Asymptotic analysis of high order soliton for the Hirota equation
arXiv:2008.12631 · doi:10.1016/j.physd.2021.132982
Abstract
In this paper, we mainly analyze the long-time asymptotics of high-order soliton for the Hirota equation. Two different Riemann-Hilbert representations of Darboux matrix with high-order soliton are given to establish the relationships between inverse scattering method and Darboux transformation. The asymptotic analysis with single spectral parameter is derived through the formulas of determinant directly. Furthermore, the long-time asymptotics with spectral parameters is given by combining the iterated Darboux matrix and the result of high-order soliton with single spectral parameter, which discloses the structure of high-order soliton clearly and is possible to be utilized in the optic experiments.
arXiv comment32pages, 7 figures
References in corpus (9)
- Nonlinear Schrödinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions
- High Order Solutions and Generalized Darboux Transformations of Derivative Schrödinger Equation
- Soliton solutions of the Kadomtsev-Petviashvili II equation
- Extreme Superposition: Rogue Waves of Infinite Order and the Painlevé-III Hierarchy
- Classification of the line-soliton solutions of KPII
- Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrödinger equation
- General high-order rogue waves of the (1+1)-dimensional Yajima-Oikawa system
- Integrable nonlocal Hirota equations
- Asymptotic and scattering behaviour for degenerate multi-solitons in the Hirota equation