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The Kadomtsev-Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg-de Vries equation for purely uni-directional waves. In this Letter we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, this new equation is also valid for waves on deep water. These properties are inherited from the AB-equation (E. van Groesen, Andonowati, 2007 ) which is the unidirectional improvement of the KdV equation. The derivation of the equation uses the variational formulation of surface water waves, and inherits the basic Hamiltonian structure.

CERN Document Server

We develop a theory of Smectic A - Smectic C phase transition with anomalously weak smectic layer contraction. We construct a phenomenological description of this transition by generalizing the Chen-Lubensky model. Using a mean-field molecular model, we demonstrate that a relatively simple interaction potential suffices to describe the transition. The theoretical results are in excellent agreement with experimental data.