Multidimensional integrable boundary problems
I.T.Habibullin
TL;DR
This paper introduces a method for identifying boundary conditions compatible with the integrability of multidimensional KP-type equations, proposing new classes of boundary conditions and solving specific boundary problems.
Contribution
It presents a novel approach based on Lax pair involutions to find integrable boundary conditions for multidimensional KP equations and related models.
Findings
New boundary conditions for KP and Hirota equations
Exact solutions for boundary problems on a stripe
Discussion of discrete Toda chain boundary issues
Abstract
A method of looking for boundary conditions consistent with the integrability property of multidimensional Kadomtsev-Petviashvili (KP) type equations is discussed. The method is based on involutions of the Lax pair taken at the border plane. New classes of boundary conditions for the KP and Hirota equations are proposed consistent with the Lax pair. The boundary problem on the stripe 0<y<1 for the KP equation is discussed, its exact solutions are found. Ward's problem on discrete versions of the generalized Toda chains is briefly discussed.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Differential Equations and Numerical Methods · Nonlinear Waves and Solitons