The Matrix KadomtsevPetviashvili Equation as a Source of Integrable Nonlinear Equations
Copyright policy )The Matrix KadomtsevPetviashvili Equation as a Source of Integrable Nonlinear Equations
A new integrable class of Davey--Stewartson type systems of nonlinear partial differential equations (NPDEs) in 2+1 dimensions is derived from the matrix Kadomtsev--Petviashvili equation by means of an asymptotically exact nonlinear reduction method based on Fourier expansion and spatio-temporal rescaling. The integrability by the inverse scattering method is explicitly demonstrated, by applying the reduction technique also to the Lax pair of the starting matrix equation and thereby obtaining the Lax pair for the new class of systems of equations. The characteristics of the reduction method suggest that the new systems are likely to be of applicative relevance. A reduction to a system of two interacting complex fields is briefly described.
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Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems, nonlinear reduction method, inverse scattering method, KdV equations (Korteweg-de Vries equations), Lax pair, Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Exactly Solvable and Integrable Systems (nlin.SI), Davey-Stewartson type systems
Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems, nonlinear reduction method, inverse scattering method, KdV equations (Korteweg-de Vries equations), Lax pair, Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Exactly Solvable and Integrable Systems (nlin.SI), Davey-Stewartson type systems
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