Asymptotic and scattering behaviour for degenerate multi-solitons in the Hirota equation

PHYSICA D-NONLINEAR PHENOMENA

卷:397

Article

Cen, Julia¹  Fring, Andreas¹ 

[1] City Univ London, Dept Math, Northampton Sq, London EC1V 0HB, England

关键词: Hirota equation;    PT-symmetry;    Darboux-Crum-Crum transformation;    Multi-soliton solutions;   

DOI  :  10.1016/j.physd.2019.05.005

来源: Elsevier

【 摘 要 】

We construct all higher order conserved charges from a general two-dimensional zero curvature condition using a Gardner transformation. Employing two of those charges in the definition of a Hamiltonian allows to view the Hirota equations as an integrable PT-symmetric extension of the nonlinear Schrodinger equation. We construct new degenerate multi-soliton solutions from Hirota's direct method as well as Darboux-Crum transformations based on Jordan states. We study the properties of these solutions, computing their asymptotic time-dependent displacements and also show that their scattering process has a distinct characteristic behaviour different from the nondegenerate counterparts allowing only for interactions of absorb-emit type. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free