Lump type solutions: Bäcklund transformation and spectral properties
Copyright policy )Lump type solutions: Bäcklund transformation and spectral properties
There are various different ways to obtain traveling waves of lump type for the KP equation. We propose a general and simple approach to derive them via a Backlund transformation. This enables us to establish an explicit connection between those low energy solutions and high energy ones. Based on this construction, spectral analysis of the degree $6$ solutions is then carried out in details. The analysis of higher energy ones can be done in an inductive way.
25 pages
Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems, KP-I equation, Mathematics - Analysis of PDEs, KdV equations (Korteweg-de Vries equations), Asymptotic distributions of eigenvalues in context of PDEs, FOS: Mathematics, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Bäcklund transformation, PDEs in connection with fluid mechanics, spectral analysis, Traveling wave solutions, Analysis of PDEs (math.AP)
Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems, KP-I equation, Mathematics - Analysis of PDEs, KdV equations (Korteweg-de Vries equations), Asymptotic distributions of eigenvalues in context of PDEs, FOS: Mathematics, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Bäcklund transformation, PDEs in connection with fluid mechanics, spectral analysis, Traveling wave solutions, Analysis of PDEs (math.AP)
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