilton-Jacobi (H-J) equations and therefore on classical dynamics. Based on complex quantum Hamilton-Jacobi theory, complex spacetime is a natural consequence of including quantum effects in the relativistic mechanics, and is a bridge connecting the causality in special relativity and the non-locality in quantum mechanics, i.e. extending special relativity to the complex domain leads to relativistic quantum mechanics. So that, considering both relativistic and quantum effects, the Klein-Gordon equation could be derived as a special form of the Hamilton-Jacobi equation. Characterizing the complex time involved in an entangled energy state and writing the general form of energy considering quantum potential, two sets of positive and negative energies will be realized. The new states enable us to study the spacetime in a relativistic entangled “space-time” state leading to 12 extra wave functions than the four solutions of Dirac equation for a free particle. Arguing the entanglement of particle and antiparticle leads to a contradiction with experiments. So, in order to correct the results, along with a previous investigation [1], we realize particles and antiparticles as physical entities with positive energy instead of considering antiparticles with negative energy. As an application of modified descriptions for entangled (space

Sine-Gordon breather form factors and quantum field equations

International Nuclear Information System (INIS)

Babujian, H; Karowski, M

2002-01-01

Using the results of previous investigations on sine-Gordon form factors, exact expressions of all breather matrix elements are obtained for several operators: all powers of the fundamental Bose field, general exponentials of it, the energy-momentum tensor and all higher currents. Formulae for the asymptotic behaviour of bosonic form factors are presented which are motivated by Weinberg's power counting theorem in perturbation theory. It is found that the quantum sine-Gordon field equation holds, and an exact relation between the 'bare' mass and the renormalized mass is obtained. Also a quantum version of a classical relation for the trace of the energy-momentum is proved. The eigenvalue problem for all higher conserved charges is solved. All results are compared with perturbative Feynman graph expansions and full agreement is found

Approximate treatment of two soliton solutions of the sine-Gordon equation

International Nuclear Information System (INIS)

Mihaly, L.

1979-05-01

The so called breather solution of the sine-Gordon equation is phenomenologically described by an appropri.ately choosen potential acting between two particles. For some applications the method proves to be equivalent to other classical and quantum calculations. (author)

Solution of Duffin-Kemmer-Petiau equations for finite and infinite square well potential

International Nuclear Information System (INIS)

Boztosun, I.; Taskin, F.; Burtebayev, N.

2002-01-01

The solution of the Duffin-Kemmer-Petiau relativistic equation for spinless boson in a central field has a long standing problem and the mathematical difficulty in attempting to reach the solution even for simple problems has caused the use this equation to be regarded as quite unattractive among scientists. In this paper we first derive the system of the first-order coupled differential equation which enable the energy eigenvalues to be evaluated and show that these equations can be reduced to the second-order Schroedinger type radial differential equation. We then consider some of the properties of this equation, which are needed for practical calculations, and show that using this the second-order radial equation, the physical observables can be found in a very simple way. As an example, we consider a pionic atoms in the finite and infinite square-well potentials and calculate the eigen-energies as well as the wave functions using the relativistic Duffin-Kemmer-Petiau equation. We show that our findings are in excellent agreement with the results of the Klein-Gordon equation

Relativistic quantum motion of spin-0 particles under the influence of noninertial effects in the cosmic string spacetime

Energy Technology Data Exchange (ETDEWEB)

Santos, L.C.N.; Barros, C.C. [Universidade Federal de Santa Catarina, Dept. de Fisica - CFM, Florianopolis, SC (Brazil)

2018-01-15

We study solutions for the Klein-Gordon equation with vector and scalar potentials of the Coulomb types under the influence of noninertial effects in the cosmic string spacetime. We also investigate a quantum particle described by the Klein-Gordon oscillator in the background spacetime generated by a cosmic string. An important result obtained is that the noninertial effects restrict the physical region of the spacetime where the particle can be placed. In addition, we show that these potentials can form bound states for the Klein-Gordon equation in this kind of background. (orig.)

Arbitrarily large numbers of kink internal modes in inhomogeneous sine-Gordon equations

Energy Technology Data Exchange (ETDEWEB)

González, J.A., E-mail: jalbertgonz@yahoo.es [Department of Physics, Florida International University, Miami, FL 33199 (United States); Department of Natural Sciences, Miami Dade College, 627 SW 27th Ave., Miami, FL 33135 (United States); Bellorín, A., E-mail: alberto.bellorin@ucv.ve [Escuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, Apartado Postal 47586, Caracas 1041-A (Venezuela, Bolivarian Republic of); García-Ñustes, M.A., E-mail: monica.garcia@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059 (Chile); Guerrero, L.E., E-mail: lguerre@usb.ve [Departamento de Física, Universidad Simón Bolívar, Apartado Postal 89000, Caracas 1080-A (Venezuela, Bolivarian Republic of); Jiménez, S., E-mail: s.jimenez@upm.es [Departamento de Matemática Aplicada a las TT.II., E.T.S.I. Telecomunicación, Universidad Politécnica de Madrid, 28040-Madrid (Spain); Vázquez, L., E-mail: lvazquez@fdi.ucm.es [Departamento de Matemática Aplicada, Facultad de Informática, Universidad Complutense de Madrid, 28040-Madrid (Spain)

2017-06-28

We prove analytically the existence of an infinite number of internal (shape) modes of sine-Gordon solitons in the presence of some inhomogeneous long-range forces, provided some conditions are satisfied. - Highlights: • We have found exact kink solutions to the perturbed sine-Gordon equation. • We have been able to study analytically the kink stability problem. • A kink equilibrated by an exponentially-localized perturbation has a finite number of oscillation modes. • A sufficiently broad equilibrating perturbation supports an infinite number of soliton internal modes.

Geometry of Kaluza-Klein theory. II. Field equations

International Nuclear Information System (INIS)

Maia, M.D.

1985-01-01

In the preceding paper a geometric formulation of Kaluza-Klein theory was presented with the basic assumption that the space-time is locally and isometrically embedded in the high-dimensional space which emerged at the big bang. In the present note the Gauss-Codazzi-Ricci equations which are the integrability equations for the embedding are interpreted as the dynamical equations for a low-energy observer. The second quadratic form which results from the embedding is interpreted as a fundamental spin-two massless field. The dynamics for an observer with high-energy probes is described as usual by the Einstein-Hilbert action defined in the high-dimensional space and dimensionally reduced by integration over the internal space. The behavior of fermion masses under different gravitational field strengths is implemented by use of the mass operator defined with the second-order Casimir operator of the embedding symmetry group

Scattering of quantized solitary waves in the cubic Schrodinger equation

International Nuclear Information System (INIS)

Dolan, L.

1976-01-01

The quantum mechanics for N particles interacting via a delta-function potential in one space dimension and one time dimension is known. The second-quantized description of this system has for its Euler-Lagrange equations of motion the cubic Schrodinger equation. This nonlinear differential equation supports solitary wave solutions. A quantization of these solitons reproduces the weak-coupling limit to the known quantum mechanics. The phase shift for two-body scattering and the energy of the N-body bound state is derived in this approximation. The nonlinear Schrodinger equation is contrasted with the sine-Gordon theory in respect to the ideas which the classical solutions play in the description of the quantum states

Observation problems posed for the Klein-Gordon equation

Directory of Open Access Journals (Sweden)

András Szijártó

2012-01-01

Sufficient conditions are obtained that guarantee the solvability of each of four observation problems with given state functions $f, \\ g$ at two distinct time instants $-\\inftys+i}(0,l$ (introduced in [2] of a Sobolev space $H^{s+i} (0,l$, where $i=1,2$ depending on the type of the observation problem, and the representability of $t_2-t_1$ as a rational multiple of $\\frac{2l}{a}$. The reconstruction of the unknown initial data $(u(x,0, u_t(x,0$ as the elements of $D^{s+1}(0,l \\times D^s(0,l$ are given by means of the method of Fourier expansions.

Solving Non-Isospectral mKdV Equation and Sine-Gordon Equation Hierarchies with Self-Consistent Sources via Inverse Scattering Transform

International Nuclear Information System (INIS)

Li Qi; Zhang Dajun; Chen Dengyuan

2010-01-01

N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources and the hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scattering transform. (general)

Solitons and separable elliptic solutions of the sine-Gordon equation

International Nuclear Information System (INIS)

Bryan, A.C.; Haines, C.R.; Stuart, A.E.G.

1979-01-01

It is pointed out that the two-soliton (antisoliton) solutions of the sine-Gordon equation may be obtained as limiting cases of a separable, two-parameter family of elliptic solutions. The solitons are found on the boundary of the parameter space for the elliptic solutions when the latter are considered over their usual complex domain. (Auth.)

Microlocal analysis of quantum fields on curved space-times: Analytic wave front sets and Reeh-Schlieder theorems

International Nuclear Information System (INIS)

Strohmaier, Alexander; Verch, Rainer; Wollenberg, Manfred

2002-01-01

We show in this article that the Reeh-Schlieder property holds for states of quantum fields on real analytic curved space-times if they satisfy an analytic microlocal spectrum condition. This result holds in the setting of general quantum field theory, i.e., without assuming the quantum field to obey a specific equation of motion. Moreover, quasifree states of the Klein-Gordon field are further investigated in the present work and the (analytic) microlocal spectrum condition is shown to be equivalent to simpler conditions. We also prove that any quasifree ground or KMS state of the Klein-Gordon field on a stationary real analytic space-time fulfills the analytic microlocal spectrum condition

Digging into the Elusive Localised Solutions of (2+1) Dimensional sine-Gordon Equation

Science.gov (United States)

Radha, R.; Senthil Kumar, C.

2018-05-01

In this paper, we revisit the (2+1) dimensional sine-Gordon equation analysed earlier [R. Radha and M. Lakshmanan, J. Phys. A Math. Gen. 29, 1551 (1996)] employing the Truncated Painlevé Approach. We then generate the solutions in terms of lower dimensional arbitrary functions of space and time. By suitably harnessing the arbitrary functions present in the closed form of the solution, we have constructed dromion solutions and studied their collisional dynamics. We have also constructed dromion pairs and shown that the dynamics of the dromion pairs can be turned ON or OFF desirably. In addition, we have also shown that the orientation of the dromion pairs can be changed. Apart from the above classes of solutions, we have also generated compactons, rogue waves and lumps and studied their dynamics.

Absorbing Boundary Conditions in Quantum Relativistic Mechanics for Spinless Particles Subject to a Classical Electromagnetic Field

Science.gov (United States)

Sater, Julien

The theory of Artificial Boundary Conditions described by Antoine et al. [2,4-6] for the Schrodinger equation is applied to the Klein-Gordon (KG) in two-dimensions (2-D) for spinless particles subject to electromagnetic fields. We begin by providing definitions for a basic understanding of the theory of operators, differential geometry and wave front sets needed to discuss the factorization theorem thanks to Nirenberg and Hormander [14, 16]. The laser-free Klein-Gordon equation in 1-D is then discussed, followed by the case including electrodynamics potentials, concluding with the KG equation in 2-D space with electrodynamics potentials. We then consider numerical simulations of the laser-particle KG equation, which includes a brief analysis of a finite difference scheme. The conclusion integrates a discussion of the numerical results, the successful completion of the objective set forth, a declaration of the unanswered encountered questions and a suggestion of subjects for further research.

Wave Equation Inversion of Skeletonized SurfaceWaves

KAUST Repository

Zhang, Zhendong

2015-08-19

We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh dispersion curve for the fundamental-mode. We call this wave equation inversion of skeletonized surface waves because the dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Results with synthetic and field data illustrate the benefits and limitations of this method.

Stability of squashed Kaluza-Klein black holes

International Nuclear Information System (INIS)

Kimura, Masashi; Ishihara, Hideki; Murata, Keiju; Soda, Jiro

2008-01-01

The stability of squashed Kaluza-Klein black holes is studied. The squashed Kaluza-Klein black hole looks like a five-dimensional black hole in the vicinity of horizon and looks like a four-dimensional Minkowski spacetime with a circle at infinity. In this sense, squashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes. Using the symmetry of squashed Kaluza-Klein black holes, SU(2)xU(1)≅U(2), we obtain master equations for a part of the metric perturbations relevant to the stability. The analysis based on the master equations gives strong evidence for the stability of squashed Kaluza-Klein black holes. Hence, the squashed Kaluza-Klein black holes deserve to be taken seriously as realistic black holes in the Kaluza-Klein spacetime.

Nondispersive Wave Packets.

Science.gov (United States)

Shaarawi, Amr Mohamed

In this work, nondispersive wavepacket solutions to linear partial differential equations are investigated. These solutions are characterized by infinite energy content; otherwise they are continuous, nonsingular and propagate in free space without spreading out. Examples of such solutions are Berry and Balazs' Airy packet, MacKinnon's wave packet and Brittingham's Focus Wave Mode (FWM). It is demonstrated in this thesis that the infinite energy content is not a basic problem per se and that it can be dealt with in two distinct ways. First these wave packets can be used as bases to construct highly localized, slowly decaying, time-limited pulsed solutions. In the case of the FWMs, this path leads to the formulation of the bidirectional representation, a technique that provides the most natural basis for synthesizing Brittingham-like solutions. This representation is used to derive new exact solutions to the 3-D scalar wave equation. It is also applied to problems involving boundaries, in particular to the propagation of a localized pulse in a infinite acoustic waveguide and to the launchability of such a pulse from the opening of a semi-infinite waveguide. The second approach in dealing with the infinite energy content utilizes the bump-like structure of nondispersive solutions. With an appropriate choice of parameters, these bump fields have very large amplitudes around the centers, in comparison to their tails. In particular, the FWM solutions are used to model massless particles and are capable of providing an interesting interpretation to the results of Young's two slit experiment and to the wave-particle duality of light. The bidirectional representation provides, also, a systematic way of deriving packet solutions to the Klein-Gordon, the Schrodinger and the Dirac equations. Nondispersive solutions of the former two equations are compared to previously derived ones, e.g., the Airy packet and MacKinnon's wave packet.

New results on the mathematical problems in nonlinear physics; Nuevos resultados sobre problemas matematicos en fisica no-linear

Energy Technology Data Exchange (ETDEWEB)

NONE

1980-07-01

The main topics treated in this report are: I) Existence of generalized Lagrangians. II) Conserved densities for odd-order polynomial evolution equations and linear evolution systems. III ) Conservation laws for Klein-Gordon, Di rae and Maxwell equations. IV) Stability conditions for finite-energy solutions of a non-linear Klein-Gordon equation. V) Hamiltonian approach to non-linear evolution equations and Backlund transformations. VI) Anharmonic vibrations: Status of results and new possible approaches. (Author) 83 refs.

New results on the mathematical problems in nonlinear physics

International Nuclear Information System (INIS)

1980-01-01

The main topics treated in this report are: I) Existence of generalized Lagrangians. II) Conserved densities for odd-order polynomial evolution equations and linear evolution systems. III ) Conservation laws for Klein-Gordon, Di rae and Maxwell equations. IV) Stability conditions for finite-energy solutions of a non-linear Klein-Gordon equation. V) Hamiltonian approach to non-linear evolution equations and Backlund transformations. VI) Anharmonic vibrations: Status of results and new possible approaches. (Author) 83 refs

Solutions for the motion of an electron in electromagnetic fields

International Nuclear Information System (INIS)

Bagrov, V.G.; Gitman, D.M.; Jushin, A.V.

1975-01-01

New exact solutions of the Lorentz, Hamilton--Jacobi, Klein--Gordon, and Dirac equations for an electron moving in the field of a plane wave and in electric and magnetic fields were found. The electric and magnetic fields are parallel to the direction of propagation of the plane wave. The magnetic field is constant and the electric field is an arbitrary function of the combination ct-z

A Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge

International Nuclear Information System (INIS)

Davis, Paul

2006-01-01

In this paper, we study the recently discovered family of higher dimensional Kerr-AdS black holes with an extra NUT-like parameter. We show that the inverse metric is additively separable after multiplication by a simple function. This allows us to separate the Hamilton-Jacobi equation, showing that geodesic motion is integrable on this background. The separation of the Hamilton-Jacobi equation is intimately linked to the existence of an irreducible Killing tensor, which provides an extra constant of motion. We also demonstrate that the Klein-Gordon equation for this background is separable

De Broglie's Wavefunction and Wave-Particle Dualism

International Nuclear Information System (INIS)

Leydolt, Hans J.

2005-01-01

A different approach to wave mechanics is presented in accordance with de Broglie's original hypothesis applying the case of photons to all material particles. It derives propagating matter waves conceptually from a theory of evolution, and not by the formal setting of eigenvalue equations. The quality of explanation is at issue, and not the mere description of phenomena. A monoenergetic particle transport along two directions is described by a partial differential equation and by a random walk model. The dual description is applied to the particle picture and the wave picture; it leads with identical initial values to identical causal and timelike solutions in either picture. The partial differential equations are a Telegrapher equation in 1-d space and its analytic continuation, a modified Klein Gordon equation; the solutions represent a density distribution and an amplitude profile, respectively. However, only the corresponding random walk models - equivalent to Feynman's integral over all paths - derive the solutions as path-end distributions with the additional information about the flight direction. This allows following up momentum dissipation along two directions by means of two particle beams and their profiles. Thereby the total number of particles is divided up onto the two beams according to linear or squared fractions depending on the beam configuration putting up a 1-d or a 2-d space. This aspect escapes conventional descriptions but serves to describe the transport in the particle or in the wave picture in dependence on the knowledge/ignorance of the particle's flight direction

Soliton-type solutions for two models in mathematical physics

Science.gov (United States)

Al-Ghafri, K. S.

2018-04-01

In this paper, the generalised Klein-Gordon and Kadomtsov-Petviashvili Benjamin-Bona-Mahony equations with power law nonlinearity are investigated. Our study is based on reducing the form of both equations to a first-order ordinary differential equation having the travelling wave solutions. Subsequently, soliton-type solutions such as compacton and solitary pattern solutions are obtained analytically. Additionally, the peaked soliton has been derived where it exists under a specific restrictions. In addition to the soliton solutions, the mathematical method which is exploited in this work also creates a few amount of travelling wave solutions.

Relativistic analysis

International Nuclear Information System (INIS)

Unterberger, A.

1987-01-01

We study the Klein-Gordon symbolic calculus of operators acting on solutions of the free Klein-Gordon equation. It contracts to the Weyl calculus as c→∞. Mathematically, it may also be considered as a pseudodifferential analysis on the unit ball of R n [fr

Wave-equation dispersion inversion

KAUST Repository

Li, Jing

2016-12-08

We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

On inverse problem of calculus of variations

Energy Technology Data Exchange (ETDEWEB)

Tao, Z-L [College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044 (China)], E-mail: zaolingt@nuist.edu.cn

2008-02-15

Using the semi-inverse method proposed by Ji-Huan He, variational principles are established for some nonlinear equations arising in physics, including the (p, 2p)-mZK equation, Klein-Gordon equation, sine-Gordon equation, Liouville equation, Dodd- Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation.

Blow up of solutions to ordinary differential equations arising in nonlinear dispersive problems

Directory of Open Access Journals (Sweden)

Milena Dimova

2018-03-01

Full Text Available We study a new class of ordinary differential equations with blow up solutions. Necessary and sufficient conditions for finite blow up time are proved. Based on the new differential equation, a revised version of the concavity method of Levine is proposed. As an application we investigate the non-existence of global solutions to the Cauchy problem of Klein-Gordon, and to the double dispersive equations. We obtain necessary and sufficient condition for finite time blow up with arbitrary positive energy. A very general sufficient condition for blow up is also given.

A Klein-Gordon acoustic theory

Energy Technology Data Exchange (ETDEWEB)

Anno, P.D.

1992-12-01

Geophysicists do not associate traveltime variation with density variation in acoustic or elastic wavefield interpretation. Rather, given a constant index of refraction, density variation within the medium of propagation is associated only with amplitudes. This point of view prevails because density does not occur as a variable in classical results such as Snell's Law or the eikonal equation. Nevertheless, in this paper I predict, analytically, a continuum of density effects on acoustic wavefields-including a dispersive traveltime delay when density variation is rapid. I also examine the ability of a common imaging algorithm to cope with this time delay.

A Klein-Gordon acoustic theory

Energy Technology Data Exchange (ETDEWEB)

Anno, Phil D. [Colorado School of Mines, Golden, CO (United States)

1992-12-01

Geophysicists do not associate traveltime variation with density variation in acoustic or elastic wavefield interpretation. Rather, given a constant index of refraction, density variation within the medium of propagation is associated only with amplitudes. This point of view prevails because density does not occur as a variable in classical results such as Snell`s Law or the eikonal equation. Nevertheless, in this paper I predict, analytically, a continuum of density effects on acoustic wavefields-including a dispersive traveltime delay when density variation is rapid. I also examine the ability of a common imaging algorithm to cope with this time delay.

The sine-Gordon wobble

International Nuclear Information System (INIS)

Kaelbermann, G

2004-01-01

Nonperturbative, oscillatory, winding number 1 solutions of the sine-Gordon equation are presented and studied numerically. We call these nonperturbative shape modes wobble solitons. Perturbed sine-Gordon kinks are found to decay to wobble solitons

Computational derivation of quantum relativist electromagnetic systems with forward-backward space-time shifts

International Nuclear Information System (INIS)

Dubois, Daniel M.

2000-01-01

This paper is a continuation of our preceding paper dealing with computational derivation of the Klein-Gordon quantum relativist equation and the Schroedinger quantum equation with forward and backward space-time shifts. The first part introduces forward and backward derivatives for discrete and continuous systems. Generalized complex discrete and continuous derivatives are deduced. The second part deduces the Klein-Gordon equation from the space-time complex continuous derivatives. These derivatives take into account forward-backward space-time shifts related to an internal phase velocity u. The internal group velocity v is related to the speed of light u.v=c 2 and to the external group and phase velocities u.v=v g .v p . Without time shift, the Schroedinger equation is deduced, with a supplementary term, which could represent a reference potential. The third part deduces the Quantum Relativist Klein-Gordon equation for a particle in an electromagnetic field

New optical solitons of space-time conformable fractional perturbed Gerdjikov-Ivanov equation by sine-Gordon equation method

Science.gov (United States)

Yaşar, Elif; Yıldırım, Yakup; Yaşar, Emrullah

2018-06-01

This paper devotes to conformable fractional space-time perturbed Gerdjikov-Ivanov (GI) equation which appears in nonlinear fiber optics and photonic crystal fibers (PCF). We consider the model with full nonlinearity in order to give a generalized flavor. The sine-Gordon equation approach is carried out to model equation for retrieving the dark, bright, dark-bright, singular and combined singular optical solitons. The constraint conditions are also reported for guaranteeing the existence of these solitons. We also present some graphical simulations of the solutions for better understanding the physical phenomena of the behind the considered model.

A new approach to the I/N-expansion for the Dirac equation

International Nuclear Information System (INIS)

Stepanov, S.S.; Tutik, R.S.

1991-01-01

The difficulties associated with application of the I/N-expansion to the Dirac equation have been resolved by applying the method of (h/2π)-expansion. This technique does not involve converting the initial equation into the Schroedinger-like or Klein-Gordon-like form. Obtained recurrence formulae have a simple form and allow one to find the I/N-corrections of an arbitrary order in any of the I/N-expansion scheme. The method restores the exact results for the Coulomb potential. 17 refs. (author)

An Implicit Scheme of Lattice Boltzmann Method for Sine-Gordon Equation

International Nuclear Information System (INIS)

Hui-Lin, Lai; Chang-Feng, Ma

2008-01-01

We establish an implicit scheme of lattice Boltzmann method for simulating the sine-Gordon equation, which can be transformed into the explicit one, so the computation of the scheme is simple. Moreover, the parameter θ of the implicit scheme is independent of the relaxation time, which makes the model more flexible. The numerical results show that this method is very effective. (fundamental areas of phenomenology (including applications))

Closed-form expressions for integrals of MKdV and sine-Gordon maps

International Nuclear Information System (INIS)

Kamp, Peter H van der; Rojas, O; Quispel, G R W

2007-01-01

We present closed-form expressions for approximately N integrals of 2N-dimensional maps. The maps are obtained by travelling wave reductions of the modified Korteweg-de Vries equation and of the sine-Gordon equation, respectively. We provide the integrating factors corresponding to the integrals. Moreover we show how the integrals and the integrating factors relate to the staircase method

Wave Equation Inversion of Skeletonized SurfaceWaves

KAUST Repository

Zhang, Zhendong; Liu, Yike; Schuster, Gerard T.

2015-01-01

We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh dispersion curve for the fundamental-mode. We call this wave equation inversion of skeletonized surface waves because the dispersion curve

Greybody factor of scalar fields from black strings

Energy Technology Data Exchange (ETDEWEB)

Ahmed, Jamil [Quaid-i-Azam University, Department of Mathematics, Islamabad (Pakistan); University of Waterloo, Department of Physics and Astronomy, Waterloo, ON (Canada); Saifullah, K. [Quaid-i-Azam University, Department of Mathematics, Islamabad (Pakistan); Harvard University, Center for the Fundamental Laws of Nature, Cambridge, MA (United States)

2017-12-15

The greybody factor of massless, uncharged scalar fields is studied in the background of cylindrically symmetric spacetimes, in the low-energy approximation. We discuss two cases. In the first case we derive analytical expression for the absorption probability when the spacetime is kinetically coupled with the Einstein tensor. In the second case we do the analysis in the absence of the coupling constant. For this purpose we analyze the wave equation which is obtained from Klein-Gordon equation. The radial part of the wave equation is solved in the form of the hypergeometric function in the near horizon region, whereas in the far region the solution is of the form of Bessel's function. Finally, considering continuity of the wave function we smoothly match the two solutions in the low-energy approximation to get the formula for the absorption probability. (orig.)

Dixon-Souriau equations from a 5-dimensional spinning particle in a Kaluza-Klein framework

International Nuclear Information System (INIS)

Cianfrani, F.; Milillo, I.; Montani, G.

2007-01-01

The dimensional reduction of Papapetrou equations is performed in a 5-dimensional Kaluza-Klein background and Dixon-Souriau results for the motion of a charged spinning body are obtained. The splitting provides an electric dipole moment, and, for elementary particles, the induced parity and time-reversal violations are explained

EPR & Klein Paradoxes in Complex Hamiltonian Dynamics and Krein Space Quantization

Science.gov (United States)

Payandeh, Farrin

2015-07-01

Negative energy states are applied in Krein space quantization approach to achieve a naturally renormalized theory. For example, this theory by taking the full set of Dirac solutions, could be able to remove the propagator Green function's divergences and automatically without any normal ordering, to vanish the expected value for vacuum state energy. However, since it is a purely mathematical theory, the results are under debate and some efforts are devoted to include more physics in the concept. Whereas Krein quantization is a pure mathematical approach, complex quantum Hamiltonian dynamics is based on strong foundations of Hamilton-Jacobi (H-J) equations and therefore on classical dynamics. Based on complex quantum Hamilton-Jacobi theory, complex spacetime is a natural consequence of including quantum effects in the relativistic mechanics, and is a bridge connecting the causality in special relativity and the non-locality in quantum mechanics, i.e. extending special relativity to the complex domain leads to relativistic quantum mechanics. So that, considering both relativistic and quantum effects, the Klein-Gordon equation could be derived as a special form of the Hamilton-Jacobi equation. Characterizing the complex time involved in an entangled energy state and writing the general form of energy considering quantum potential, two sets of positive and negative energies will be realized. The new states enable us to study the spacetime in a relativistic entangled “space-time” state leading to 12 extra wave functions than the four solutions of Dirac equation for a free particle. Arguing the entanglement of particle and antiparticle leads to a contradiction with experiments. So, in order to correct the results, along with a previous investigation [1], we realize particles and antiparticles as physical entities with positive energy instead of considering antiparticles with negative energy. As an application of modified descriptions for entangled (space

Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane

Science.gov (United States)

Huang, Lin; Lenells, Jonatan

2018-03-01

Using the Unified Transform, also known as the Fokas method, the solution of the sine-Gordon equation in the quarter plane can be expressed in terms of the solution of a matrix Riemann-Hilbert problem whose definition involves four spectral functions a , b , A , B. The functions a (k) and b (k) are defined via a nonlinear Fourier transform of the initial data, whereas A (k) and B (k) are defined via a nonlinear Fourier transform of the boundary values. In this paper, we provide an extensive study of these nonlinear Fourier transforms and the associated eigenfunctions under weak regularity and decay assumptions on the initial and boundary values. The results can be used to determine the long-time asymptotics of the sine-Gordon quarter-plane solution via nonlinear steepest descent techniques.

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

Science.gov (United States)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

Lie symmetries in differential equations

International Nuclear Information System (INIS)

Pleitez, V.

1979-01-01

A study of ordinary and Partial Differential equations using the symmetries of Lie groups is made. Following such a study, an application to the Helmholtz, Line-Gordon, Korleweg-de Vries, Burguer, Benjamin-Bona-Mahony and wave equations is carried out [pt

Exact Solutions in 3D New Massive Gravity

Science.gov (United States)

Ahmedov, Haji; Aliev, Alikram N.

2011-01-01

We show that the field equations of new massive gravity (NMG) consist of a massive (tensorial) Klein-Gordon-type equation with a curvature-squared source term and a constraint equation. We also show that, for algebraic type D and N spacetimes, the field equations of topologically massive gravity (TMG) can be thought of as the “square root” of the massive Klein-Gordon-type equation. Using this fact, we establish a simple framework for mapping all types D and N solutions of TMG into NMG. Finally, we present new examples of types D and N solutions to NMG.

Skeletonized wave equation of surface wave dispersion inversion

KAUST Repository

Li, Jing

2016-09-06

We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel-time inversion, the complicated surface-wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the (kx,ω) domain. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2D or 3D velocity models. This procedure, denoted as wave equation dispersion inversion (WD), does not require the assumption of a layered model and is less prone to the cycle skipping problems of full waveform inversion (FWI). The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distribution in laterally heterogeneous media.

Pseudodifferential equations over non-Archimedean spaces

CERN Document Server

Zúñiga-Galindo, W A

2016-01-01

Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applica...

Discrete phase space - II: The second quantization of free relativistic wave fields

International Nuclear Information System (INIS)

Das, A.

2010-01-01

The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential equations in the arena of discrete phase space and continuous time. The scalar field and electromagnetic fields are quantized with commutation relations. The spin-1/2 field is quantized with anti-commutation relations. Moreover, the total momentum, energy and charge of these free relativisitic quantized fields in the discrete phase space and continuous time are computed exactly. The results agree completely with those computed from the relativisitic fields defined on the space-time continuum. (author)

On a wave-particle in closed and open isotropic universes

International Nuclear Information System (INIS)

Campos, L. M. B. C.

2011-01-01

The Klein-Gordon equation satisfied by the wave function in general relativity is solved for the metric of the closed and open universe corresponding to Einstein-De Sitter-Friedmann isotropic cosmological model. The angular dependences are specified by spherical harmonics for the longitude and latitude, and for the hyperlatitude by modified spherical harmonics having as variable circular functions for the closed universe and hyperbolic functions for the open universes. The time dependence of the probabilistic wave function is similar for the closed and open universes and is obtained in the following three cases: (I) constant Hubble parameter, (II) constant decceleration parameter, and (III) uniform matter and energy distribution, which corresponds to the Hubble parameter a linear function of time. Thus six solutions are obtained, namely, the three cases I-III each for closed and open isotropic universes. For each of these six solutions is considered: (i) the existence of singularities in space-time including asymptotic time in the future or past, (ii) the square integrability of the wave function over the full extent of the four-dimensional space-time, and (iii) the existence or otherwise of a positive probability density associated with the wave function.

Gordon S. Fulcher: Renaissance Man of Glass Science

Science.gov (United States)

Mauro, John

2014-11-01

To a glass scientist, the name “Fulcher” conjures images of viscosity vs. temperature diagrams for glass-forming liquids. Indeed, Gordon Fulcher’s seminal 1925 publication, in which he proposed his three-parameter model of viscosity, is one of the most significant and influential papers ever published in the field of glass science. Fulcher developed this equation during the early part of his 14-year career at Corning Glass Works (1920-1934). However, Fulcher’s work in viscosity represents a small fraction of his highly diverse and accomplished career, which included pioneering the field of electrocast ceramics and developing the modern system of scientific abstracting that it still in use today. Fulcher also had a keen interest in social and economic problems, and his latter research focused heavily on the field of metacognition, i.e., the process of thinking.

The Klein paradox: a new treatment

International Nuclear Information System (INIS)

Truebenbacher, E

2015-01-01

The Dirac equation requires a treatment of the step potential that differs fundamentally from the traditional treatment, because the Dirac plane waves, besides momentum and spin, are characterized by a quantum number with the physical meaning of sign of charge. Since the Hermitean operator corresponding to this quantum number does not commute with the step potential, the time displacement parameter used in the ansatz of the stationary state does not have the physical meaning of energy. Therefore there are no paradoxal values of the ‘energy’. The new solution of the Dirac equation with a step potential is obtained. This solution, again, allows for phenomena of the Klein paradox type, but in addition it contains a positron amplitude localized at the threshold point of the step potential. (paper)

A new numerical treatment based on Lucas polynomials for 1D and 2D sinh-Gordon equation

Science.gov (United States)

Oruç, Ömer

2018-04-01

In this paper, a new mixed method based on Lucas and Fibonacci polynomials is developed for numerical solutions of 1D and 2D sinh-Gordon equations. Firstly time variable discretized by central finite difference and then unknown function and its derivatives are expanded to Lucas series. With the help of these series expansion and Fibonacci polynomials, matrices for differentiation are derived. With this approach, finding the solution of sinh-Gordon equation transformed to finding the solution of an algebraic system of equations. Lucas series coefficients are acquired by solving this system of algebraic equations. Then by plugginging these coefficients into Lucas series expansion numerical solutions can be obtained consecutively. The main objective of this paper is to demonstrate that Lucas polynomial based method is convenient for 1D and 2D nonlinear problems. By calculating L2 and L∞ error norms of some 1D and 2D test problems efficiency and performance of the proposed method is monitored. Acquired accurate results confirm the applicability of the method.

Mass renormalization in sine-Gordon model

International Nuclear Information System (INIS)

Xu Bowei; Zhang Yumei

1991-09-01

With a general gaussian wave functional, we investigate the mass renormalization in the sine-Gordon model. At the phase transition point, the sine-Gordon system tends to a system of massless free bosons which possesses conformal symmetry. (author). 8 refs, 1 fig

The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies

Science.gov (United States)

Sabirov, K.; Rakhmanov, S.; Matrasulov, D.; Susanto, H.

2018-04-01

We consider the stationary sine-Gordon equation on metric graphs with simple topologies. Exact analytical solutions are obtained for different vertex boundary conditions. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.

Wave-equation Qs Inversion of Skeletonized Surface Waves

KAUST Repository

Li, Jing

2017-02-08

We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is the one that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs inversion (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to full waveform inversion (FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsurface Qs distribution as long as the Vs model is known with sufficient accuracy.

Skeletonized wave-equation Qs tomography using surface waves

KAUST Repository

Li, Jing

2017-08-17

We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is then found that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs tomography (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to Q full waveform inversion (Q-FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsur-face Qs distribution as long as the Vs model is known with sufficient accuracy.

Wave-equation Qs Inversion of Skeletonized Surface Waves

KAUST Repository

Li, Jing; Dutta, Gaurav; Schuster, Gerard T.

2017-01-01

We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is the one that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs inversion (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to full waveform inversion (FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsurface Qs distribution as long as the Vs model is known with sufficient accuracy.

The (ℎ/2π)-expansion for Regge-trajectories. 2. Relativistic equations

International Nuclear Information System (INIS)

Stepanov, S.S.; Tutik, R.S.

1992-01-01

The (h/2π)-expansion method, proposed earlier for deriving Regge trajectories for bound states of central potentials in the Schroedinger equation framework, is extended to the Klein-Gordon and Dirac equations with potentials having vector and scalar components. The simple recursion formulae, with the same form both for the parent and daughter Regge trajectories, are obtained. They provide, in principle, the calculation of the (h/2π)-expansion terms up to an arbitrary order. As an illustration, a superposition of the vector and scalar Coulomb potentials, and the funnel-shaped potential are treated with the technique developed. 20 refs.; 3 figs.; 1 table. (author)

New multidimensional partially integrable generalization of S-integrable N-wave equation

International Nuclear Information System (INIS)

Zenchuk, A. I.

2007-01-01

This paper develops a modification of the dressing method based on the inhomogeneous linear integral equation with integral operator having nonempty kernel. The method allows one to construct the systems of multidimensional partial differential equations having differential polynomial structure in any dimension n. The associated solution space is not full, although it is parametrized by certain number of arbitrary functions of (n-1) variables. We consider four-dimensional generalization of the classical (2+1)-dimensional S-integrable N-wave equation as an example

Mass spectrum in 5D Warped Einstein Universe and El Naschie's quantum golden field theory

International Nuclear Information System (INIS)

Dariescu, Marina-Aura; Dariescu, Ciprian; Pirghie, Ana-Camelia

2009-01-01

The present paper deals with the massive bosons evolving in a 5D manifold, where the four-dimensional slices are the S 3 xR spacetime. By solving the Einstein equations with a perfect fluid source, we find the expression of the warp factor and write down the corresponding Gordon equation in the bulk, near one of the degenerated vacua of an effective potential with a spontaneously broken Z 2 -symmetry. We obtain the general form of the wave functions and analyze how the Kaluza-Klein-type spectrum is affecting the mass of the scalar on the brane. By inspecting the mass spectrum, we point out a connection with the golden mean based El Naschie's field theory.

Scalar bosons under the influence of noninertial effects in the cosmic string spacetime

Energy Technology Data Exchange (ETDEWEB)

Santos, L.C.N.; Barros, C.C. [Universidade Federal de Santa Catarina, Dept. de Fisica, CFM, Florianopolis, SC (Brazil)

2017-03-15

In this paper we present two different classes of solutions for the Klein-Gordon equation in the presence of a scalar potential under the influence of noninertial effects in the cosmic string spacetime. We show that noninertial effects restrict the physical region of the spacetime where the particle can be placed, and furthermore that the energy levels are shifted by these effects. In addition, we show that the presence of a Coulomb-like scalar potential allows the formation of bound states when the Klein-Gordon equation is considered in this kind of spacetime. (orig.)

Aliasing modes in the lattice Schwinger model

International Nuclear Information System (INIS)

Campos, Rafael G.; Tututi, Eduardo S.

2007-01-01

We study the Schwinger model on a lattice consisting of zeros of the Hermite polynomials that incorporates a lattice derivative and a discrete Fourier transform with many properties. Such a lattice produces a Klein-Gordon equation for the boson field and the exact value of the mass in the asymptotic limit if the boundaries are not taken into account. On the contrary, if the lattice is considered with boundaries new modes appear due to aliasing effects. In the continuum limit, however, this lattice yields also a Klein-Gordon equation with a reduced mass

Coherent quantum states of a relativistic particle in an electromagnetic plane wave and a parallel magnetic field

International Nuclear Information System (INIS)

Colavita, E.; Hacyan, S.

2014-01-01

We analyze the solutions of the Klein–Gordon and Dirac equations describing a charged particle in an electromagnetic plane wave combined with a magnetic field parallel to the direction of propagation of the wave. It is shown that the Klein–Gordon equation admits coherent states as solutions, while the corresponding solutions of the Dirac equation are superpositions of coherent and displaced-number states. Particular attention is paid to the resonant case in which the motion of the particle is unbounded. -- Highlights: •We study a relativistic electron in a particular electromagnetic field configuration. •New exact solutions of the Klein–Gordon and Dirac equations are obtained. •Coherent and displaced number states can describe a relativistic particle

Symmetry and exact solutions of nonlinear spinor equations

International Nuclear Information System (INIS)

Fushchich, W.I.; Zhdanov, R.Z.

1989-01-01

This review is devoted to the application of algebraic-theoretical methods to the problem of constructing exact solutions of the many-dimensional nonlinear systems of partial differential equations for spinor, vector and scalar fields widely used in quantum field theory. Large classes of nonlinear spinor equations invariant under the Poincare group P(1, 3), Weyl group (i.e. Poincare group supplemented by a group of scale transformations), and the conformal group C(1, 3) are described. Ansaetze invariant under the Poincare and the Weyl groups are constructed. Using these we reduce the Poincare-invariant nonlinear Dirac equations to systems of ordinary differential equations and construct large families of exact solutions of the nonlinear Dirac-Heisenberg equation depending on arbitrary parameters and functions. In a similar way we have obtained new families of exact solutions of the nonlinear Maxwell-Dirac and Klein-Gordon-Dirac equations. The obtained solutions can be used for quantization of nonlinear equations. (orig.)

Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation

International Nuclear Information System (INIS)

Duval, C.; Kuenzle, H.P.

1983-02-01

The role of the Bargmann group (11-dimensional extended Galilei group) in non relativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as General Relativity and couples minimally to a complex scalar field leading to a fourdimensionally covariant Schroedinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory

Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation

International Nuclear Information System (INIS)

Duval, C.; Kuenzle, H.P.

1984-01-01

The role of the Bargmann group (11-dimensional extended Galilei group) in nonrelativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as general relativity and couples minimally to a complex scalar field leading to a four-dimensionally covariant Schroedinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory. (author)

On the spectral theory and dispersive estimates for a discrete Schroedinger equation in one dimension

International Nuclear Information System (INIS)

Pelinovsky, D. E.; Stefanov, A.

2008-01-01

Based on the recent work [Komech et al., 'Dispersive estimates for 1D discrete Schroedinger and Klein-Gordon equations', Appl. Anal. 85, 1487 (2006)] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schroedinger operator, Hφ=(-Δ+V)φ=-(φ n+1 +φ n-1 -2φ n )+V n φ n . We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicities and the essential (absolutely continuous) spectrum, while the resolvent satisfies the limiting absorption principle and the Puiseux expansions near the edges. These properties imply the dispersive estimates parallel e itH P a.c. (H) parallel l σ 2 →l -σ 2 -3/2 for any fixed σ>(5/2) and any t>0, where P a.c. (H) denotes the spectral projection to the absolutely continuous spectrum of H. In addition, based on the scattering theory for the discrete Jost solutions and the previous results by Stefanov and Kevrekidis [''Asymptotic behaviour of small solutions for the discrete nonlinear Schroedinger and Klein-Gordon equations,'' Nonlinearity 18, 1841 (2005)], we find new dispersive estimates parallel e itH P a.c. (H) parallel l 1 →l ∞ -1/3 , which are sharp for the discrete Schroedinger operators even for V=0

Comparison of a noncausal with a causal relativistic wave-packet evolution

International Nuclear Information System (INIS)

Castro, A.N. de; Jabs, A.

1991-01-01

In order to study causality violation in more detail we contrast the Klein-Gordon wave packet of Rosenstein und Usher with the Dirac wave packet of Bakke and Wergeland. Both packets are initially localized with exponentially bounded tails but just outside the condition of the general Hegerfeldt theorem for causality violation. It turns out that the wave packet of Bakke and Wergeland exhibits all the features investigated by Rosenstein and Usher, except that it never violates relativistic causality. Thus none of those features, in particular the back- and forerunners emerging from the light cone, can be held responsible for causality violation, and the Ruijsenaars integral is not necessarily a measure of the amount of causality violation. (orig.)

Homothetic and conformal symmetries of solutions to Einstein's equations

International Nuclear Information System (INIS)

Eardley, D.; Isenberg, J.; Marsden, J.; Moncrief, V.; Yale Univ., New Haven, CT

1986-01-01

We present several results about the nonexistence of solutions of Einstein's equations with homoethetic or conformal symmetry. We show that the only spatially compact, globally hyperbolic spacetimes admitting a hypersurface of constant mean extrinsic curvature, and also admitting an infinitesimal proper homothetic symmetry, are everywhere locally flat; this assumes that the matter fields either obey certain energy conditions, or are the Yang-Mills or massless Klein-Gordon fields. We find that the only vacuum solutions admitting an infinitesimal proper conformal symmetry are everywhere locally flat spacetimes and certain plane wave solutions. We show that if the dominant energy condition is assumed, then Minkowski spacetime is the only asymptotically flat solution which has an infinitesimal conformal symmetry that is asymptotic to a dilation. In other words, with the exceptions cited, homothetic or conformal Killing fields are in fact Killing in spatially compact or asymptotically flat spacetimes. In the conformal procedure for solving the initial value problem, we show that data with infinitesimal conformal symmetry evolves to a spacetime with full isometry. (orig.)

Quantum singularities in (2+1) dimensional matter coupled black hole spacetimes

International Nuclear Information System (INIS)

Unver, O.; Gurtug, O.

2010-01-01

Quantum singularities considered in the 3D Banados-Teitelboim-Zanelli (BTZ) spacetime by Pitelli and Letelier [Phys. Rev. D 77, 124030 (2008)] is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurrence of naked singularities in the Einstein-Maxwell extension of the BTZ spacetime both in linear and nonlinear electrodynamics as well as in the Einstein-Maxwell-dilaton gravity spacetimes are analyzed with the quantum test fields obeying the Klein-Gordon and Dirac equations. We show that with the inclusion of the matter fields, the conical geometry near r=0 is removed and restricted classes of solutions are admitted for the Klein-Gordon and Dirac equations. Hence, the classical central singularity at r=0 turns out to be quantum mechanically singular for quantum particles obeying the Klein-Gordon equation but nonsingular for fermions obeying the Dirac equation. Explicit calculations reveal that the occurrence of the timelike naked singularities in the considered spacetimes does not violate the cosmic censorship hypothesis as far as the Dirac fields are concerned. The role of horizons that clothes the singularity in the black hole cases is replaced by repulsive potential barrier against the propagation of Dirac fields.

Skeletonized Least Squares Wave Equation Migration

KAUST Repository

Zhan, Ge

2010-10-17

The theory for skeletonized least squares wave equation migration (LSM) is presented. The key idea is, for an assumed velocity model, the source‐side Green\\'s function and the geophone‐side Green\\'s function are computed by a numerical solution of the wave equation. Only the early‐arrivals of these Green\\'s functions are saved and skeletonized to form the migration Green\\'s function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF for every trial image point. The key to an efficient implementation of iterative LSM is that at each conjugate gradient iteration, the MGF is reused and no new finitedifference (FD) simulations are needed to get the updated migration image. It is believed that this procedure combined with phase‐encoded multi‐source technology will allow for the efficient computation of wave equation LSM images in less time than that of conventional reverse time migration (RTM).

Orbital stability of solitary waves for Kundu equation

Science.gov (United States)

Zhang, Weiguo; Qin, Yinghao; Zhao, Yan; Guo, Boling

In this paper, we consider the Kundu equation which is not a standard Hamiltonian system. The abstract orbital stability theory proposed by Grillakis et al. (1987, 1990) cannot be applied directly to study orbital stability of solitary waves for this equation. Motivated by the idea of Guo and Wu (1995), we construct three invariants of motion and use detailed spectral analysis to obtain orbital stability of solitary waves for Kundu equation. Since Kundu equation is more complex than the derivative Schrödinger equation, we utilize some techniques to overcome some difficulties in this paper. It should be pointed out that the results obtained in this paper are more general than those obtained by Guo and Wu (1995). We present a sufficient condition under which solitary waves are orbitally stable for 2c+sυ1995) only considered the case 2c+sυ>0. We obtain the results on orbital stability of solitary waves for the derivative Schrödinger equation given by Colin and Ohta (2006) as a corollary in this paper. Furthermore, we obtain orbital stability of solitary waves for Chen-Lee-Lin equation and Gerdjikov-Ivanov equation, respectively.

True amplitude wave equation migration arising from true amplitude one-way wave equations

Science.gov (United States)

Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

2003-10-01

One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

Quantum Hall bilayers and the chiral sine-Gordon equation

International Nuclear Information System (INIS)

Naud, J.D.; Pryadko, Leonid P.; Sondhi, S.L.

2000-01-01

The edge state theory of a class of symmetric double-layer quantum Hall systems with interlayer electron tunneling reduces to the sum of a free field theory and a field theory of a chiral Bose field with a self-interaction of the sine-Gordon form. We argue that the perturbative renormalization group flow of this chiral sine-Gordon theory is distinct from the standard (non-chiral) sine-Gordon theory, contrary to a previous assertion by Renn, and that the theory is manifestly sensible only at a discrete set of values of the inverse period of the cosine interaction (β-circumflex). We obtain exact solutions for the spectra and correlation functions of the chiral sine-Gordon theory at the two values of β-circumflex at which electron tunneling in bilayers is not irrelevant. Of these, the marginal case (β-circumflex 2 =4) is of greatest interest: the spectrum of the interacting theory is that of two Majorana fermions with different, dynamically generated, velocities. For the experimentally observed bilayer 331 state at filling factor 1/2, this implies the trifurcation of electrons added to the edge. We also present a method for fermionizing the theory at the discrete points (β-circumflex 2 is an element of Z + ) by the introduction of auxiliary degrees of freedom that could prove useful in other problems involving quantum Hall multi-layers

On a rigorously classical approach to the Sine-Gordon theory

International Nuclear Information System (INIS)

Ulmer, W.

1979-01-01

It is shown that the continuum limit of an infinite set of coupled pendula yields the Sine-Gordon theory. The extension of the model to more dimensions with respect to the propagation yields a generalized Sine-Gordon equation for vector fields, containing Proca equations as a first order approximation. (author)

A game with geometry and quantum mechanics

International Nuclear Information System (INIS)

Caianiello, E.R.

1981-01-01

An attempt is made to geometrize quantum mechanics. A hermitian metric has been taken as a dogma. The Heisenberg commutation relations in cartesian coordinates were taken for the single particle. Position and momentum operators become covariant derivatives, whose commutator is the curvature tensor. The Bohz-Sommerfeld rules are derived both for rotation and vibration degrees of freedom. The Klein-Gordon equation is determined by the first Beltrami parameters. The Dirac equation splits into two sets coupling 8-component semispinors of first and second kind. The only invariance allowed is found to be CPT. A study of the solutions of the Klein-Gordon equation shows that the free particle described by this formalism has inner degrees of freedom [ru

Mathematical and numerical study of non-linear models used in plasma physics

International Nuclear Information System (INIS)

Ebrard, G.

2005-12-01

We study the interaction of several crossing beams with a plasma in the Laser-Megajoule context. We start from Euler-Maxwell. The formal asymptotic is the Zakharov system. For simplified systems of Klein-Gordon-wave type, we justify an approximation by a Zakharov equation for solutions of large amplitude. We construct a new system that simulates the interaction of 2 beams and present a whole hierarchy of models. We introduce a numerical scheme using the known results on Zakharov-wave equations which are valid for short pulses. We give a scheme which eliminate the backscattering wave. We give some numerical results. Finally, we do several numerical simulations of laser-plasma interaction for the initial value problem and the boundary value problem. (author)

Semiclassical Klein-Kramers and Smoluchowski equations for the Brownian motion of a particle in an external potential

International Nuclear Information System (INIS)

Coffey, W T; Kalmykov, Yu P; Titov, S V; Mulligan, B P

2007-01-01

The quantum Brownian motion of a particle in an external potential V(x) is treated using the master equation for the Wigner distribution function W(x, p, t) in phase space (x, p). A heuristic method of determination of diffusion coefficients in the master equation is proposed. The time evolution equation so obtained contains explicit quantum correction terms up to o(ℎ 4 ) and in the classical limit, ℎ → 0, reduces to the Klein-Kramers equation. For a quantum oscillator, the method yields an evolution equation for W(x, p, t) coinciding with that of Agarwal (1971 Phys. Rev. A 4 739). In the non-inertial regime, by applying the Brinkman expansion of the momentum distribution in Weber functions (Brinkman 1956 Physica 22 29), the corresponding semiclassical Smoluchowski equation is derived. (fast track communication)

Non-linear electrodynamics in Kaluza-Klein theory

International Nuclear Information System (INIS)

Kerner, R.

1987-01-01

The most general variational principle based on the invariants of the Riemann tensor and leading to the second order differential equations should contain, in dimensions higher than four, the invariants of the Gauss-Bonnet type. In five dimensions the lagrangian should be a linear combination of the scalar curvature and the second-order invariant. The equations of the electromagnetic field are derived in the absence of scalar and gravitational fields of the Kaluza-Klein model. They yield the unique extension of Maxwell's system in the Kaluza-Klein theory. Some properties of eventual solutions are discussed [fr

On the supersymmetric sine-Gordon model

International Nuclear Information System (INIS)

Hruby, J.

1977-01-01

The sine-Gordon model as the theory of a massless scalar field in one space and one time dimension with interaction Lagrangian density proportional to cosβsub(phi) is generalized for a scalar superfield and it is shown that the solution of the supercovariant sine-Gordon equation is the ''supersoliton'', it is the superfield, which has all ordinary fields in two dimensions as a type of the soliton solution. We also obtain the massive Thirring model and the new equations of motion coupling the Fermi field and the Bose field. The notice about supersymmetric ''SLAC-BAG'' model is done

On the generalization of the Kaluza-Klein theory

International Nuclear Information System (INIS)

Rosu, Ion

2003-01-01

The goal of this paper is to present the Kaluza-Klein theory. In the first part we will discuss the theory elaborated by Kaluza and Klein, in a Riemann space with five dimensions, which unifies the gravitation with electromagnetism. The second part debates the generalization of this theory in a space with 4+n dimensions. This is a mathematical product between the Riemann 4-dimension variety and the G/H n-dimensional homogenous space. In the last part we will propose a theory Kaluza-Klein like in the fiber bundle space with 4+n dimensions. Every part is structured as follows: the metric tensor G will be identified for the gravitation and the potentials Yang-Mills; then the equations of geodesics and the equations of the field will be deduced. (author)

Reshaping-induced spatiotemporal chaos in driven, damped sine-Gordon systems

Energy Technology Data Exchange (ETDEWEB)

Chacon, R. [Departamento de Electronica e Ingenieria Electromecanica, Escuela de Ingenierias Industriales, Universidad de Extremadura, E-06071 Badajoz (Spain)]. E-mail: rchacon@unex.es

2007-03-15

Spatiotemporal chaos arising from the competition between sine-Gordon-breather and kink-antikink-pair solitons by reshaping an ac force is demonstrated. After introducing soliton collective coordinates, Melnikov's method is applied to the resulting effective equation of motion to estimate the parameter-space regions of the ac force where homoclinic bifurcations are induced. The analysis reveals that the chaos-order threshold exhibits sensitivity to small changes in the force shape. Computer simulations of the sine-Gordon system show good agreement with these theoretical predictions.

Killing spinors for the bosonic string and Kaluza-Klein theory with scalar potentials

International Nuclear Information System (INIS)

Liu, Haishan; Lue, H.; Wang, Zhao-Long

2012-01-01

The paper consists mainly of two parts. In the first part, we obtain well-defined Killing spinor equations for the low-energy effective action of the bosonic string with the conformal anomaly term. We show that the conformal anomaly term is the only scalar potential that one can add into the action that is consistent with the Killing spinor equations. In the second part, we demonstrate that Kaluza-Klein theory can be gauged so that the Killing spinors are charged under the Kaluza-Klein vector. This gauging process generates a scalar potential with a maximum that gives rise to an AdS spacetime. We also construct solutions of these theories. (orig.)

Kaluza-Klein inflation

International Nuclear Information System (INIS)

Ishihara, Hideki.

1984-05-01

Dynamical evolution of the Kaluza-Klein space-time is studied using higher dimensional Einstein equation with dust matter. The difference of the topology between the usual space and the internal space gives rise to the segregation of these subspaces. Furthermore the contraction of the internal space causes the inflation of the usual space. (author)

A wave equation interpolating between classical and quantum mechanics

Science.gov (United States)

Schleich, W. P.; Greenberger, D. M.; Kobe, D. H.; Scully, M. O.

2015-10-01

We derive a ‘master’ wave equation for a family of complex-valued waves {{Φ }}\\equiv R{exp}[{{{i}}S}({cl)}/{{\\hbar }}] whose phase dynamics is dictated by the Hamilton-Jacobi equation for the classical action {S}({cl)}. For a special choice of the dynamics of the amplitude R which eliminates all remnants of classical mechanics associated with {S}({cl)} our wave equation reduces to the Schrödinger equation. In this case the amplitude satisfies a Schrödinger equation analogous to that of a charged particle in an electromagnetic field where the roles of the scalar and the vector potentials are played by the classical energy and the momentum, respectively. In general this amplitude is complex and thereby creates in addition to the classical phase {S}({cl)}/{{\\hbar }} a quantum phase. Classical statistical mechanics, as described by a classical matter wave, follows from our wave equation when we choose the dynamics of the amplitude such that it remains real for all times. Our analysis shows that classical and quantum matter waves are distinguished by two different choices of the dynamics of their amplitudes rather than two values of Planck’s constant. We dedicate this paper to the memory of Richard Lewis Arnowitt—a pioneer of many-body theory, a path finder at the interface of gravity and quantum mechanics, and a true leader in non-relativistic and relativistic quantum field theory.

Analyses of pion-40Ca elastic scattering data using the Klein–Gordon equation

International Nuclear Information System (INIS)

Shehadeh, Z.F.

2009-01-01

The elastic scattering data for incident pion energies of 130, 163.3, 180, and 230 MeV on 40 Ca have been analyzed using the full Klein–Gordon equation (KGE), as opposed to its approximate form which renders it to the format of a Schroedinger equation with an energy-dependent potential (RSE). Calculated angular distributions, using KGE and RSE, for all four cases are nearly the same up to about 70° but differ significantly at larger angles. To fit the large-angle data of 163.3 MeV, the nature of the old potential determined by using RSE needs to be revised. The new potentials in four cases are presented and they are compatible with those determined from the inverse scattering theory at a fixed energy in the surface region. (author)

Born's reciprocity principle in stochastic phase space

International Nuclear Information System (INIS)

Prugovecki, E.

1981-01-01

It is shown that the application of Born's reciprocity principle to relativistic quantum mechanics in stochastic phase space (by the requirement that the proper wave functions of extended particles satisfy the Born-Lande as well as the Klein-Gordon equation) leads to the unique determination of these functions for any given value of their rms radius. The resulting particle propagators display not only Lorentz but also reciprocal invariance. This feature remains true even in the case of mass-zero particles, such as photons, when their localization is achieved by means of extended test particles whose proper wave functions obey the reciprocity principle. (author)

Greybody factor of scalar fields from black strings

Science.gov (United States)

Ahmed, Jamil; Saifullah, K.

2017-12-01

The greybody factor of massless, uncharged scalar fields is studied in the background of cylindrically symmetric spacetimes, in the low-energy approximation. We discuss two cases. In the first case we derive analytical expression for the absorption probability when the spacetime is kinetically coupled with the Einstein tensor. In the second case we do the analysis in the absence of the coupling constant. For this purpose we analyze the wave equation which is obtained from Klein-Gordon equation. The radial part of the wave equation is solved in the form of the hypergeometric function in the near horizon region, whereas in the far region the solution is of the form of Bessel's function. Finally, considering continuity of the wave function we smoothly match the two solutions in the low-energy approximation to get the formula for the absorption probability.

Relativistic Bosons in Time-Harmonic Electric Fields

Science.gov (United States)

Buhucianu, Ovidiu; Dariescu, Marina-Aura; Dariescu, Ciprian

2012-02-01

In the present paper, we consider a bi-dimensional thin sample, placed in a strong harmonically oscillating electric field and a static magnetic induction, both directed along the normal to the sample's plane. The Klein-Gordon equation describing the relativistic bosons leads to a Mathieu's type equation for the temporal part of the wave functions. It follows that, for the electric field pulsation inside a computable range, depending on the external fields intensities, the amplitude functions are turning from oscillatory to exponentially growing modes. For ultra-relativistic particles, one can recover the periodic stationary amplitude behavior.

Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory

Science.gov (United States)

Bridges, Thomas J.; Ratliff, Daniel J.

2018-04-01

The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Boussinesq equation. This equation is universal in the same sense as Whitham theory. Moreover, it is dispersive, and it has a wide range of interesting multi-periodic, quasi-periodic and multi-pulse localized solutions. For illustration the theory is applied to a complex nonlinear 2+1 Klein-Gordon equation which has two Lighthill surfaces in the manifold of periodic travelling waves. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

Initial-value problem for the Gardner equation applied to nonlinear internal waves

Science.gov (United States)

Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim

2017-04-01

., Talipova T. Internal solitary waves // Chapter 4 in the book ``Solitary Waves in Fluids''. WIT Press. Southampton, Boston. 2007. P. 85 - 110. Rouvinskaya E., Kurkina O., Kurkin A. Dynamics of nonlinear internal gravity waves in layered fluids // NNSTU n.a. R.E. Alekseev Press - Nizhny Novgorod, 2014 - 160 p. [In Russian] Trillo S., Klein M., Clauss G., Onorato M. Observation of dispersive shock waves developing from initial depressions in shallow water // Physica D, 2016. - http://dx.doi.org/10.1016/j.physd.2016.01.007.

Wave equations in higher dimensions

CERN Document Server

Dong, Shi-Hai

2011-01-01

Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativisti...

Covariant approach of perturbations in Lovelock type brane gravity

Science.gov (United States)

Bagatella-Flores, Norma; Campuzano, Cuauhtemoc; Cruz, Miguel; Rojas, Efraín

2016-12-01

We develop a covariant scheme to describe the dynamics of small perturbations on Lovelock type extended objects propagating in a flat Minkowski spacetime. The higher-dimensional analogue of the Jacobi equation in this theory becomes a wave type equation for a scalar field Φ . Whithin this framework, we analyse the stability of membranes with a de Sitter geometry where we find that the Jacobi equation specializes to a Klein-Gordon (KG) equation for Φ possessing a tachyonic mass. This shows that, to some extent, these types of extended objects share the symmetries of the Dirac-Nambu-Goto (DNG) action which is by no means coincidental because the DNG model is the simplest included in this type of gravity.

The Schroedinger-Newton equation as model of self-gravitating quantum systems

International Nuclear Information System (INIS)

Grossardt, Andre

2013-01-01

The Schroedinger-Newton equation (SN equation) describes a quantummechanical one-particle-system with gravitational self-interaction and might play a role answering the question if gravity must be quantised. As non-relativistic limit of semi-classical gravity, it provides testable predictions of the effects that classical gravity has on genuinely quantum mechanical systems in the mass regime between a few thousand proton masses and the Planck mass, which is experimentally unexplored. In this thesis I subsume the mathematical properties of the SN equation and justify it as a physical model. I will give a short outline of the controversial debate around semi-classical gravity as a fundamental theory, along with the idea of the SN equation as a model of quantum state reduction. Subsequently, I will respond to frequent objections against nonlinear Schrodinger equations. I will show how the SN equation can be obtained from Einstein's General Relativity coupled to either a KleinGordon or a Dirac equation, in the same sense as the linear Schroedinger equation can be derived in flat Minkowski space-time. The equation is, to this effect, a non-relativistic approximation of the semi-classical Einstein equations. Additionally, I will discuss, first by means of analytic estimations and later numerically, in which parameter range effects of gravitational selfinteraction - e.g. in molecular-interferometry experiments - should be expected. Besides the one-particle SN equation I will provide justification for a modified equation describing the centre-of-mass wave-function of a many-particle system. Furthermore, for this modified equation, I will examine, numerically, the consequences for experiments. Although one arrives at the conclusion that no effects of the SN equation can be expected for masses up to six or seven orders of magnitude above those considered in contemporary molecular interferometry experiments, tests of the equation, for example in satellite experiments, seem

Electron acoustic waves and parametric instabilities in a 4-component relativistic quantum plasma with Thomas-Fermi distributed electrons

Science.gov (United States)

Ikramullah, Ahmad, Rashid; Sharif, Saqib; Khattak, Fida Younus

2018-01-01

The interaction of Circularly Polarized Electro-Magnetic (CPEM) waves with a 4-component relativistic quantum plasma is studied. The plasma constituents are: relativistic-degenerate electrons and positrons, dynamic degenerate ions, and Thomas-Fermi distributed electrons in the background. We have employed the Klein-Gordon equations for the electrons as well as for the positrons, while the ions are represented by the Schrödinger equation. The Maxwell and Poisson equations are used for electromagnetic waves. Three modes are observed: one of the modes is associated with the electron acoustic wave, a second mode at frequencies greater than the electron acoustic wave mode could be associated with the positrons, and the third one at the lowest frequencies could be associated with the ions. Furthermore, Stimulated Raman Scattering (SRS), Modulational, and Stimulated Brillouin Scattering (SBS) instabilities are studied. It is observed that the growth rates of both the SRS and SBS instabilities decrease with increase in the quantum parameter of the plasma. It is also observed that the scattering spectra in both the SRS and SBS get restricted to very small wavenumber regions. It is shown that for low amplitude CPEM wave interaction with the quantum plasma, the positron concentration has no effect on the SRS and SBS spectra. In the case of large amplitude CPEM wave interaction, however, one observes spectral changes with varying positron concentrations. An increase in the positron concentration also enhances the scattering instability growth rates. Moreover, the growth rate first increases and then decreases with increasing intensity of the CPEM wave, indicating an optimum value of the CPEM wave intensity for the growth of these scattering instabilities. The modulational instability also shows dependence on the quantum parameter as well as on the positron concentration.

Stability of time-dependent particle-like solutions of some wave equations

International Nuclear Information System (INIS)

Voronov, N.A.

1978-01-01

The proof of the nonstability of the one-dimensional periodical localized solutions of the equation with a spontaneously broken symmetry is given. The stability of the one-dimensional oscillating solutions of the sine-Gordon equation was also considered with regard to such perturbations. As it was expected these solutions proved to be stable

Computational study on full-wave inversion based on the elastic wave-equation; Dansei hado hoteishiki full wave inversion no model keisan ni yoru kento

Energy Technology Data Exchange (ETDEWEB)

Uesaka, S [Kyoto University, Kyoto (Japan). Faculty of Engineering; Watanabe, T; Sassa, K [Kyoto University, Kyoto (Japan)

1997-05-27

Algorithm is constructed and a program developed for a full-wave inversion (FWI) method utilizing the elastic wave equation in seismic exploration. The FWI method is a method for obtaining a physical property distribution using the whole observed waveforms as the data. It is capable of high resolution which is several times smaller than the wavelength since it can handle such phenomena as wave reflection and dispersion. The method for determining the P-wave velocity structure by use of the acoustic wave equation does not provide information about the S-wave velocity since it does not consider S-waves or converted waves. In an analysis using the elastic wave equation, on the other hand, not only P-wave data but also S-wave data can be utilized. In this report, under such circumstances, an inverse analysis algorithm is constructed on the basis of the elastic wave equation, and a basic program is developed. On the basis of the methods of Mora and of Luo and Schuster, the correction factors for P-wave and S-wave velocities are formulated directly from the elastic wave equation. Computations are performed and the effects of the hypocenter frequency and vibration transmission direction are examined. 6 refs., 8 figs.

Dirac equation in low dimensions: The factorization method

Energy Technology Data Exchange (ETDEWEB)

Sánchez-Monroy, J.A., E-mail: antosan@if.usp.br [Instituto de Física, Universidade de São Paulo, 05508-090, São Paulo, SP (Brazil); Quimbay, C.J., E-mail: cjquimbayh@unal.edu.co [Departamento de Física, Universidad Nacional de Colombia, Bogotá, D. C. (Colombia); CIF, Bogotá (Colombia)

2014-11-15

We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equations in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to two Klein–Gordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials. - Highlights: • The low-dimensional Dirac equation in the presence of static potentials is solved. • The factorization method is generalized for energy-dependent Hamiltonians. • The shape invariance is generalized for energy-dependent Hamiltonians. • The stability of the Dirac sea is related to the existence of supersymmetric partner Hamiltonians.

A novel solution to the Klein–Gordon equation in the presence of a strong rotating electric field

Energy Technology Data Exchange (ETDEWEB)

Raicher, E., E-mail: erez.raicher@mail.huji.ac.il [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel); Department of Applied Physics, Soreq Nuclear Research Center, Yavne 81800 (Israel); Eliezer, S. [Department of Applied Physics, Soreq Nuclear Research Center, Yavne 81800 (Israel); Nuclear Fusion Institute, Polytechnic University of Madrid, Madrid (Spain); Zigler, A. [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel)

2015-11-12

The Klein–Gordon equation in the presence of a strong electric field, taking the form of the Mathieu equation, is studied. A novel analytical solution is derived for particles whose asymptotic energy is much lower or much higher than the electromagnetic field amplitude. The condition for which the new solution recovers the familiar Volkov wavefunction naturally follows. When not satisfied, significant deviation from the Volkov wavefunction is demonstrated. The new condition is shown to differ by orders of magnitudes from the commonly used one. As this equation describes (neglecting spin effects) the emission processes and the particle motion in Quantum Electrodynamics (QED) cascades, our results suggest that the standard theoretical approach towards this phenomenon should be revised.

An integrable noncommutative version of the sine-Gordon system

International Nuclear Information System (INIS)

Grisaru, Marcus T.; Penati, Silvia

2003-01-01

Using the bicomplex approach we discuss an integrable noncommutative system in two-dimensional Euclidean space. It is described by an equation of motion which reduces to the ordinary sine-Gordon equation when the noncommutation parameter is removed, plus a constraint equation which is nontrivial only in the noncommutative case. The implications of this constraint, which is required by integrability but seems to reduce the space of classical solutions, remain to be understood. We show that the system has an infinite number of conserved currents and we give the general recursive relation for constructing them. For the particular cases of lower spin nontrivial currents we work out the explicit expressions and perform a direct check of their conservation. These currents reduce to the usual sine-Gordon currents in the commutative limit. We find classical 'localized' solutions to first order in the noncommutativity parameter and describe the Backlund transformations for our system. Finally, we comment on the relation of our noncommutative system to the commutative sine-Gordon system

Reassessing the clinical affinity between Melanie Klein and D.W. Winnicott (1935-51): Klein's unpublished "Notes on baby" in historical context.

Science.gov (United States)

Aguayo, Joseph

2002-10-01

The author investigates the clinical affinity between Klein and Winnicott (1935-46) asa way to historically situate Winnicott 's later criticism of Klein's 'temperamental' inability to understand the impact of the environment on the infant's development. By setting out Klein s theories at the time when Winnicott began supervision with her in 1935, a context is established for the analysis of an unpublished 1937 manuscript by Klein ('Notes on baby'). The author argues that this direct and extensive infant observation demonstrates Klein's sensitivity to the familial environment. While Winnicott as a paediatrician showed enthusiasm for Klein s ideas, he also demonstrated a difference of opinion in emphasising the maternal environment of provision after his wartime evacuation experiences with London children. The factors leading to their mutual distancing are outlined as follows: (1) the post-Controversial Discussion atmosphere of the British Psycho-Analytical Society in 1944. The new non-aligned psychoanalytic 'middle group' allowed Winnicott to take a pick and choose attitude towards available analytic theories; (2) Winnicott us new clinical practices and theory differed from Klein 's, leading to a widening gap between 1946 and 1951. Winnicott's new theory and practice simultaneously represented his technical marginalisation of Klein s emphasis on the direct analysis of the patient s destructiveness by the time he delivered the 'Transitional objects' paper in 1951.

On Palacios-Gordon's theory of relativity

International Nuclear Information System (INIS)

Gulati, P.S.

1981-01-01

Since the early days of Einstein's special theory of relativity (1905), it is known that this theory suffers from some epistemological problems. Over the years, many theoreticians have endeavored to overcome these problems, rejecting either the 'Principle of Relativity' or the 'Light Principle'. Palacios and Gordon rejected the former and advanced an alternative theory governed by Voigt's transformation equations (1887). In the present paper, Palacios-Gordon's theory has been critically examined and some of its drawbacks are discovered. It becomes obvious that neither Einstein's special theory of relativity nor Palacios-Gordon's theory of relativity provides a flawless fit to the real world. It is speculated that suitable synthesis of these two theories might resolve all the controversial issues of special theory of relativity. (author)

Linear fractional diffusion-wave equation for scientists and engineers

CERN Document Server

Povstenko, Yuriy

2015-01-01

This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier’s, Fick’s and Darcy’s laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and ...

Gauge bridges in classical field theory; Eichbruecken in der klassischen Feldtheorie

Energy Technology Data Exchange (ETDEWEB)

Jakobs, S.

2009-03-15

In this thesis Poisson structures of two classical gauge field theories (Maxwell-Klein-Gordon- and Maxwell-Dirac-system) are constructed using the parametrix construction of Green's functions. Parametrices for the Maxwell-Klein-Gordon- and Maxwell-Dirac-system are constructed in Minkowski space and this construction is later generalized to curved space times for the Maxwell-Klein-Gordon-system. With these Green's functions Poisson brackets will be defined as Peierls brackets. Finally non-local, gauge invariant observables, the so-called 'gauge bridges'are constructed. Gauge bridges are the matrix elements of holonomy operators. It is shown, that these emerge from Poisson brackets of local, gauge invariant observables. (orig.)

Rogue periodic waves of the modified KdV equation

Science.gov (United States)

Chen, Jinbing; Pelinovsky, Dmitry E.

2018-05-01

Rogue periodic waves stand for rogue waves on a periodic background. Two families of travelling periodic waves of the modified Korteweg–de Vries (mKdV) equation in the focusing case are expressed by the Jacobian elliptic functions dn and cn. By using one-fold and two-fold Darboux transformations of the travelling periodic waves, we construct new explicit solutions for the mKdV equation. Since the dn-periodic wave is modulationally stable with respect to long-wave perturbations, the new solution constructed from the dn-periodic wave is a nonlinear superposition of an algebraically decaying soliton and the dn-periodic wave. On the other hand, since the cn-periodic wave is modulationally unstable with respect to long-wave perturbations, the new solution constructed from the cn-periodic wave is a rogue wave on the cn-periodic background, which generalizes the classical rogue wave (the so-called Peregrine’s breather) of the nonlinear Schrödinger equation. We compute the magnification factor for the rogue cn-periodic wave of the mKdV equation and show that it remains constant for all amplitudes. As a by-product of our work, we find explicit expressions for the periodic eigenfunctions of the spectral problem associated with the dn and cn periodic waves of the mKdV equation.

Quasi-bound state resonances of charged massive scalar fields in the near-extremal Reissner-Nordstroem black-hole spacetime

Energy Technology Data Exchange (ETDEWEB)

Hod, Shahar [The Ruppin Academic Center, Emeq Hefer (Israel); The Hadassah Academic College, Jerusalem (Israel)

2017-05-15

The quasi-bound states of charged massive scalar fields in the near-extremal charged Reissner-Nordstroem black-hole spacetime are studied analytically. These discrete resonant modes of the composed black-hole-field system are characterized by the physically motivated boundary condition of ingoing waves at the black-hole horizon and exponentially decaying (bounded) radial eigenfunctions at spatial infinity. Solving the Klein-Gordon wave equation for the linearized scalar fields in the black-hole spacetime, we derive a remarkably compact analytical formula for the complex frequency spectrum which characterizes the quasi-bound state resonances of the composed Reissner-Nordstroem-black-hole-charged-massive-scalar-field system. (orig.)

The generalized Fubini instanton

International Nuclear Information System (INIS)

Yurova, A.A.; Yurov, A.V.

2008-01-01

We show that (1+2) nonlinear Klein-Gordon equation with negative coupling admits an exact solution which appears to be the linear superposition of the plane wave and the nonsingular rational soliton. We show that the same approach allows to construct the solution of similar properties for the Euclidean φ 4 model with broken symmetry. Interestingly, this regular solution will be of instanton type only in the D≤5 Euclidean space. Thus one can use the generalized Fubini instantons (in quantum cosmology for example) only for the case of the single infinite extra dimension

A novel solution to the Klein–Gordon equation in the presence of a strong rotating electric field

Directory of Open Access Journals (Sweden)

E. Raicher

2015-11-01

Full Text Available The Klein–Gordon equation in the presence of a strong electric field, taking the form of the Mathieu equation, is studied. A novel analytical solution is derived for particles whose asymptotic energy is much lower or much higher than the electromagnetic field amplitude. The condition for which the new solution recovers the familiar Volkov wavefunction naturally follows. When not satisfied, significant deviation from the Volkov wavefunction is demonstrated. The new condition is shown to differ by orders of magnitudes from the commonly used one. As this equation describes (neglecting spin effects the emission processes and the particle motion in Quantum Electrodynamics (QED cascades, our results suggest that the standard theoretical approach towards this phenomenon should be revised.

Dirac equation in a de Sitter expansion for massive neutrinos from modern Kaluza-Klein theory

International Nuclear Information System (INIS)

Sánchez, Pablo Alejandro; Anabitarte, Mariano; Bellini, Mauricio

2012-01-01

Using the modern Kaluza-Klein theory of gravity (or the Induced Matter theory), we study the Dirac equation for massive neutrinos on a de Sitter background metric from a 5D Riemann-flat (and hence Ricci-flat) extended de Sitter metric, on which is defined the vacuum for test massless 1/2-spin neutral fields minimally coupled to gravity and free of any other interactions. We obtain that the effective 4D masses of the neutrinos can only take three possible values, which are related to the (static) foliation of the fifth and noncompact extra dimension.

Extension of a theory of Feynman

International Nuclear Information System (INIS)

Blaquiere, Augustin

1979-01-01

We propose a relativistic extension of a method through which Feynman derives the Schroedinger equation. The equation of Klein-Gordon for a charged particle in a magnetic field is obtained. Some connections with the nonrelativistic and the classical approximations are discussed [fr

Fulltext PDF

Indian Academy of Sciences (India)

IAS Admin

2015-03-15

Mar 15, 2015 ... 2: Angular momentum theory and identical particles and spin; Module 3: Perturbation theory (degenerate and non- degenerate) and scattering theory; Module 4: Quantum theory of radiation and Relativistic Quantum mechanics-. Klein-Gordon equation and Dirac Equation. Resource Persons: Professors ...

Signatures of extra dimensions in gravitational waves

Energy Technology Data Exchange (ETDEWEB)

Andriot, David; Gómez, Gustavo Lucena, E-mail: andriotphysics@gmail.com, E-mail: glucenag@aei.mpg.de [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14467 Potsdam-Golm (Germany)

2017-06-01

Considering gravitational waves propagating on the most general 4+ N -dimensional space-time, we investigate the effects due to the N extra dimensions on the four-dimensional waves. All wave equations are derived in general and discussed. On Minkowski{sub 4} times an arbitrary Ricci-flat compact manifold, we find: a massless wave with an additional polarization, the breathing mode, and extra waves with high frequencies fixed by Kaluza-Klein masses. We discuss whether these two effects could be observed.

Didactic derivation of the special theory of relativity from the Klein–Gordon equation

International Nuclear Information System (INIS)

Arodź, H

2014-01-01

We present a didactic derivation of the special theory of relativity in which Lorentz transformations are ‘discovered’ as symmetry transformations of the Klein–Gordon equation. The interpretation of Lorentz boosts as transformations to moving inertial reference frames is not assumed at the start, but it naturally appears at a later stage. The relative velocity v of two inertial reference frames is defined in terms of the elements of the pertinent Lorentz matrix, and the bound |v|< c is presented as a simple theorem that follows from the structure of the Lorentz group. The polar decomposition of Lorentz matrices is used to explain noncommutativity and nonassociativity of the relativistic composition (‘addition’) of velocities. (paper)

Quantum influence of topological defects in Goedel-type space-times

Energy Technology Data Exchange (ETDEWEB)

Carvalho, Josevi [Universidade Federal de Campina Grande, Unidade Academica de Tecnologia de Alimentos, Centro de Ciencias e Tecnologia Agroalimentar, Pombal, PB (Brazil); Carvalho, M.; Alexandre, M. de [Universidade Federal de Alagoas, Instituto de Fisica, Maceio, AL (Brazil); Furtado, Claudio [Universidade Federal da Paraiba, Cidade Universitaria, Departamento de Fisica, CCEN, Joao Pessoa, PB (Brazil)

2014-06-15

In this contribution, some solutions of the Klein-Gordon equation in Goedel-type metrics with an embedded cosmic string are considered. The quantum dynamics of a scalar particle in three spaces whose metrics are described by different classes of Goedel solutions, with a cosmic string passing through the spaces, is found. The energy levels and eigenfunctions of the Klein-Gordon operator are obtained. We show that these eigenvalues and eigenfunctions depend on the parameter characterizing the presence of a cosmic string in the space-time. We note that the presence of topological defects breaks the degeneracy of energy levels. (orig.)

Skeletonized wave equation of surface wave dispersion inversion

KAUST Repository

Li, Jing; Schuster, Gerard T.

2016-01-01

We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel

Linear superposition solutions to nonlinear wave equations

International Nuclear Information System (INIS)

Liu Yu

2012-01-01

The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed

Internal structure of relativistic astrophysical objects in the wave approximation

International Nuclear Information System (INIS)

Bogdanov, I.V.; Demkov, Yu.N.

1987-01-01

Spherically symmetric inverse problems for the scattering of quantum particles by a static gravitational field are considered within the framework of general relativity theory. Methods are developed for determining the metric tensor on the basis of scattering data for a fixed energy or zero angular momentum for the Klein-Fock-Gordon equation in the Schwarzschild metric. The relation between the S-matrix and squared 4-momentum operator in curved space is investigated. The main elements of the algorithms developed are two definite nonlinear ordinary differential equations of the third and fourth order based on the scattering data. On the one hand, the inverse problems studied extend the classical inverse problems for the gravitational field, solved previously, to the quantum case. On the other hand, they extend the Marchenko and Regge-Newton methods familiar in quantum theory to the case of a gravitational field. An analogy is established between the motion of a scalar particle in a strong gravitational field and the motion in a field with a potential depending on the angular momentum or energy in nonrelativistic quantum mechanics

Cosmological applications in Kaluza—Klein theory

International Nuclear Information System (INIS)

Wanas, M.I.; Nashed, Gamal G. L.; Nowaya, A.A.

2012-01-01

The field equations of Kaluza—Klein (KK) theory have been applied in the domain of cosmology. These equations are solved for a flat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylor's expansion of cosmological function, Λ(t), up to the first order of the time t. The cosmological parameters are calculated and some cosmological problems are discussed. (geophysics, astronomy, and astrophysics)

Generalized quantum sine-Gordon equation and its relation to the Thirring model in quantum field theory

International Nuclear Information System (INIS)

Skagerstam, B.K.

1976-01-01

We discuss a generalization of the conventional sine-Gordon quantum field theory by using methods recently developed by Coleman. As a result we can argue that the equivalence between the sine-Gordon theory and the massive Thirring model is unaffected if we perturb the sine-Gordon Hamiltonian by a bounded perturbation consisting of a continuous sum of sine-Gordon type interactions

The nonsymmetric Kaluza-Klein (Jordan-Thiry) theory in the electromagnetic case

International Nuclear Information System (INIS)

Kalinowski, M.W.

1992-01-01

We present the nonsymmetric Kaluza-Klein and Jordan-Thiry theories as interesting propositions of physics in higher dimensions. We consider the five-dimensional (electromagnetic) case. The work is devoted to a five-dimensional unification of the NGT (nonsymmetric theory of gravitation), electromagnetism, and scalar forces in a Jordan-Thiry manner. We find open-quotes interference effectsclose quotes between gravitational and electromagnetic fields which appear to be due to the skew-symmetric part of the metric. Our unification, called the nonsymmetric Jordan-Thiry theory, becomes the classical Jordan-Thiry theory if the skew-symmetric part of the metric is zero. It becomes the classical Kaluza-Klein theory if the scalar field ρ=1 (Kaluza's Ansatz). We also deal with material sources in the nonsymmetric Kaluza-Klein theory for the electromagnetic case. We consider phenomenological sources with a nonzero fermion current, a nonzero electric current, and a nonzero spin density tensor. From the Palatini variational principle we find equations for the gravitational and electromagnetic fields. We also consider the geodetic equations in the theory and the equation of motion for charged test particles. We consider some numerical predictions of the nonsymmetric Kaluza-Klein theory with nonzero (and with zero) material sources. We prove that they do not contradict any experimental data for the solar system and on the surface of a neutron star. We deal also with spin sources in the nonsymmetric Kaluza-Klein theory. We find an exact, static, spherically symmetric solution in the nonsymmetric Kaluza-Klein theory in the electromagnetic case. This solution has the remarkable property of describing open-quotes mass without massclose quotes and open-quotes charge without charge.close quotes We examine its properties and a physical interpretation. 91 refs., 7 figs

Analysis of wave equation in electromagnetic field by Proca equation

International Nuclear Information System (INIS)

Pamungkas, Oky Rio; Soeparmi; Cari

2017-01-01

This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)

Bifurcation analysis and the travelling wave solutions of the Klein

Indian Academy of Sciences (India)

In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by ...

Generalized Killing-Yano equations in D=5 gauged supergravity

International Nuclear Information System (INIS)

Kubiznak, David; Kunduri, Hari K.; Yasui, Yukinori

2009-01-01

We propose a generalization of the (conformal) Killing-Yano equations relevant to D=5 minimal gauged supergravity. The generalization stems from the fact that the dual of the Maxwell flux, the 3-form *F, couples naturally to particles in the background as a 'torsion'. Killing-Yano tensors in the presence of torsion preserve most of the properties of the standard Killing-Yano tensors - exploited recently for the higher-dimensional rotating black holes of vacuum gravity with cosmological constant. In particular, the generalized closed conformal Killing-Yano 2-form gives rise to the tower of generalized closed conformal Killing-Yano tensors of increasing rank which in turn generate the tower of Killing tensors. An example of a generalized Killing-Yano tensor is found for the Chong-Cvetic-Lue-Pope black hole spacetime [Z.W. Chong, M. Cvetic, H. Lu, C.N. Pope, (hep-th/0506029)]. Such a tensor stands behind the separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations in this background.

Quantum field theory of universe

International Nuclear Information System (INIS)

Hosoya, Akio; Morikawa, Masahiro.

1988-08-01

As is well-known, the wave function of universe dictated by the Wheeler-DeWitt equation has a difficulty in its probabilistic interpretation. In order to overcome this difficulty, we explore a theoretical possibility of the second quantization of universe, following the same passage historically taken for the Klein-Gordon particles and the Nambu-Goto strings. It turns out that multiple production of universes is an inevitable consequence even if the initial state is nothing. The problematical interpretation of wave function of universe is circumvented by introducing an internal comoving model detector, which is an analogue of the DeWitt-Unruh detector in the quantum field theory in curved space-time. (author)

Parsimonious wave-equation travel-time inversion for refraction waves

KAUST Repository

Fu, Lei

2017-02-14

We present a parsimonious wave-equation travel-time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N geophones evenly deployed along the line. These two reciprocal shots contain approximately 2N refraction travel times, which can be spawned into O(N2) refraction travel times by an interferometric transformation. Then, these virtual refraction travel times are used with a source wavelet to create N virtual refraction shot gathers, which are the input data for wave-equation travel-time inversion. Numerical results show that the parsimonious wave-equation travel-time tomogram has about the same accuracy as the tomogram computed by standard wave-equation travel-time inversion. The most significant benefit is that a reciprocal survey is far less time consuming than the standard refraction survey where a source is excited at each geophone location.

Scalar formalism for quantum electrodynamics

International Nuclear Information System (INIS)

Hostler, L.C.

1985-01-01

A set of Feynman rules, similar to the rules of scalar electrodynamics, is derived for a full quantum electrodynamics based on the relativistic Klein--Gordon--type wave equation ]Pi/sub μ/Pi/sub μ/+m 2 +ie sigma x (E +iB)]phi = 0, Pi/sub μ/ equivalent-i partial/sub μ/-eA/sub μ/, for spin- 1/2 particles [J. Math. Phys. 23, 1179 (1982); J. Math. Phys. 24, 2366 (1983)]. In this equation, phi is a 2 x 1 Pauli spinor and sigma/sub a/, a = 1,2,3, are the usual 2 x 2 Pauli spin matrices. The irreducible self-energy parts are compared to those of conventional quantum electrodynamics

Elastic Wave-equation Reflection Traveltime Inversion Using Dynamic Warping and Wave Mode Decomposition

KAUST Repository

Wang, T.

2017-05-26

Elastic full waveform inversion (EFWI) provides high-resolution parameter estimation of the subsurface but requires good initial guess of the true model. The traveltime inversion only minimizes traveltime misfits which are more sensitive and linearly related to the low-wavenumber model perturbation. Therefore, building initial P and S wave velocity models for EFWI by using elastic wave-equation reflections traveltime inversion (WERTI) would be effective and robust, especially for the deeper part. In order to distinguish the reflection travletimes of P or S-waves in elastic media, we decompose the surface multicomponent data into vector P- and S-wave seismogram. We utilize the dynamic image warping to extract the reflected P- or S-wave traveltimes. The P-wave velocity are first inverted using P-wave traveltime followed by the S-wave velocity inversion with S-wave traveltime, during which the wave mode decomposition is applied to the gradients calculation. Synthetic example on the Sigbee2A model proves the validity of our method for recovering the long wavelength components of the model.

A New Understanding of Particles by G-Flow Interpretation of Differential Equation

Directory of Open Access Journals (Sweden)

Mao L.

2015-07-01

Full Text Available Applying mathematics to the understanding of particles classically with an assumption that if the variables t and x 1 , x 2 , x 3 hold with a system of dynamical equations (1.4, then they are a point ( t , x 1 , x 2 , x 3 in R 4 . However, if we put off this assumption, how can we interpret the solution space of equations? And are the se resultants important for understanding the world? Recently, the author extended Ban ach and Hilbert spaces on a topological graph to introduce −→ G -flows and showed that all such flows on a topological graph −→ G also form a Banach or Hilbert space, which enables one to find t he multiverse solution of these equations on −→ G . Applying this result, this paper discusses the −→ G -flow solutions on Schrödinger equation, Klein-Gordon equation and Dirac equation, i.e., the field equations of particles, bosons or fermions, answers previous questions by ”yes“, and establishes the many world interpretation of quantum mechanics of H. Everett by purely mathematics in logic, i.e., mathematical combinatorics.

Integrable discretization s of derivative nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Tsuchida, Takayuki

2002-01-01

We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations. (author)

Causal wave propagation for relativistic massive particles: physical asymptotics in action

International Nuclear Information System (INIS)

Berry, M V

2012-01-01

Wavepackets representing relativistic quantum particles injected into a half-space, from a source that is switched on at a definite time, are represented by superpositions of plane waves that must include negative frequencies. Propagation is causal: it is a consequence of analyticity that at time t no part of the wave has travelled farther than ct, corresponding to the front of the signal. Nevertheless, interference fringes behind the front travel superluminally. For Klein-Gordon and Dirac wavepackets, the spatially integrated density increases because current is injected at the boundary. Even in the simplest causal model, understanding the shape of the wave after long times is an instructive exercise in the asymptotics of integrals, illustrating several techniques at a level suitable for graduate students; different spatial features involve contributions from a pole and from two saddle points, the uniform asymptotics for the pole close to a saddle, and the coalescence of two saddles into the Sommerfeld precursor immediately behind the front. (paper)

Spinning Kerr black holes with stationary massive scalar clouds: the large-coupling regime

Energy Technology Data Exchange (ETDEWEB)

Hod, Shahar [Marine sciences, The Ruppin Academic Center,Ruppin, Emeq Hefer 40250 (Israel); Biotechnology, The Hadassah Academic College,37 Hanevi’im St., Jerusalem 9101001 (Israel)

2017-01-09

We study analytically the Klein-Gordon wave equation for stationary massive scalar fields linearly coupled to spinning Kerr black holes. In particular, using the WKB approximation, we derive a compact formula for the discrete spectrum of scalar field masses which characterize the stationary composed Kerr-black-hole-massive-scalar-field configurations in the large-coupling regime Mμ≫1 (here M and μ are respectively the mass of the central black hole and the proper mass of the scalar field). We confirm our analytically derived formula for the Kerr-scalar-field mass spectrum with numerical data that recently appeared in the literature.

Fermi problem in disordered systems

Science.gov (United States)

Menezes, G.; Svaiter, N. F.; de Mello, H. R.; Zarro, C. A. D.

2017-10-01

We revisit the Fermi two-atom problem in the framework of disordered systems. In our model, we consider a two-qubit system linearly coupled with a quantum massless scalar field. We analyze the energy transfer between the qubits under different experimental perspectives. In addition, we assume that the coefficients of the Klein-Gordon equation are random functions of the spatial coordinates. The disordered medium is modeled by a centered, stationary, and Gaussian process. We demonstrate that the classical notion of causality emerges only in the wave zone in the presence of random fluctuations of the light cone. Possible repercussions are discussed.

Spacetime causality in the study of the Hankel tranform

CERN Document Server

Burnol, J

2006-01-01

We study Hilbert space aspects of the Klein-Gordon equation in two-dimensional spacetime. We associate to its restriction to a spacelike wedge a scattering from the past light cone to the future light cone, which is then shown to be (essentially) the Hankel transform of order zero. We apply this to give a novel proof, solely based on the causality of this spatio-temporal wave propagation, of the theorem of de~Branges and V.~Rovnyak concerning Hankel pairs with a support property. We recover their isometric expansion as an application of Riemann's general method for solving Cauchy-Goursat problems of hyperbolic type.

Hidden regularity for a strongly nonlinear wave equation

International Nuclear Information System (INIS)

Rivera, J.E.M.

1988-08-01

The nonlinear wave equation u''-Δu+f(u)=v in Q=Ωx]0,T[;u(0)=u 0 ,u'(0)=u 1 in Ω; u(x,t)=0 on Σ= Γx]0,T[ where f is a continuous function satisfying, lim |s| sup →+∞ f(s)/s>-∞, and Ω is a bounded domain of R n with smooth boundary Γ, is analysed. It is shown that there exist a solution for the presented nonlinear wave equation that satisfies the regularity condition: |∂u/∂ η|ε L 2 (Σ). Moreover, it is shown that there exist a constant C>0 such that, |∂u/∂ η|≤c{ E(0)+|v| 2 Q }. (author) [pt

Nonlinear wave equations

CERN Document Server

Li, Tatsien

2017-01-01

This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.

The extended hyperbolic function method and exact solutions of the long-short wave resonance equations

International Nuclear Information System (INIS)

Shang Yadong

2008-01-01

The extended hyperbolic functions method for nonlinear wave equations is presented. Based on this method, we obtain a multiple exact explicit solutions for the nonlinear evolution equations which describe the resonance interaction between the long wave and the short wave. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for S and L, (b) the solitary wave solutions of kink-type for S and bell-type for L, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for S and L, (d) the singular travelling wave solutions, (e) periodic travelling wave solutions of triangle function types, and solitary wave solutions of rational function types. The variety of structure to the exact solutions of the long-short wave equation is illustrated. The methods presented here can also be used to obtain exact solutions of nonlinear wave equations in n dimensions

Free fields on the Poincare group

Energy Technology Data Exchange (ETDEWEB)

Toller, M; Vanzo, L [Dipartimento di Matematica e Fisica della Libera Universita di Trento, Italy

1978-07-01

Using a general formalism the tensor and spinor free fields as fields defined on the Poincare group manifold is treated. From an action principle it is deduced, besides the usual Klein-Gordon or Dirac equations, also the equations which describe the transformation properties of the fields under proper Lorentz transformations.

Whirling modes and parametric instabilities in the discrete Sine-Gordon equation: Experimental tests in Josephson rings

International Nuclear Information System (INIS)

Watanabe, S.; Strogatz, S.H.; van der Zant, H.S.J.; Orlando, T.P.

1995-01-01

We analyze the damped driven discrete sine-Gordon equation. For underdamped, highly discrete systems, we show that whirling periodic solutions undergo parametric instabilities at certain drive strengths. The theory predicts novel resonant steps in the current-voltage characteristics of discrete Josephson rings, occurring in the return path of the subgap region. We have observed these steps experimentally in a ring of 8 underdamped junctions. An unusual prediction, verified experimentally, is that such steps occur even if there are no vortices in the ring. Numerical simulations indicate that complex spatiotemporal behavior occurs past the onset of instability

dS/CFT correspondence from a holographic description of massless scalar fields in Minkowski space-time

International Nuclear Information System (INIS)

Loran, Farhang

2004-01-01

We solve Klein-Gordon equation for massless scalars on (d+1)-dimensional Minkowski (Euclidean) space in terms of the Cauchy data on the hypersurface t=0. By inserting the solution into the action of massless scalars in Minkowski (Euclidean) space we obtain the action of dual theory on the boundary t=0 which is exactly the holographic dual of conformally coupled scalars on (d+1)-dimensional (Euclidean anti) de Sitter space obtained in (A)dS/CFT correspondence. The observed equivalence of dual theories is explained using the one-to-one map between conformally coupled scalar fields on Minkowski (Euclidean) space and (Euclidean anti) de Sitter space which is an isomorphism between the hypersurface t=0 of Minkowski (Euclidean) space and the boundary of (A)dS space

On the Kaluza/Klein miracle

International Nuclear Information System (INIS)

Wallner, R.P.; Urbantke, H.K.

1982-01-01

Using suitable adaptions of the calculus of exterior forms, we point out that the derivation of the Einstein/Yang-Mills Lagrangian with a (formal) cosmological term from the (Riemannian) scalar curvature density of a G-bundle space can be performed almost by inspection. This method also provides a simple explanation of this so-called 'Kaluza/Klein miracle'. The equivalence of the corresponding bundle field equations with the Einstein/Yang-Mills equations over the base is shown (i.e. there is no need for an 'integration over the group degrees of freedom'). The inclusion of matter fields is discussed briefly. (Author)

Travelling wave solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations

Directory of Open Access Journals (Sweden)

M. Arshad

Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method

Benney's long wave equations

International Nuclear Information System (INIS)

Lebedev, D.R.

1979-01-01

Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown

GORDON RAMSAY’S POLITENESS STRATEGIES IN MASTERCHEF AND MASTERCHEF JUNIOR US

OpenAIRE

Annisa Friska Safa; Eri Kurniawan

2015-01-01

Abstract This research aims to investigate the types of politeness strategies that are performed by Gordon Ramsay in judging the Masterchef US and Masterchef Junior US contestants’ dishes and to reveal whether Gordon Ramsay performs any different politeness strategies between the Master chef and Masterchef Junior contestants. The data spring from Gordon Ramsay utterances, taken from the elimination test of two episodes of Masterchef season 4 (episode 9 and 12) and the elimination test of ...

Approche Kaluza-Klein et Supersymetrie de Jauge

Science.gov (United States)

Pare, Jean-Pierre

This thesis presents a non-Abelian gauge-supersymmetric Kaluza-Klein approach for charged spinning particles and strings in a background of gravitational and Yang-Mills fields. In the classical Kaluza-Klein approach, the basic mathematical structure is a principal bundle of which the base manifold is space-time. This principal bundle is endowed with a pseudo-Riemannian metric, invariant under the action of the structural group of the bundle, and a connection. Geodesic equations on the bundle lead to the Maxwell-Lorentz equation for curved space-time and Yang -Mills fields, and to a conservation law of a non-Abelian (bosonic) charge. This conservation law originates from the invariance of the free-particle action on the bundle under the action of the structural group of the bundle (gauge group). Firstly, we generalize this approach for a spinning particle. The spin of the particle is described by Grassmannian variables added to the principal bundle. This supersymmetrization gives rise, in addition to the bosonic non-Abelian charge, a fermionic one. This leads to a search for a supergroup action on the superprincipal bundle which leaves invariant the action of the spinning particle. The invariance of this action would lead to the conservation of a non-Abelian super-charge, generalizing the conservation law obtained for particles without spin. We present Lagrangian and Hamiltonian formulations, both invariant under a super -group action. The equations of motion are derived and discussed. Different terms in these equations are well known in the literature. The invariance of these formulations under a supergroup action leads to a conservation law of a non-Abelian supercharge. The bosonic part of this supercharge corresponds to the non-Abelian (bosonic) charge obtained for a particle without spin. The fermionic part is a non -physical charge. It turns out in the supersymmetric case that this decouples from all other dynamical variables, and hence it does not influence

Bethe ansatz approach to quantum sine Gordon thermodynamics and finite temperature excitations

International Nuclear Information System (INIS)

Zotos, X.

1982-01-01

Takahashi and Suzuki (TS) using the Bethe ansatz method developed a formalism for the thermodynamics of the XYZ spin chain. Translating their formalism to the quantum sine-Gordon system, the thermodynamics and finite temperature elementary excitations are analyzed. Criteria imposed by TS on the allowed states simply correspond to the condition of normalizability of the wave functions. A set of coupled nonlinear integral equations for the thermodynamic equilibrium densities for particular values of the coupling constant in the attractive regime is derived. Solving numerically these Bethe ansatz equations, curves of the specific heat as a function of temperature are obtained. The soliton contribution peaks at a temperature of about 0.4 soliton masses shifting downward as the classical limit is approached. The weak coupling regime is analyzed by deriving the Bethe ansatz equations including the charged vacuum excitations. It is shown that they are necessary for a consistent presentation of the thermodynamics

Collective coordinates theory for discrete soliton ratchets in the sine-Gordon model

Science.gov (United States)

Sánchez-Rey, Bernardo; Quintero, Niurka R.; Cuevas-Maraver, Jesús; Alejo, Miguel A.

2014-10-01

A collective coordinate theory is developed for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as an approximated solution of the discrete nonlinear equation. The dynamical equations of these two collective coordinates, obtained by means of the generalized travelling wave method, explain the mechanism underlying the soliton ratchet and capture qualitatively all the main features of this phenomenon. The numerical simulation of these equations accounts for the existence of a nonzero depinning threshold, the nonsinusoidal behavior of the average velocity as a function of the relative phase between the harmonics of the driver, the nonmonotonic dependence of the average velocity on the damping, and the existence of nontransporting regimes beyond the depinning threshold. In particular, it provides a good description of the intriguing and complex pattern of subspaces corresponding to different dynamical regimes in parameter space.

Ultra Deep Wave Equation Imaging and Illumination

Energy Technology Data Exchange (ETDEWEB)

Alexander M. Popovici; Sergey Fomel; Paul Sava; Sean Crawley; Yining Li; Cristian Lupascu

2006-09-30

In this project we developed and tested a novel technology, designed to enhance seismic resolution and imaging of ultra-deep complex geologic structures by using state-of-the-art wave-equation depth migration and wave-equation velocity model building technology for deeper data penetration and recovery, steeper dip and ultra-deep structure imaging, accurate velocity estimation for imaging and pore pressure prediction and accurate illumination and amplitude processing for extending the AVO prediction window. Ultra-deep wave-equation imaging provides greater resolution and accuracy under complex geologic structures where energy multipathing occurs, than what can be accomplished today with standard imaging technology. The objective of the research effort was to examine the feasibility of imaging ultra-deep structures onshore and offshore, by using (1) wave-equation migration, (2) angle-gathers velocity model building, and (3) wave-equation illumination and amplitude compensation. The effort consisted of answering critical technical questions that determine the feasibility of the proposed methodology, testing the theory on synthetic data, and finally applying the technology for imaging ultra-deep real data. Some of the questions answered by this research addressed: (1) the handling of true amplitudes in the downward continuation and imaging algorithm and the preservation of the amplitude with offset or amplitude with angle information required for AVO studies, (2) the effect of several imaging conditions on amplitudes, (3) non-elastic attenuation and approaches for recovering the amplitude and frequency, (4) the effect of aperture and illumination on imaging steep dips and on discriminating the velocities in the ultra-deep structures. All these effects were incorporated in the final imaging step of a real data set acquired specifically to address ultra-deep imaging issues, with large offsets (12,500 m) and long recording time (20 s).

Some applications on tangent bundle with Kaluza-Klein metric

Directory of Open Access Journals (Sweden)

Murat Altunbaş

2017-01-01

Full Text Available In this paper, differential equations of geodesics; parallelism, incompressibility and closeness conditions of the horizontal and complete lift of the vector fields are investigated with respect to Kaluza-Klein metric on tangent bundle.

Derivation of equations for scalar and fermion fields using properties of dispersion-codispersion operators

International Nuclear Information System (INIS)

Raoelina Andriambololona; Ranaivoson, R.T.R; Hanitriarivo, R.; Harison, V.

2014-01-01

We establish equations for scalar and fermion fields using results obtained from a study on a phase space representation of quantum theory that we have performed in a previous work. Our approaches are similar to the historical ones to obtain Klein-Gordon and Dirac equations but the main difference is that ours are based on the use of properties of operators called dispersion-codispersion operators. We begin with a brief recall about the dispersion-codispersion operators. Then, introducing a mass operator with its canonical conjugate coordinate and applying rules of quantization, based on the use of dispersion - codispersion operators , we deduce a second order differential operator relation from the relativistic expression relying energy, momentum and mass. Using Dirac matrices, we derive from this second order differential operator relation a first order one. The application of the second order differential operator relation on a scalar function gives the equation for the scalar field and the use of the first order differential operator relation leads to the equation for fermion field.

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

Science.gov (United States)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

Spatial evolution equation of wind wave growth

Institute of Scientific and Technical Information of China (English)

WANG; Wei; (王; 伟); SUN; Fu; (孙; 孚); DAI; Dejun; (戴德君)

2003-01-01

Based on the dynamic essence of air-sea interactions, a feedback type of spatial evolution equation is suggested to match reasonably the growing process of wind waves. This simple equation involving the dominant factors of wind wave growth is able to explain the transfer of energy from high to low frequencies without introducing the concept of nonlinear wave-wave interactions, and the results agree well with observations. The rate of wave height growth derived in this dissertation is applicable to both laboratory and open sea, which solidifies the physical basis of using laboratory experiments to investigate the generation of wind waves. Thus the proposed spatial evolution equation provides a new approach for the research on dynamic mechanism of air-sea interactions and wind wave prediction.

Physical dynamics of quasi-particles in nonlinear wave equations

International Nuclear Information System (INIS)

Christov, Ivan; Christov, C.I.

2008-01-01

By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field

Physical dynamics of quasi-particles in nonlinear wave equations

Energy Technology Data Exchange (ETDEWEB)

Christov, Ivan [Department of Mathematics, Texas A and M University, College Station, TX 77843-3368 (United States)], E-mail: christov@alum.mit.edu; Christov, C.I. [Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010 (United States)], E-mail: christov@louisiana.edu

2008-02-04

By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field.

Cnoidal waves governed by the Kudryashov–Sinelshchikov equation

International Nuclear Information System (INIS)

Randrüüt, Merle; Braun, Manfred

2013-01-01

The evolution equation for waves propagating in a mixture of liquid and gas bubbles as proposed by Kudryashov and Sinelshchikov allows, in a special case, the propagation of solitary waves of the sech 2 type. It is shown that these waves represent the solitary limit separating two families of periodic waves. One of them consists of the same cnoidal waves that are solutions of the Korteweg–de Vries equation, while the other one does not have a corresponding counterpart. It is pointed out how the ordinary differential equations governing traveling-wave solutions of the Kudryashov–Sinelshchikov and the Korteweg–de Vries equations are related to each other.

Cnoidal waves governed by the Kudryashov–Sinelshchikov equation

Energy Technology Data Exchange (ETDEWEB)

Randrüüt, Merle, E-mail: merler@cens.ioc.ee [Tallinn University of Technology, Faculty of Mechanical Engineering, Department of Mechatronics, Ehitajate tee 5, 19086 Tallinn (Estonia); Braun, Manfred [University of Duisburg–Essen, Chair of Mechanics and Robotics, Lotharstraße 1, 47057 Duisburg (Germany)

2013-10-30

The evolution equation for waves propagating in a mixture of liquid and gas bubbles as proposed by Kudryashov and Sinelshchikov allows, in a special case, the propagation of solitary waves of the sech{sup 2} type. It is shown that these waves represent the solitary limit separating two families of periodic waves. One of them consists of the same cnoidal waves that are solutions of the Korteweg–de Vries equation, while the other one does not have a corresponding counterpart. It is pointed out how the ordinary differential equations governing traveling-wave solutions of the Kudryashov–Sinelshchikov and the Korteweg–de Vries equations are related to each other.

Invariant measures for stochastic nonlinear beam and wave equations

Czech Academy of Sciences Publication Activity Database

Brzezniak, Z.; Ondreját, Martin; Seidler, Jan

2016-01-01

Roč. 260, č. 5 (2016), s. 4157-4179 ISSN 0022-0396 R&D Projects: GA ČR GAP201/10/0752 Institutional support: RVO:67985556 Keywords : stochastic partial differential equation * stochastic beam equation * stochastic wave equation * invariant measure Subject RIV: BA - General Mathematics Impact factor: 1.988, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/ondrejat-0453412.pdf

Separate P‐ and SV‐wave equations for VTI media

KAUST Repository

Pestana, Reynam C.; Ursin, Bjø rn; Stoffa, Paul L.

2011-01-01

In isotropic media we use the scalar acoustic wave equation to perform reverse time migration RTM of the recorded pressure wavefleld data. In anisotropic media P- and SV-waves are coupled and the elastic wave equation should be used for RTM. However, an acoustic anisotropic wave equation is often used instead. This results in significant shear wave energy in both modeling and RTM. To avoid this undesired SV-wave energy, we propose a different approach to separate P- and SV-wave components for vertical transversely isotropic VTI media. We derive independent pseudo-differential wave equations for each mode. The derived equations for P- and SV-waves are stable and reduce to the isotropic case. The equations presented here can be effectively used to model and migrate seismic data in VTI media where ε - δ is small. The SV-wave equation we develop is now well-posed and triplications in the SV wavefront are removed resulting in stable wave propagation. We show modeling and RTM results using the derived pure P-wave mode in complex VTI media and use the rapid expansion method REM to propagate the waveflelds in time. © 2011 Society of Exploration Geophysicists.

NLIE of Dirichlet sine-Gordon model for boundary bound states

International Nuclear Information System (INIS)

Ahn, Changrim; Bajnok, Zoltan; Palla, Laszlo; Ravanini, Francesco

2008-01-01

We investigate boundary bound states of sine-Gordon model on the finite-size strip with Dirichlet boundary conditions. For the purpose we derive the nonlinear integral equation (NLIE) for the boundary excited states from the Bethe ansatz equation of the inhomogeneous XXZ spin 1/2 chain with boundary imaginary roots discovered by Saleur and Skorik. Taking a large volume (IR) limit we calculate boundary energies, boundary reflection factors and boundary Luescher corrections and compare with the excited boundary states of the Dirichlet sine-Gordon model first considered by Dorey and Mattsson. We also consider the short distance limit and relate the IR scattering data with that of the UV conformal field theory

On a functional equation related to the intermediate long wave equation

International Nuclear Information System (INIS)

Hone, A N W; Novikov, V S

2004-01-01

We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain. (letter to the editor)

New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

Directory of Open Access Journals (Sweden)

Aly R. Seadawy

2018-03-01

Full Text Available This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM in exactly solving a well-known nonlinear equation of partial differential equations (PDEs. In this respect, the longitudinal wave equation (LWE that arises in mathematical physics with dispersion caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method. Keywords: Extended trial equation method, Longitudinal wave equation in a MEE circular rod, Dark solitons, Bright solitons, Solitary wave, Periodic solitary wave

Linear integral equations and soliton systems

International Nuclear Information System (INIS)

Quispel, G.R.W.

1983-01-01

A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)

From critical phenomena to gauge gields

International Nuclear Information System (INIS)

Le Bellac, M.

1988-01-01

In this book the author gives an introduction to the following questions: critical phenomena (Landau theory, renormalization group, two dimensional models); Perturbation theory and renormalization, scalar euclidian field (Feynman diagrams, Callan-Symanzik equations); Quantum theory of scalar fields (path integrals in quantum mechanics and statistical mechanics, green functions and S matrix, quantization of Klein-Gordon field); Gauge theories (quantization of Dirac field and electromagnetic field, quantum electrodynamics, non-abelian gauge theories) [fr

Finite element and discontinuous Galerkin methods for transient wave equations

CERN Document Server

Cohen, Gary

2017-01-01

This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem ...

The relation between relativistic and nonrelativistic solitons and kinks

International Nuclear Information System (INIS)

Baby, B.V.; Barut, A.O.

1988-01-01

The solutions of the nonlinear Klein-Gordon (KG) equations and nonlinear Schroedinger equations (NLSE) are usually dealt with separately. We study here some consequences of the simple observation that these equations and the corresponding solutions belong to the same family and the latter are the limiting cases of the former. This study leads to several new exact solutions for both the NLSE and nonlinear KG equations. 33 refs

Stochastic displacement group and its application in physics

International Nuclear Information System (INIS)

Namsraj, Kh.; Tsehrehn, D.; Sehrdamba, L.

1978-01-01

Within the stochastic displacement the equation of the brownian motion and the Dirac and Klein-Gordon equations are obtained. It is noted that the existance of a new equation describing four states with certain energy is possible. The notion of stochastic groups and its representations with illustrations in concrete examples and applications are given. The diffusion equation is obtained on the basis of the notion of stochastic rotation

Partial Differential Equations and Solitary Waves Theory

CERN Document Server

Wazwaz, Abdul-Majid

2009-01-01

"Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II w...

Comment on "Peres experiment using photons: No test for hypercomplex (quaternionic) quantum theories"

Science.gov (United States)

Procopio, Lorenzo M.; Rozema, Lee A.; Dakić, Borivoje; Walther, Philip

2017-09-01

In his recent article [Phys. Rev. A 95, 060101(R) (2017), 10.1103/PhysRevA.95.060101], Adler questions the usefulness of the bound found in our experimental search for genuine effects of hypercomplex quantum mechanics [Nat. Commun. 8, 15044 (2017), 10.1038/ncomms15044]. Our experiment was performed using a black-box (instrumentalist) approach to generalized probabilistic theories; therefore, it does not assume a priori any particular underlying mechanism. From that point of view our experimental results do indeed place meaningful bounds on the possible effects of "postquantum theories," including quaternionic quantum mechanics. In his article, Adler compares our experiment to nonrelativistic and Möller formal scattering theories within quaternionic quantum mechanics. With a particular set of assumptions, he finds that quaternionic effects would likely not manifest themselves in general. Although these assumptions are justified in the nonrelativistic case, a proper calculation for relativistic particles is still missing. Here, we provide a concrete relativistic example of Klein-Gordon scattering wherein the quaternionic effects persist. We note that when the Klein-Gordon equation is formulated using a Hamiltonian formalism it displays a so-called "indefinite metric," a characteristic feature of relativistic quantum wave equations. In Adler's example this is directly forbidden by his assumptions, and therefore our present example is not in contradiction to his work. In complex quantum mechanics this problem of an indefinite metric is solved in a second quantization. Unfortunately, there is no known algorithm for canonical field quantization in quaternionic quantum mechanics.

The conservation laws for deformed classical models

International Nuclear Information System (INIS)

Klimek, M.

1994-01-01

The problem of deriving the conservation laws for deformed linear equations of motion is investigated. The conserved currents are obtained in explicit form and used in the construction of constants of motion. The equations for the set of non-interacting oscillators with arbitrary scale-time as well as the κ-Klein-Gordon equation are considered as an example of application of the method. (author) 9 refs

Wave-equation dispersion inversion of surface waves recorded on irregular topography

KAUST Repository

Li, Jing; Schuster, Gerard T.; Lin, Fan-Chi; Alam, Amir

2017-01-01

Significant topographic variations will strongly influence the amplitudes and phases of propagating surface waves. Such effects should be taken into account, otherwise the S-velocity model inverted from the Rayleigh dispersion curves will contain significant inaccuracies. We now show that the recently developed wave-equation dispersion inversion (WD) method naturally takes into account the effects of topography to give accurate S-velocity tomograms. Application of topographic WD to demonstrates that WD can accurately invert dispersion curves from seismic data recorded over variable topography. We also apply this method to field data recorded on the crest of mountainous terrain and find with higher resolution than the standard WD tomogram.

Wave-equation dispersion inversion of surface waves recorded on irregular topography

KAUST Repository

Li, Jing

2017-08-17

Significant topographic variations will strongly influence the amplitudes and phases of propagating surface waves. Such effects should be taken into account, otherwise the S-velocity model inverted from the Rayleigh dispersion curves will contain significant inaccuracies. We now show that the recently developed wave-equation dispersion inversion (WD) method naturally takes into account the effects of topography to give accurate S-velocity tomograms. Application of topographic WD to demonstrates that WD can accurately invert dispersion curves from seismic data recorded over variable topography. We also apply this method to field data recorded on the crest of mountainous terrain and find with higher resolution than the standard WD tomogram.

Blowing-up Semilinear Wave Equation with Exponential ...

Indian Academy of Sciences (India)

Blowing-up Semilinear Wave Equation with Exponential Nonlinearity in Two Space ... We investigate the initial value problem for some semi-linear wave equation in two space dimensions with exponential nonlinearity growth. ... Current Issue

Phases of Kaluza-Klein black holes

DEFF Research Database (Denmark)

Elvang, Henriette; Obers, Niels; Harmark, Troels

2004-01-01

We review the latest progress in understanding the phase structure of static and neutral Kaluza-Klein black holes, i.e. static and neutral solutions of pure gravity with an event horizon and with asymptotics Md × S1, Md being d-dimensional Minkowski space.......We review the latest progress in understanding the phase structure of static and neutral Kaluza-Klein black holes, i.e. static and neutral solutions of pure gravity with an event horizon and with asymptotics Md × S1, Md being d-dimensional Minkowski space....

Theories of Matter, Space and Time, Volume 2; Quantum theories

Science.gov (United States)

Evans, N.; King, S. F.

2018-06-01

This book and its prequel Theories of Matter Space and Time: Classical Theories grew out of courses that we have both taught as part of the undergraduate degree program in Physics at Southampton University, UK. Our goal was to guide the full MPhys undergraduate cohort through some of the trickier areas of theoretical physics that we expect our undergraduates to master. Here we teach the student to understand first quantized relativistic quantum theories. We first quickly review the basics of quantum mechanics which should be familiar to the reader from a prior course. Then we will link the Schrödinger equation to the principle of least action introducing Feynman's path integral methods. Next, we present the relativistic wave equations of Klein, Gordon and Dirac. Finally, we convert Maxwell's equations of electromagnetism to a wave equation for photons and make contact with quantum electrodynamics (QED) at a first quantized level. Between the two volumes we hope to move a student's understanding from their prior courses to a place where they are ready, beyond, to embark on graduate level courses on quantum field theory.

A membrane wave equation for Q.C.D. (SU(infinity))

International Nuclear Information System (INIS)

Botelho, L.C.L.

1988-01-01

It is proposed a quantum membrane wave functional describing the interaction between a colored SU(N c ) membrane and a quantized Yang-Mills field. Additionally, its associated wave equation in the t'Hooft N c ->infinity limit is deduced. (A.C.A.S.) [pt

The sine-Gordon model revisited I

Energy Technology Data Exchange (ETDEWEB)

Niccoli, G.; Teschner, J.

2009-10-15

We study integrable lattice regularizations of the Sine-Gordon model with the help of the Separation of Variables method of Sklyanin and the Baxter Q-operators. This allows us to characterize the spectrum (eigenvalues and eigenstates) completely in terms of polynomial solutions of the Baxter equation with certain properties. This result is analogous to the completeness of the Bethe ansatz. (orig.)

Soliton annihilation in the perturbed sine-Gordon system

DEFF Research Database (Denmark)

Pedersen, Niels Falsig; Samuelsen, Mogens Rugholm; Welner, D.

1984-01-01

Fluxon-antifluxon annihilation in the perturbed sine-Gordon equation with loss and driving terms is investigated. For the infinite line we find a simple analytic expression for the threshold driving term corresponding to annihilation. With the application of the results to a Josephson junction...

Massive Kaluza-Klein theories and their spontaneously broken symmetries

International Nuclear Information System (INIS)

Hohm, O.

2006-07-01

In this thesis we investigate the effective actions for massive Kaluza-Klein states, focusing on the massive modes of spin-3/2 and spin-2 fields. To this end we determine the spontaneously broken gauge symmetries associated to these 'higher-spin' states and construct the unbroken phase of the Kaluza-Klein theory. We show that for the particular background AdS 3 x S 3 x S 3 a consistent coupling of the first massive spin-3/2 multiplet requires an enhancement of local supersymmetry, which in turn will be partially broken in the Kaluza-Klein vacuum. The corresponding action is constructed as a gauged maximal supergravity in D=3. Subsequently, the symmetries underlying an infinite tower of massive spin-2 states are analyzed in case of a Kaluza-Klein compactification of four-dimensional gravity to D=3. It is shown that the resulting gravity-spin-2 theory is given by a Chern-Simons action of an affine algebra and also allows a geometrical interpretation in terms of 'algebra-valued' differential geometry. The global symmetry group is determined, which contains an affine extension of the Ehlers group. We show that the broken phase can in turn be constructed via gauging a certain subgroup of the global symmetry group. Finally, deformations of the Kaluza-Klein theory on AdS 3 x S 3 x S 3 and the corresponding symmetry breakings are analyzed as possible applications for the AdS/CFT correspondence. (Orig.)

An approach to rogue waves through the cnoidal equation

Science.gov (United States)

Lechuga, Antonio

2014-05-01

Lately it has been realized the importance of rogue waves in some events happening in open seas. Extreme waves and extreme weather could explain some accidents, but not all of them. Every now and then inflicted damages on ships only can be reported to be caused by anomalous and elusive waves, such as rogue waves. That's one of the reason why they continue attracting considerable interest among researchers. In the frame of the Nonlinear Schrödinger equation(NLS), Witham(1974) and Dingemans and Otta (2001)gave asymptotic solutions in moving coordinates that transformed the NLS equation in a ordinary differential equation that is the Duffing or cnoidal wave equation. Applying the Zakharov equation, Stiassnie and Shemer(2004) and Shemer(2010)got also a similar equation. It's well known that this ordinary equation can be solved in elliptic functions. The main aim of this presentation is to sort out the domains of the solutions of this equation, that, of course, are linked to the corresponding solutions of the partial differential equations(PDEs). That being, Lechuga(2007),a simple way to look for anomalous waves as it's the case with some "chaotic" solutions of the Duffing equation.

Travelling wave solutions for a surface wave equation in fluid mechanics

Directory of Open Access Journals (Sweden)

Tian Yi

2016-01-01

Full Text Available This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.

Mathematical issues in eternal inflation

Science.gov (United States)

Singh Kohli, Ikjyot; Haslam, Michael C.

2015-04-01

In this paper, we consider the problem of the existence and uniqueness of solutions to the Einstein field equations for a spatially flat Friedmann-Lemaître-Robertson-Walker universe in the context of stochastic eternal inflation, where the stochastic mechanism is modelled by adding a stochastic forcing term representing Gaussian white noise to the Klein-Gordon equation. We show that under these considerations, the Klein-Gordon equation actually becomes a stochastic differential equation. Therefore, the existence and uniqueness of solutions to Einstein’s equations depend on whether the coefficients of this stochastic differential equation obey Lipschitz continuity conditions. We show that for any choice of V(φ ), the Einstein field equations are not globally well-posed, hence, any solution found to these equations is not guaranteed to be unique. Instead, the coefficients are at best locally Lipschitz continuous in the physical state space of the dynamical variables, which only exist up to a finite explosion time. We further perform Feller’s explosion test for an arbitrary power-law inflaton potential and prove that all solutions to the Einstein field equations explode in a finite time with probability one. This implies that the mechanism of stochastic inflation thus considered cannot be described to be eternal, since the very concept of eternal inflation implies that the process continues indefinitely. We therefore argue that stochastic inflation based on a stochastic forcing term would not produce an infinite number of universes in some multiverse ensemble. In general, since the Einstein field equations in both situations are not well-posed, we further conclude that the existence of a multiverse via the stochastic eternal inflation mechanism considered in this paper is still very much an open question that will require much deeper investigation.

[Jan Kusberg, Kleine Geschichte St. Petersburgs. (Regensburg, 2009) ; Ingrid Bohn. Kleine Geschichte Stockholms. (Regensburg, 2008) ; Konrad Dittrich. Kleine Lübecker Stadtgeschichte. (Regensburg, 2007)] / Dennis Hortmuth

Index Scriptorium Estoniae

Hormuth, Dennis

2011-01-01

Arvustus: Jan Kusberg, Kleine Geschichte St. Petersburgs. (Regensburg, 2009) ; Ingrid Bohn. Kleine Geschichte Stockholms. (Regensburg, 2008) ; Konrad Dittrich. Kleine Lübecker Stadtgeschichte. (Regensburg, 2007)

Critical values of the Yang-Yang functional in the quantum sine-Gordon model

International Nuclear Information System (INIS)

Lukyanov, Sergei L.

2011-01-01

The critical values of the Yang-Yang functional corresponding to the vacuum states of the sine-Gordon QFT in the finite-volume are studied. Two major applications are discussed: (i) generalization of Fendley-Saleur-Zamolodchikov relations to arbitrary values of the sine-Gordon coupling constant, and (ii) connection problem for a certain two-parameter family of solutions of the Painleve III equation.

Exact traveling wave solutions of the Boussinesq equation

International Nuclear Information System (INIS)

Ding Shuangshuang; Zhao Xiqiang

2006-01-01

The repeated homogeneous balance method is used to construct exact traveling wave solutions of the Boussinesq equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions of the Boussinesq equation are successfully obtained

Special relativity of Kaluza-Klein

International Nuclear Information System (INIS)

Maia, M.D.

1984-01-01

Kaluza-Klein theory is formulated from the point of view of the Gauss geometry of embedded manifolds. According to this view, space-time is regarded as locally and isometrically embedded in the high dimensional space predicted by that theory. The high dimensional Minkowski space is considered as a particular solution of the high dimensional vacuum Einstein's equations and it is assumed to represent the ground state of the theory. In this particular case it is shown that the compactification of the space of internal variables follows from the second quadratic forms of the Gaussian geometry of space-time. The Gauss-Codazzi-Ricci integrability conditions are interpreted as the field equations for a low energy observer. The space-time reduced Einstein-Hilbert action is interpreted as an integral equation on the size of the internal space. 13 references

A Bohmian approach to the perturbations of non-linear Klein ...

Indian Academy of Sciences (India)

2016-07-13

Jul 13, 2016 ... 2School of Physics, Institute for Research in Fundamental Science (IPM), Tehran, Iran ... In the framework of Bohmian quantum mechanics, the Klein–Gordon equation ... field theory is the limit of the quantum mechanics when.

Reshaping-induced spatiotemporal chaos in driven, damped sine-Gordon systems

International Nuclear Information System (INIS)

Chacon, R.

2007-01-01

Spatiotemporal chaos arising from the competition between sine-Gordon-breather and kink-antikink-pair solitons by reshaping an ac force is demonstrated. After introducing soliton collective coordinates, Melnikov's method is applied to the resulting effective equation of motion to estimate the parameter-space regions of the ac force where homoclinic bifurcations are induced. The analysis reveals that the chaos-order threshold exhibits sensitivity to small changes in the force shape. Computer simulations of the sine-Gordon system show good agreement with these theoretical predictions

Wave equations on a de Sitter fiber bundle. [Semiclassical wave function, bundle space, L-S coupling

Energy Technology Data Exchange (ETDEWEB)

Drechsler, W [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany)

1975-01-01

A gauge theory of strong interaction is developed based on fields defined on a fiber bundle. The structural group of the bundle is taken to be the Lsub(4,1) de Sitter group. An internal variable xi, varying in the fiber over a space-time point x, is introduced as a means to describe - with the help of a semiclassical wave function psi(x,xi) defined on the bundle space - the internal structure of extended hadrons in a framework using differential geometric techniques. Three basic nonlinear wave equations for psi(x,xi) are established which are of integro-differential type. The nonlinear coupling terms in these de Sitter gauge invariant equations represent physically a generalized spin orbit coupling or a generalized spin coupling for the motion taking place in the fiber. The motivation for using a bigger space for the definition of hadronic matter wave functions as well as the implications of this geometric approach to strong interaction physics is discussed in detail, in particular with respect to the problem of hadronic constituents. The proposed fiber bundle formalism allows a dynamical description of extended structures for hadrons without implying the necessity of introducing any constituents.

Black Hole Monodromy and Conformal Field Theory

NARCIS (Netherlands)

Castro, A.; Lapan, J.M.; Maloney, A.; Rodriguez, M.J.

2013-01-01

The analytic structure of solutions to the Klein-Gordon equation in a black hole background, as represented by monodromy data, is intimately related to black hole thermodynamics. It encodes the "hidden conformal symmetry" of a nonextremal black hole, and it explains why features of the inner event

Travelling wave solutions to the Kuramoto-Sivashinsky equation

International Nuclear Information System (INIS)

Nickel, J.

2007-01-01

Combining the approaches given by Baldwin [Baldwin D et al. Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs. J Symbol Comput 2004;37:669-705], Peng [Peng YZ. A polynomial expansion method and new general solitary wave solutions to KS equation. Comm Theor Phys 2003;39:641-2] and by Schuermann [Schuermann HW, Serov VS. Weierstrass' solutions to certain nonlinear wave and evolution equations. Proc progress electromagnetics research symposium, 28-31 March 2004, Pisa. p. 651-4; Schuermann HW. Traveling-wave solutions to the cubic-quintic nonlinear Schroedinger equation. Phys Rev E 1996;54:4312-20] leads to a method for finding exact travelling wave solutions of nonlinear wave and evolution equations (NLWEE). The first idea is to generalize ansaetze given by Baldwin and Peng to find elliptic solutions of NLWEEs. Secondly, conditions used by Schuermann to find physical (real and bounded) solutions and to discriminate between periodic and solitary wave solutions are used. The method is shown in detail by evaluating new solutions of the Kuramoto-Sivashinsky equation

Wave-equation Q tomography

KAUST Repository

Dutta, Gaurav

2016-10-12

Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. The amplitude and the dispersion losses from attenuation are often compensated for during prestack depth migration. However, most attenuation compensation or Qcompensation migration algorithms require an estimate of the background Q model. We have developed a wave-equation gradient optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ∈, where ∈ is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early arrivals. The gradient is computed by migrating the observed traces weighted by the frequency shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests determined that an improved accuracy of the Q model by wave-equation Q tomography leads to a noticeable improvement in migration image quality. © 2016 Society of Exploration Geophysicists.

Wave-equation Q tomography

KAUST Repository

Dutta, Gaurav; Schuster, Gerard T.

2016-01-01

Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. The amplitude and the dispersion losses from attenuation are often compensated for during prestack depth migration. However, most attenuation compensation or Qcompensation migration algorithms require an estimate of the background Q model. We have developed a wave-equation gradient optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ∈, where ∈ is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early arrivals. The gradient is computed by migrating the observed traces weighted by the frequency shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests determined that an improved accuracy of the Q model by wave-equation Q tomography leads to a noticeable improvement in migration image quality. © 2016 Society of Exploration Geophysicists.

Spin effects in strong-field laser-electron interactions

International Nuclear Information System (INIS)

Ahrens, S; Bauke, H; Müller, T-O; Villalba-Chávez, S; Müller, C

2013-01-01

The electron spin degree of freedom can play a significant role in relativistic scattering processes involving intense laser fields. In this contribution we discuss the influence of the electron spin on (i) Kapitza-Dirac scattering in an x-ray laser field of high intensity, (ii) photo-induced electron-positron pair production in a strong laser wave and (iii) multiphoton electron-positron pair production on an atomic nucleus. We show that in all cases under consideration the electron spin can have a characteristic impact on the process properties and their total probabilities. To this end, spin-resolved calculations based on the Dirac equation in the presence of an intense laser field are performed. The predictions from Dirac theory are also compared with the corresponding results from the Klein-Gordon equation.

[An unpublished contribution of Melanie Klein "On Reassurance"].

Science.gov (United States)

Frank, Claudia; Klein, Melanie

2005-01-01

Melanie Klein's unpublished paper on reassurance is presented in German translation. The author shows that it was a contribution to Glover's investigation on psychoanalytic technique in the 1930s. The paper is discussed against the background of the technical discussions conducted in London at that time (e. g. M. Schmideberg, J. Strachey) and of Klein's relevant publications. Although Klein consistently considered "correct" interpretation to be the most effective means of reassurance, she occasionally also accepted a non-interpreting approach. In this respect the paper presented here goes further than any other of her writings.

Massive Kaluza-Klein theories and their spontaneously broken symmetries

Energy Technology Data Exchange (ETDEWEB)

Hohm, O.

2006-07-15

In this thesis we investigate the effective actions for massive Kaluza-Klein states, focusing on the massive modes of spin-3/2 and spin-2 fields. To this end we determine the spontaneously broken gauge symmetries associated to these 'higher-spin' states and construct the unbroken phase of the Kaluza-Klein theory. We show that for the particular background AdS{sub 3} x S{sup 3} x S{sup 3} a consistent coupling of the first massive spin-3/2 multiplet requires an enhancement of local supersymmetry, which in turn will be partially broken in the Kaluza-Klein vacuum. The corresponding action is constructed as a gauged maximal supergravity in D=3. Subsequently, the symmetries underlying an infinite tower of massive spin-2 states are analyzed in case of a Kaluza-Klein compactification of four-dimensional gravity to D=3. It is shown that the resulting gravity-spin-2 theory is given by a Chern-Simons action of an affine algebra and also allows a geometrical interpretation in terms of 'algebra-valued' differential geometry. The global symmetry group is determined, which contains an affine extension of the Ehlers group. We show that the broken phase can in turn be constructed via gauging a certain subgroup of the global symmetry group. Finally, deformations of the Kaluza-Klein theory on AdS{sub 3} x S{sup 3} x S{sup 3} and the corresponding symmetry breakings are analyzed as possible applications for the AdS/CFT correspondence. (Orig.)

Rotating black string and the effective Teukolsky equation in the braneworld

International Nuclear Information System (INIS)

Kanno, Sugumi; Soda, Jiro

2004-01-01

In the Randall-Sundrum two-brane (RS1) model, a large Kerr black hole on the brane can be naturally identified with a section of a rotating black string. To estimate Kaluza-Klein (KK) corrections on gravitational waves emitted by perturbed rotating black strings, we give the effective Teukolsky equation on the brane, which is a separable equation and hence numerically manageable. In this process, we derive the master equation for the electric part of the Weyl tensor, E μν , which is also useful in discussing the transition from black strings to localized black holes triggered by Gregory-Laflamme instability

Gordon Browni valitsuslaevuke sõitis karidele / Heiki Suurkask

Index Scriptorium Estoniae

Suurkask, Heiki, 1972-

2008-01-01

Briti peaministri Gordon Browni partei kaotas Inglismaa ja Walesi kohalikel valimistel. Autori väitel võis kõige rängema hoobi valitsusele anda madalaima, 10-protsendilise tulumaksumäära kaotamine

Traveling wave behavior for a generalized fisher equation

International Nuclear Information System (INIS)

Feng Zhaosheng

2008-01-01

There is the widespread existence of wave phenomena in physics, chemistry and biology. This clearly necessitates a study of traveling waves in depth and of the modeling and analysis involved. In the present paper, we study a nonlinear reaction-diffusion equation, which can be regarded as a generalized Fisher equation. Applying the Cole-Hopf transformation and the first integral method, we obtain a class of traveling solitary wave solutions for this generalized Fisher equation

Parsimonious wave-equation travel-time inversion for refraction waves

KAUST Repository

Fu, Lei; Hanafy, Sherif M.; Schuster, Gerard T.

2017-01-01

We present a parsimonious wave-equation travel-time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N

Travelling Wave Solutions of Coupled Burger’s Equations of Time-Space Fractional Order by Novel (Gʹ/G-Expansion Method

Directory of Open Access Journals (Sweden)

Rashida Hussain

2017-04-01

Full Text Available In this paper, Novel (Gʹ/G-expansion method is used to find new generalized exact travelling wave solutions of fractional order coupled Burger’s equations in terms of trigonometric functions, rational functions and hyperbolic functions with arbitrary parameters. For the conversion of the partial differential equation to the ordinary differential equation, complex transformation method is used. Novel (Gʹ/G-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear equations. Moreover, for the representation of these exact solutions we have plotted graphs for different values of parameters which were in travelling waveform.

Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

KAUST Repository

Zhang, Zhendong

2016-07-26

We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized surface waves because the skeletonized dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the multi-dimensional elastic wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Our method can invert for lateral velocity variations and also can mitigate the local minimum problem in full waveform inversion with a reasonable computation cost for simple models. Results with synthetic and field data illustrate the benefits and limitations of this method. © 2016 Elsevier B.V.

Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

Science.gov (United States)

Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

2014-01-01

Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

Wave-equation reflection traveltime inversion

KAUST Repository

Zhang, Sanzong

2011-01-01

The main difficulty with iterative waveform inversion using a gradient optimization method is that it tends to get stuck in local minima associated within the waveform misfit function. This is because the waveform misfit function is highly nonlinear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. No travel-time picking is needed and no high-frequency approximation is assumed. The mathematical derivation and the numerical examples are presented to partly demonstrate its efficiency and robustness. © 2011 Society of Exploration Geophysicists.

Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations.

Science.gov (United States)

Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

2015-12-01

The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

Quasi-exactly solvable relativistic soft-core Coulomb models

Energy Technology Data Exchange (ETDEWEB)

Agboola, Davids, E-mail: davagboola@gmail.com; Zhang, Yao-Zhong, E-mail: yzz@maths.uq.edu.au

2012-09-15

By considering a unified treatment, we present quasi exact polynomial solutions to both the Klein-Gordon and Dirac equations with the family of soft-core Coulomb potentials V{sub q}(r)=-Z/(r{sup q}+{beta}{sup q}){sup 1/q}, Z>0, {beta}>0, q{>=}1. We consider cases q=1 and q=2 and show that both cases are reducible to the same basic ordinary differential equation. A systematic and closed form solution to the basic equation is obtained using the Bethe ansatz method. For each case, the expressions for the energies and the allowed parameters are obtained analytically and the wavefunctions are derived in terms of the roots of a set of Bethe ansatz equations. - Highlights: Black-Right-Pointing-Pointer The relativistic bound-state solutions of the soft-core Coulomb models. Black-Right-Pointing-Pointer Quasi-exact treatments of the Dirac and Klein-Gordon equations for the soft-core Coulomb models. Black-Right-Pointing-Pointer Solutions obtained in terms of the roots to the Bethe ansatz equations. Black-Right-Pointing-Pointer The hidden Lie algebraic structure discussed for the models. Black-Right-Pointing-Pointer Results useful in describing mesonic atoms and interaction of intense laser fields with atom.

Non-Hermitian interaction representation and its use in relativistic quantum mechanics

Czech Academy of Sciences Publication Activity Database

Znojil, Miloslav

2017-01-01

Roč. 385, č. 10 (2017), s. 162-179 ISSN 0003-4916 R&D Projects: GA ČR GA16-22945S Institutional support: RVO:61389005 Keywords : unitary quantum systems * non-Hermitian version of Dirac's interaction picture * complete set of time-evolution equations * application in relativistic quantum mechanics * Klein-Gordon example with space-time-dependent mass Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 2.465, year: 2016

Behaviour of Magnetoacoustic Waves in the Neighbourhood of a ...

Indian Academy of Sciences (India)

behaviour of the fast magnetoacoustic wave in terms of the Klein–Gordon equation. ..... In other words, the y-components of v1 and b (namely vy and by) entirely decouple from the x- ..... implemented to focus the majority of the grid points close to the origin. .... we choose to set β0 = 0.25 and we present these results below.

Paraxial WKB solution of a scalar wave equation

International Nuclear Information System (INIS)

Pereverzev, G.V.

1993-04-01

An asymptotic method of solving a scalar wave equation in inhomogeneous media is developed. This method is an extension of the WKB method to the multidimensional case. It reduces a general wave equation to a set of ordinary differential equations similar to that of the eikonal approach and includes the latter as a particular case. However, the WKB method makes use of another kind of asymptotic expansion and, unlike the eikonal approach, describes the wave properties, i.e. diffraction and interference. At the same time, the three-dimensional WKB method is more simple for numerical treatment because the number of equations is less than in the eikonal approach. The method developed may be used for a calculation of wave fields in problems of RF heating, current drive and plasma diagnostics with microwave beams. (orig.)

Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

KAUST Repository

Zhang, Zhendong; Schuster, Gerard T.; Liu, Yike; Hanafy, Sherif M.; Li, Jing

2016-01-01

We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized

Green's Functions Construction and Applications

CERN Document Server

Melnikov, Yuri A

2012-01-01

This monograph is looking at applied elliptic and parabolic type partial differential equations in two variables. The elliptic type includes the Laplace, static Klein-Gordon and biharmonic equation. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has emerged as a mathematical model in financial mathematics. This book is a useful source for everyone who is studying or working in the fields of science, finance, or engineering that involve practical solution of partial differential equations.

Traveling waves of the regularized short pulse equation

International Nuclear Information System (INIS)

Shen, Y; Horikis, T P; Kevrekidis, P G; Frantzeskakis, D J

2014-01-01

The properties of the so-called regularized short pulse equation (RSPE) are explored with a particular focus on the traveling wave solutions of this model. We theoretically analyze and numerically evolve two sets of such solutions. First, using a fixed point iteration scheme, we numerically integrate the equation to find solitary waves. It is found that these solutions are well approximated by a finite sum of hyperbolic secants powers. The dependence of the soliton's parameters (height, width, etc) to the parameters of the equation is also investigated. Second, by developing a multiple scale reduction of the RSPE to the nonlinear Schrödinger equation, we are able to construct (both standing and traveling) envelope wave breather type solutions of the former, based on the solitary wave structures of the latter. Both the regular and the breathing traveling wave solutions identified are found to be robust and should thus be amenable to observations in the form of few optical cycle pulses. (paper)

N-body bound state relativistic wave equations

International Nuclear Information System (INIS)

Sazdjian, H.

1988-06-01

The manifestly covariant formalism with constraints is used for the construction of relativistic wave equations to describe the dynamics of N interacting spin 0 and/or spin 1/2 particles. The total and relative time evolutions of the system are completely determined by means of kinematic type wave equations. The internal dynamics of the system is 3 N-1 dimensional, besides the contribution of the spin degrees of freedom. It is governed by a single dynamical wave equation, that determines the eigenvalue of the total mass squared of the system. The interaction is introduced in a closed form by means of two-body potentials. The system satisfies an approximate form of separability

Obituary: Gordon Donaldson Obituary: Gordon Donaldson

Science.gov (United States)

Pegrum, Colin; Campbell, Archie; Hampshire, Damian

2013-07-01

Gordon Donaldson died in Glasgow on 28 November 2012 at the age of 71. He was born in Edinburgh and brought up and educated in Glasgow, which was his home city for much of his life. He was educated first at Glasgow Academy, and then with a scholarship at Christ's College Cambridge. Here he read Natural Sciences, finishing with first class honors in Physics. He then did a PhD on tunneling in superconductors in the Mond Laboratory, supervised by John Adkins. These were interesting times, since type II superconductors had only recently been identified, and the Mond was a leading player in the physics of vortices and other quantum effects. It was headed by Pippard and Shoenberg, and colleagues around that time were Brian Josephson, John Clarke, Colin Gough and John Waldram. On finishing his PhD in 1966 Gordon went straight to a lectureship at the University of Lancaster. In 1975 during a sabbatical at the University of California, Berkeley, with John Clarke's group, Gordon co-invented thin-film gradiometers with integrated DC SQUIDs. He then moved back to Glasgow, to the Department of Applied Physics at Strathclyde University, where he founded a new research group to make and use superconducting devices, especially SQUIDs and gradiometers. From modest beginnings the group grew steadily, acquiring new facilities and members, until in the 1990s it had over 20 members and a host of collaborators from elsewhere in Glasgow and abroad. With funding from the Wellcome Trust, Gordon and colleagues at Glasgow University and the Southern General Hospital in Glasgow set up a new biomagnetism facility in 1998 on the hospital campus to use SQUID gradiometers made at Strathclyde for measurements on patients and volunteers. Another of his main research interests was the use of SQUIDs for nondestructive evaluation (NDE). This started in the days before high temperature superconductors (HTS) with wire-wound gradiometers and niobium SQUIDs, soon moving on to miniature thin-film niobium

Ginzburg-Landau equations for a d-wave superconductor with applications to vortex structure and surface problems

International Nuclear Information System (INIS)

Xu, J.; Ren, Y.; Ting, C.S.

1995-01-01

The properties of a d x 2 -y 2 -wave superconductor in an external magnetic field are investigated on the basis of Gorkov's theory of weakly coupled superconductors. The Ginzburg-Landau (GL) equations, which govern the spatial variations of the order parameter and the supercurrent, are microscopically derived. The single vortex structure and surface problems in such a superconductor are studied using these equations. It is shown that the d-wave vortex structure is very different from the conventional s-wave vortex: the s-wave and d-wave components, with the opposite winding numbers, are found to coexist in the region near the vortex core. The supercurrent and local magnetic field around the vortex are calculated. Far away from the vortex core, both of them exhibit a fourfold symmetry, in contrast to an s-wave superconductor. The surface problem in a d-wave superconductor is also studied by solving the GL equations. The total order parameter near the surface is always a real combination of s- and d-wave components, which means that the proximity effect cannot induce a time-reversal symmetry-breaking state at the surface

Fredholm determinant representation of quantum correlation function for Sine-Gordon at special value of coupling constant

International Nuclear Information System (INIS)

Itoyama, H.; Korepin, V.E.; Thacker, H.B.

1992-01-01

In this paper, correlation functions of the Sine-Gordon model (which is equivalent of the Massive-Thirring model) are considered at the free fermion point. The authors derive a determinant formula for local correlation functions of the Sine-Gordon model, starting form Bethe ansatz wave function. Kernel of integral operator is trigonometric version of the one for Impenetrable Bosons

Wave-equation dispersion inversion

KAUST Repository

Li, Jing; Feng, Zongcai; Schuster, Gerard T.

2016-01-01

We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained

Temperature waves and the Boltzmann kinetic equation for phonons

International Nuclear Information System (INIS)

Urushev, D.; Borisov, M.; Vavrek, A.

1988-01-01

The ordinary parabolic equation for thermal conduction based on the Fourier empiric law as well as the generalized thermal conduction equation based on the Maxwell law have been derived from the Boltzmann equation for the phonons within the relaxation time approximation. The temperature waves of the so-called second sound in crystals at low temperatures are transformed into Fourier waves at low frequencies with respect to the characteristic frequency of the U-processes. These waves are transformed into temperature waves similar to the second sound waves in He II at frequences higher than the U-processes characteristic. 1 fig., 19 refs

Study of nonlinear waves described by the cubic Schroedinger equation

Energy Technology Data Exchange (ETDEWEB)

Walstead, A.E.

1980-03-12

The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables.

Exact solitary waves of the Fisher equation

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.

2005-01-01

New method is presented to search exact solutions of nonlinear differential equations. This approach is used to look for exact solutions of the Fisher equation. New exact solitary waves of the Fisher equation are given

Os anulabilismos de Klein e de Swain e o problema de Gettier

Directory of Open Access Journals (Sweden)

Emerson Carlos Valcarenghi

2010-08-01

Full Text Available In this essay, we intend to show that Peter Klein and Marshall Swain defeasibility theories do not resolve the Gettier problem. Klein postulates, to any Gettier counterexample, that there is a true proposition which, when associated with evidence-e of S, genuinely defeats the justification of p to S. Swain postulates that, to any Gettier-type counterexample, there is a true proposition which, when associated with the set of reasons-R of S, ultimately defeats the justification of S to believe p. To show that Klein an Swain proposals do not resolve that problem, this essay presents two Gettier-type counterexamples for which there are no genuine defeaters of justification of p by e to S and there are no defeaters not ultimately defeated of the justification of the belief of S that p by R. After doing that, we try to show that the obtained conclusion regarding Klein and Swain defeasibility theories can be extended to any defeasibility theory of knowledge.

Discrete mKdV and discrete sine-Gordon flows on discrete space curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2014-01-01

In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym–Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces. (paper)

Klein tunneling phenomenon with pair creation process

Science.gov (United States)

Wu, G. Z.; Zhou, C. T.; Fu, L. B.

2018-01-01

In this paper, we study the Klein tunneling phenomenon with electron-positron pair creation process. Pairs can be created from the vacuum by a supercritical single-well potential (for electrons). In the time region, the time-dependent growth pattern of the created pairs can be characterized by four distinct regimes which can be considered as four different statuses of the single well. We find that if positrons penetrate the single well by Klein tunneling in different statuses, the total number of the tunneling positrons will be different. If Klein tunneling begins at the initial stage of the first status i.e. when the sing well is empty, the tunneling process and the total number of tunneling positrons are similar to the traditional Klein tunneling case without considering the pair creation process. As the tunneling begins later, the total tunneling positron number increases. The number will finally settle to an asymptotic value when the tunneling begins later than the settling-down time t s of the single well which has been defined in this paper.

The magnetic field experiment onboard Equator-S and its scientific possibilities

Directory of Open Access Journals (Sweden)

K.-H. Fornacon

1999-12-01

Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques

The magnetic field experiment onboard Equator-S and its scientific possibilities

Directory of Open Access Journals (Sweden)

K.-H. Fornacon

Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.

Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques

The collision of multimode dromions and a firewall in the two-component long-wave-short-wave resonance interaction equation

International Nuclear Information System (INIS)

Radha, R; Kumar, C Senthil; Lakshmanan, M; Gilson, C R

2009-01-01

In this communication, we investigate the two-component long-wave-short-wave resonance interaction equation and show that it admits the Painleve property. We then suitably exploit the recently developed truncated Painleve approach to generate exponentially localized solutions for the short-wave components S (1) and S (2) while the long wave L admits a line soliton only. The exponentially localized solutions driving the short waves S (1) and S (2) in the y-direction are endowed with different energies (intensities) and are called 'multimode dromions'. We also observe that the multimode dromions suffer from intramodal inelastic collision while the existence of a firewall across the modes prevents the switching of energy between the modes. (fast track communication)

Sine-Gordon quantum field theory on the half-line with quantum boundary degrees of freedom

International Nuclear Information System (INIS)

Baseilhac, P.; Koizumi, K.

2003-01-01

The sine-Gordon model on the half-line with a dynamical boundary introduced by Delius and one of the authors is considered at quantum level. Classical boundary conditions associated with classical integrability are shown to be preserved at quantum level too. Non-local conserved charges are constructed explicitly in terms of the field and boundary operators. We solve the intertwining equation associated with a certain coideal subalgebra of U q (sl 2 -bar) generated by these non-local charges. The corresponding solution is shown to satisfy quantum boundary Yang-Baxter equations. Up to an exact relation between the quantization length of the boundary quantum mechanical system and the sine-Gordon coupling constant, we conjecture the soliton/antisoliton reflection matrix and bound states reflection matrices. The structure of the boundary state is then considered, and shown to be divided in two sectors. Also, depending on the sine-Gordon coupling constant a finite set of boundary bound states are identified. Taking the analytic continuation of the coupling, the corresponding boundary sinh-Gordon model is briefly discussed. In particular, the particle reflection factor enjoys weak-strong coupling duality

Solar atmosphere wave dynamics generated by solar global oscillating eigenmodes

Science.gov (United States)

Griffiths, M. K.; Fedun, V.; Erdélyi, R.; Zheng, R.

2018-01-01

The solar atmosphere exhibits a diverse range of wave phenomena, where one of the earliest discovered was the five-minute global acoustic oscillation, also referred to as the p-mode. The analysis of wave propagation in the solar atmosphere may be used as a diagnostic tool to estimate accurately the physical characteristics of the Sun's atmospheric layers. In this paper, we investigate the dynamics and upward propagation of waves which are generated by the solar global eigenmodes. We report on a series of hydrodynamic simulations of a realistically stratified model of the solar atmosphere representing its lower region from the photosphere to low corona. With the objective of modelling atmospheric perturbations, propagating from the photosphere into the chromosphere, transition region and low corona, generated by the photospheric global oscillations the simulations use photospheric drivers mimicking the solar p-modes. The drivers are spatially structured harmonics across the computational box parallel to the solar surface. The drivers perturb the atmosphere at 0.5 Mm above the bottom boundary of the model and are placed coincident with the location of the temperature minimum. A combination of the VALIIIC and McWhirter solar atmospheres are used as the background equilibrium model. We report how synthetic photospheric oscillations may manifest in a magnetic field free model of the quiet Sun. To carry out the simulations, we employed the magnetohydrodynamics code, SMAUG (Sheffield MHD Accelerated Using GPUs). Our results show that the amount of energy propagating into the solar atmosphere is consistent with a model of solar global oscillations described by Taroyan and Erdélyi (2008) using the Klein-Gordon equation. The computed results indicate a power law which is compared to observations reported by Ireland et al. (2015) using data from the Solar Dynamics Observatory/Atmospheric Imaging Assembly.

Gabor Wave Packet Method to Solve Plasma Wave Equations

International Nuclear Information System (INIS)

Pletzer, A.; Phillips, C.K.; Smithe, D.N.

2003-01-01

A numerical method for solving plasma wave equations arising in the context of mode conversion between the fast magnetosonic and the slow (e.g ion Bernstein) wave is presented. The numerical algorithm relies on the expansion of the solution in Gaussian wave packets known as Gabor functions, which have good resolution properties in both real and Fourier space. The wave packets are ideally suited to capture both the large and small wavelength features that characterize mode conversion problems. The accuracy of the scheme is compared with a standard finite element approach

Nonlinear dynamics of a parametrically driven sine-Gordon system

DEFF Research Database (Denmark)

Grønbech-Jensen, Niels; Kivshar, Yuri S.; Samuelsen, Mogens Rugholm

1993-01-01

We consider a sine-Gordon system, driven by an ac parametric force in the presence of loss. It is demonstrated that a breather can be maintained in a steady state at half of the external frequency. In the small-amplitude limit the effect is described by an effective nonlinear Schrodinger equation...

Diffusion phenomenon for linear dissipative wave equations

KAUST Repository

Said-Houari, Belkacem

2012-01-01

In this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for {equation presented} decays with the rate {equation presented} [0,1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data {equation presented} [0,1], and v is the solution of the related heat equation with initial data v 0 = u 0 + u 1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415-433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t -γ/2. © European Mathematical Society.

Erna and Melanie Klein.

Science.gov (United States)

Tabak de Bianchedi, Elizabeth; Etchegoyen, R Horacio; Ungar de Moreno, Virginia; Nemas de Urman, Clara; Zysman, Samuel

2003-12-01

Erna was one of the child patients treated by Melanie Klein in Berlin, employing her recently discovered play technique. Since Erna died in Chile, the authors considered the IPA Congress in Santiago an opportunity to present a paper as a homage both to Erna and, especially, to Klein. She learned much from that very disturbed child, which she later used to sustain the ongoing development of her theories. The paper explores biographic data relevant to understanding both the case and the theories. It analyses the case material to follow Klein in the discovery and the handling of the child's transference and the harsh expressions of hate, jealousy and envy, which are brought in, with sad consequences, by strong persecutory feelings. Klein's comparison of this case with that of Freud's Wolf-man is also considered, mostly to show that the similarities were less than originally claimed, and that Klein, perhaps, was introducing a theoretic shift which led her technique to gradually change from 'Nachträglichkeit' to the 'signification-resignification' pair, akin to Strachey's concept of the mutative interpretation. Lastly, the comprehension of Erna's strong psychotic traits and the links with later developments of the theory on psychosis are studied.

Nonlinear Electrostatic Wave Equations for Magnetized Plasmas

DEFF Research Database (Denmark)

Dysthe, K.B.; Mjølhus, E.; Pécseli, Hans

1984-01-01

The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed.......The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed....

Solitary Wave Solutions of the Boussinesq Equation and Its Improved Form

Directory of Open Access Journals (Sweden)

Reza Abazari

2013-01-01

Full Text Available This paper presents the general case study of previous works on generalized Boussinesq equations, (Abazari, 2011 and (Kılıcman and Abazari, 2012, that focuses on the application of G′/G-expansion method with the aid of Maple to construct more general exact solutions for the coupled Boussinesq equations. In this work, the mentioned method is applied to construct more general exact solutions of Boussinesq equation and improved Boussinesq equation, which the French scientist Joseph Valentin Boussinesq (1842–1929 described in the 1870s model equations for the propagation of long waves on the surface of water with small amplitude. Our work is motivated by the fact that the G′/G-expansion method provides not only more general forms of solutions but also periodic, solitary waves and rational solutions. The method appears to be easier and faster by means of a symbolic computation.

Julia Kristeva: Das weibliche Genie – Melanie Klein. Gießen: Psychosozial-Verlag 2008

Directory of Open Access Journals (Sweden)

Lilli Gast

2009-07-01

Full Text Available Julia Kristeva widmet sich im zweiten Teil ihrer Trilogie über das weibliche Genie dem Leben und Werk von Melanie Klein, die mit ihren Arbeiten über die früheste Verfasstheit des Psychischen das psychoanalytische Denken für die Psychosen und den Wahn aufschloss und die Rolle des Mütterlichen im psychoanalytischen Diskurs neu definierte. In ihrer Auseinandersetzung mit Klein gelingt Kristeva nicht nur eine ausgesprochen gelungene Einführung in Kleins Denken, sondern auch eine Analyse weiblicher Intellektualität im 20. Jahrhundert. Zudem werden die Schnittstellen im Denken Kleins und Kristevas sichtbar.Julia Kristeva devotes this second installment of her trilogy on feminine genius to the life and work of Melanie Klein. Klein’s work on the early state of the psyche opened psychoanalytical thinking to psychoses, delusion, and the redefined the role of the motherly in psychoanalytical discourse. In her discussion of Klein, Kristeva provides not only a markedly insightful introduction to Klein’s thinking, but also an analysis of female intellectuality in the 20th century. Moreover, the reader clearly sees the interconnections between Klein and Kristeva’s thinking.

Bifurcations of traveling wave solutions for an integrable equation

International Nuclear Information System (INIS)

Li Jibin; Qiao Zhijun

2010-01-01

This paper deals with the following equation m t =(1/2)(1/m k ) xxx -(1/2)(1/m k ) x , which is proposed by Z. J. Qiao [J. Math. Phys. 48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals 41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the cases of k=-2,-(1/2),(1/2),2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions.

Semilinear damped wave equation in locally uniform spaces

Czech Academy of Sciences Publication Activity Database

Michálek, Martin; Pražák, D.; Slavík, J.

2017-01-01

Roč. 16, č. 5 (2017), s. 1673-1695 ISSN 1534-0392 EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : damped wave equations * nonlinear damping * unbounded domains Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.801, year: 2016 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14110

The damped wave equation with unbounded damping

Czech Academy of Sciences Publication Activity Database

Freitas, P.; Siegl, Petr; Tretter, C.

2018-01-01

Roč. 264, č. 12 (2018), s. 7023-7054 ISSN 0022-0396 Institutional support: RVO:61389005 Keywords : damped wave equation * unbounded damping * essential spectrum * quadratic operator funciton with unbounded coefficients * Schrodinger operators with complex potentials Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.988, year: 2016

Multiresonance modes in sine–Gordon brane models

Energy Technology Data Exchange (ETDEWEB)

Cruz, W.T., E-mail: wilamicruz@gmail.com [Instituto Federal de Educação, Ciência e Tecnologia do Ceará (IFCE), Campus Juazeiro do Norte, 63040-540 Juazeiro do Norte-Ceará (Brazil); Maluf, R.V., E-mail: r.v.maluf@fisica.ufc.br [Universidade Federal do Ceará (UFC), Departamento de Física, Campus do Pici, Fortaleza - CE, C.P. 6030, 60455-760 (Brazil); Dantas, D.M., E-mail: davi@fisica.ufc.br [Universidade Federal do Ceará (UFC), Departamento de Física, Campus do Pici, Fortaleza - CE, C.P. 6030, 60455-760 (Brazil); Almeida, C.A.S., E-mail: carlos@fisica.ufc.br [Universidade Federal do Ceará (UFC), Departamento de Física, Campus do Pici, Fortaleza - CE, C.P. 6030, 60455-760 (Brazil)

2016-12-15

In this work, we study the localization of the vector gauge field in two five-dimensional braneworlds generated by scalar fields coupled to gravity. The sine–Gordon like potentials are employed to produce different thick brane setups. A zero mode localized is obtained, and we show the existence of reverberations with the wave solutions indicating a quasi-localized massive mode. More interesting results are achieved when we propose a double sine–Gordon potential to the scalar field. The resulting thick brane shows a more detailed topology with the presence of an internal structure composed by two kinks. The massive spectrum of the gauge field is revalued on this scenario revealing the existence of various resonant modes. Furthermore, we compute the corrections to Coulomb law coming from these massive KK vector modes in these thick scenarios, which is concluded that the dilaton parameter regulates these corrections.

Multiresonance modes in sine–Gordon brane models

International Nuclear Information System (INIS)

Cruz, W.T.; Maluf, R.V.; Dantas, D.M.; Almeida, C.A.S.

2016-01-01

In this work, we study the localization of the vector gauge field in two five-dimensional braneworlds generated by scalar fields coupled to gravity. The sine–Gordon like potentials are employed to produce different thick brane setups. A zero mode localized is obtained, and we show the existence of reverberations with the wave solutions indicating a quasi-localized massive mode. More interesting results are achieved when we propose a double sine–Gordon potential to the scalar field. The resulting thick brane shows a more detailed topology with the presence of an internal structure composed by two kinks. The massive spectrum of the gauge field is revalued on this scenario revealing the existence of various resonant modes. Furthermore, we compute the corrections to Coulomb law coming from these massive KK vector modes in these thick scenarios, which is concluded that the dilaton parameter regulates these corrections.

Interpretation of the extreme physical information principle in terms of shift information

International Nuclear Information System (INIS)

Vstovsky, G.V.

1995-01-01

It is shown that Fisher information (FI) can be considered as a limiting case of a related form of Kullback information---a shift information (SI). The compatibility of the use of SI with a basic physical principle of uncertainty is demonstrated. The scope of FI based theory is extended to the nonlinear Klein-Gordon equation

Affetto e pensiero nel modello Klein-Bion

Directory of Open Access Journals (Sweden)

Marco Innamorati

2010-01-01

Full Text Available Affect and Thought in the Klein-Bion Model - This paper investigates the development of the psychoanalytic theory of affect according to the Klein/Bion approach, with special regard to the relationship between affect and thought which has strategic importance in the complex picture in post-war Anglo-Saxon psychoanalysis. Klein’s contributions on affect are discussed and confronted with the other elements of the psychological world: representations, drives, objects and positions. The second part of the paper presents and discusses Bion’s theory of “emotional experiences”, in which a primordial identity between thought and feelings generates every form of knowledge.

Capillary-gravity waves and the Navier-Stokes equation

International Nuclear Information System (INIS)

Behroozi, F.; Podolefsky, N.

2001-01-01

Water waves are a source of great fascination for undergraduates and thus provide an excellent context for introducing some important topics in fluid dynamics. In this paper we introduce the potential theory for incompressible and inviscid flow and derive the differential equation that governs the behaviour of the velocity potential. Next we obtain the harmonic solutions of the velocity potential by a very general argument. These solutions in turn yield the equations for the velocity and displacement of a water element under the action of a harmonic wave. Finally we obtain the dispersion relation for surface waves by requiring that the harmonic solutions satisfy the Navier-Stokes equation. (author)

Extended common-image-point gathers for anisotropic wave-equation migration

KAUST Repository

Sava, Paul C.; Alkhalifah, Tariq Ali

2010-01-01

In regions characterized by complex subsurface structure, wave-equation depth migration is a powerful tool for accurately imaging the earth’s interior. The quality of the final image greatly depends on the quality of the model which includes

A new iterative solver for the time-harmonic wave equation

NARCIS (Netherlands)

Riyanti, C.D.; Erlangga, Y.A.; Plessix, R.E.; Mulder, W.A.; Vuik, C.; Oosterlee, C.

2006-01-01

The time-harmonic wave equation, also known as the Helmholtz equation, is obtained if the constant-density acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can

An acoustic wave equation for pure P wave in 2D TTI media

KAUST Repository

Zhan, Ge; Pestana, Reynam C.; Stoffa, Paul L.

2011-01-01

In this paper, a pure P wave equation for an acoustic 2D TTI media is derived. Compared with conventional TTI coupled equations, the resulting equation is unconditionally stable due to the complete isolation of the SV wave mode. To avoid numerical dispersion and produce high quality images, the rapid expansion method REM is employed for numerical implementation. Synthetic results validate the proposed equation and show that it is a stable algorithm for modeling and reverse time migration RTM in a TTI media for any anisotropic parameter values. © 2011 Society of Exploration Geophysicists.

Boosted black holes on Kaluza-Klein bubbles

International Nuclear Information System (INIS)

Iguchi, Hideo; Mishima, Takashi; Tomizawa, Shinya

2007-01-01

We construct an exact stationary solution of black-hole-bubble sequence in the five-dimensional Kaluza-Klein theory by using solitonic solution-generating techniques. The solution describes two stationary black holes with topology S 3 on a Kaluza-Klein bubble and has a linear momentum component in the compactified direction. We call the solution boosted black holes on Kaluza-Klein bubble because it has the linear momentum. The Arnowitt-Deser-Misner mass and the linear momentum depend on the two boosted velocity parameters of black holes. In the effective four-dimensional theory, the solution has an electric charge which is proportional to the linear momentum. The solution includes the static solution found by Elvang and Horowitz. The small and the big black holes limits are investigated. The relation between the solution and the single boosted black string are considered

Roughening in random sine-Gordon systems

International Nuclear Information System (INIS)

Schwartz, M.; Nattermann, T.

1991-01-01

We consider the spatial correlations of the optimal solutions of the random sine-Gordon equation as an example of the usefulness of a very simple ansatz relating the Fourier transforms of certain functions of the field Φ to the Fourier transform of the random fields. The dramatic change in the correlations when going from above to below two dimensions is directly attributed to the transfer from dominance of long range fluctuations of the randomness to the dominance of short range fluctuations. (orig.)

EXACT TRAVELLING WAVE SOLUTIONS TO BBM EQUATION

Institute of Scientific and Technical Information of China (English)

无

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.

Methodology for obtaining a solution for the three-dimensional Boltzmann transport equation and an expression for the calculation of the total doses considering Compton scattering simulated by Klein-Nishina

International Nuclear Information System (INIS)

Rodriguez, Barbara A.; Borges, Volnei; Vilhena, Marco Tullio

2005-01-01

In this work we would like to obtain a formulation of an analytic method for the solution of the three dimensional transport equation considering Compton scattering and an expression for total doses due to gamma radiation, where the deposited energy by the free electron will be considered. For that, we will work with two equations: the first one for the photon transport, considering the Klein-Nishina kernel and energy multigroup model, and the second one considering the free electron with the screened Rutherford scattering. (author)

Particle creation effect on M4 X S7 Kaluza-Klein cosmologies

International Nuclear Information System (INIS)

Koikawa, T.; Maeda, K.

1984-01-01

The particle creation effect on the higher-dimensional Kaluza-Klein cosmologies with M 4 xS 7 topology is studied. This quantum effect is found to change the classical behavior of the internal and external scale factors drastically in the early stage of the expansion, so that the dimensional reduction seems to fail. However, at the later stage two scale factors get separated from each other and the internal scale factor approaches the final singularity just like the vacuum case. (orig.)

Dissociating Word Frequency and Age of Acquisition: The Klein Effect Revived (and Reversed)

Science.gov (United States)

Dewhurst, Stephen A.; Barry, Christopher

2006-01-01

The Klein effect (G. S. Klein, 1964) refers to the finding that high-frequency words produce greater interference in a color-naming task than low-frequency words. The present study used the Klein effect to investigate the relationship between frequency and age of acquisition (AoA) by measuring their influence on color naming. Two experiments…

Robust Imaging Methodology for Challenging Environments: Wave Equation Dispersion Inversion of Surface Waves

KAUST Repository

Li, Jing

2017-12-22

A robust imaging technology is reviewed that provide subsurface information in challenging environments: wave-equation dispersion inversion (WD) of surface waves for the shear velocity model. We demonstrate the benefits and liabilities of the method with synthetic seismograms and field data. The benefits of WD are that 1) there is no layered medium assumption, as there is in conventional inversion of dispersion curves, so that the 2D or 3D S-velocity model can be reliably obtained with seismic surveys over rugged topography, and 2) WD mostly avoids getting stuck in local minima. The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic media and the inversion of dispersion curves associated with Love wave. The liability is that is almost as expensive as FWI and only recovers the Vs distribution to a depth no deeper than about 1/2~1/3 wavelength.

The Bohr-Sommerfeld quantization of n-dimensional neutral and charged pulsons

International Nuclear Information System (INIS)

Bogolubsky, I.L.

1978-01-01

The spectrum of masses of 1) neutral and 2) having elementary charge Q=1 of n-dimensional pulsons (i.e., localized oscillating extended solutions) is found by numerical integration using a computer in the framework of the Klein-Gordon equation with the logarithmic nonlinearity. Computer experiments point out that the pulsons under consideration are apparently stable at any n

Plasma analog of particle-pair production

International Nuclear Information System (INIS)

Tsidulko, Yu.A.; Berk, H.L.

1996-09-01

It is shown that the plasma axial shear flow instability satisfies the Klein-Gordon equation. The plasma instability is then shown to be analogous to spontaneous particle-pair production when a potential energy is present that is greater than twice the particle rest mass energy. Stability criteria can be inferred based on field theoretical conservation laws

Interaction with a field: a simple integrable model with backreaction

Science.gov (United States)

Mouchet, Amaury

2008-09-01

The classical model of an oscillator linearly coupled to a string captures, for a low price in technique, many general features of more realistic models for describing a particle interacting with a field or an atom in an electromagnetic cavity. The scattering matrix and the asymptotic in and out-waves on the string can be computed exactly and the phenomenon of resonant scattering can be introduced in the simplest way. The dissipation induced by the coupling of the oscillator to the string can be studied completely. In the case of a d'Alembert string, the backreaction leads to an Abraham-Lorentz-Dirac-like equation. In the case of a Klein-Gordon string, one can see explicitly how radiation governs the (meta)stability of the (quasi)bounded mode.

Anisotropic wave-equation traveltime and waveform inversion

KAUST Repository

Feng, Shihang

2016-09-06

The wave-equation traveltime and waveform inversion (WTW) methodology is developed to invert for anisotropic parameters in a vertical transverse isotropic (VTI) meidum. The simultaneous inversion of anisotropic parameters v0, ε and δ is initially performed using the wave-equation traveltime inversion (WT) method. The WT tomograms are then used as starting background models for VTI full waveform inversion. Preliminary numerical tests on synthetic data demonstrate the feasibility of this method for multi-parameter inversion.

On the Generalized Maxwell Equations and Their Prediction of Electroscalar Wave

Directory of Open Access Journals (Sweden)

Arbab A. I.

2009-04-01

Full Text Available We have formulated the basic laws of electromagnetic theory in quaternion form. The formalism shows that Maxwell equations and Lorentz force are derivable from just one quaternion equation that only requires the Lorentz gauge. We proposed a quaternion form of the continuity equation from which we have derived the ordinary continuity equation. We introduce new transformations that produces a scalar wave and generalize the continuity equation to a set of three equations. These equations imply that both current and density are waves. Moreover, we have shown that the current can not cir- culate around a point emanating from it. Maxwell equations are invariant under these transformations. An electroscalar wave propagating with speed of light is derived upon requiring the invariance of the energy conservation equation under the new transforma- tions. The electroscalar wave function is found to be proportional to the electric field component along the charged particle motion. This scalar wave exists with or without considering the Lorentz gauge. We have shown that the electromagnetic fields travel with speed of light in the presence or absence of free charges.

Single-Particle Quantum Dynamics in a Magnetic Lattice

Energy Technology Data Exchange (ETDEWEB)

Venturini, Marco

2001-02-01

We study the quantum dynamics of a spinless charged-particle propagating through a magnetic lattice in a transport line or storage ring. Starting from the Klein-Gordon equation and by applying the paraxial approximation, we derive a Schroedinger-like equation for the betatron motion. A suitable unitary transformation reduces the problem to that of a simple harmonic oscillator. As a result we are able to find an explicit expression for the particle wavefunction.

Instability of the Kaluza-Klein vacuum

International Nuclear Information System (INIS)

Witten, E.

1982-01-01

It is argued that the ground state of the Kaluza-Klein unified theory is unstable against a process of semiclassical barrier penetration. This is related to the fact that the positive energy conjecture does not hold for the Kaluza-Klein theory; an explicit counter-example is given. The reasoning presented here assumes that in general relativity one should include manifolds of non-vacuum topology. It is argued that the existence of elementary fermions (not present in the original Kaluza-Klein theory) would stabilize the Kaluza-Klein vacuum. (orig.)

Constraints on cosmic superstrings from Kaluza-Klein emission.

Science.gov (United States)

Dufaux, Jean-François

2012-07-06

Cosmic superstrings interact generically with a tower of light and/or strongly coupled Kaluza-Klein (KK) modes associated with the geometry of the internal space. We study the production of KK particles by cosmic superstring loops, and show that it is constrained by big bang nucleosynthesis. We study the resulting constraints in the parameter space of the underlying string theory model and highlight their complementarity with the regions that can be probed by current and upcoming gravitational wave experiments.

Wave equations for pulse propagation

International Nuclear Information System (INIS)

Shore, B.W.

1987-01-01

Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation

Local energy decay for linear wave equations with variable coefficients

Science.gov (United States)

Ikehata, Ryo

2005-06-01

A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].

Reduction of the Breit Coulomb equation to an equivalent Schroedinger equation, and investigation of the behavior of the wave function near the origin

International Nuclear Information System (INIS)

Malenfant, J.

1988-01-01

The Breit equation for two equal-mass spin-1/2 particles interacting through an attractive Coulomb potential is separated into its angular and radial parts, obtaining coupled sets of first-order differential equations for the radial wave functions. The radial equations for the 1 J/sub J/, 3 J/sub J/, and 3 P 0 states are further reduced to a single, one-dimensional Schroedinger equation with a relatively simple effective potential. No approximations, other than the initial one of an instantaneous Coulomb interaction, are made in deriving this equation; it accounts for all relativistic effects, as well as for mixing between different components of the wave function. Approximate solutions are derived for this Schroedinger equation, which gives the correct O(α 4 ) term for the 1 1 S 0 energy and for the n 1 J/sub J/ energies, for J>0. The radial equations for the 3 (J +- 1)/sub J/ states are reduced to two second-order coupled equations. At small r, the Breit Coulomb wave functions behave as r/sup ν//sup -1/, where ν is either √J(J+1)+1-α 2 /4 or √J(J+1)-α 2 /4 . The 1 S 0 and 3 P 0 wave functions therefore diverge at the origin as r/sup //sup √//sup 1-//sup α//sup <2//4 -1$. This divergence of the J = 0 states, however, does not occur when the spin-spin interaction, -(α/r)αxα, is added to the Coulomb potential

Topological horseshoes in travelling waves of discretized nonlinear wave equations

International Nuclear Information System (INIS)

Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming

2014-01-01

Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes

Topological horseshoes in travelling waves of discretized nonlinear wave equations

Energy Technology Data Exchange (ETDEWEB)

Chen, Yi-Chiuan, E-mail: YCChen@math.sinica.edu.tw [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China); Chen, Shyan-Shiou, E-mail: sschen@ntnu.edu.tw [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China); Yuan, Juan-Ming, E-mail: jmyuan@pu.edu.tw [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)

2014-04-15

Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.

Gauge bridges in classical field theory

International Nuclear Information System (INIS)

Jakobs, S.

2009-03-01

In this thesis Poisson structures of two classical gauge field theories (Maxwell-Klein-Gordon- and Maxwell-Dirac-system) are constructed using the parametrix construction of Green's functions. Parametrices for the Maxwell-Klein-Gordon- and Maxwell-Dirac-system are constructed in Minkowski space and this construction is later generalized to curved space times for the Maxwell-Klein-Gordon-system. With these Green's functions Poisson brackets will be defined as Peierls brackets. Finally non-local, gauge invariant observables, the so-called ''gauge bridges''are constructed. Gauge bridges are the matrix elements of holonomy operators. It is shown, that these emerge from Poisson brackets of local, gauge invariant observables. (orig.)

Wave equations on anti self dual (ASD) manifolds

Science.gov (United States)

Bashingwa, Jean-Juste; Kara, A. H.

2017-11-01

In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.