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arXiv · 1804.02013

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

Julia Cen·Andreas Fring
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Abstract

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 $\mathcal{PT}$-symmetric extension of the nonlinear Schr\"{o}dinger 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.

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Julia Cen, Andreas Fring. 2018-04-05. Asymptotic and scattering behaviour for degenerate multi-solitons in the Hirota equation. https://doi.org/10.1016/j.physd.2019.05.005

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