The multi-triple-pole solitons for the focusing mKdV hierarchy with nonzero boundary conditions

Author:

Weng Weifang12,Yan Zhenya12ORCID

Affiliation:

1. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Abstract

In this paper, the general triple-pole multi-soliton solutions are proposed for the focusing modified Korteweg–de Vries (mKdV) equation with both nonzero boundary conditions (NZBCs) and triple zeros of analytical scattering coefficients by means of the inverse scattering transform. Furthermore, we also give the corresponding trace formulae and theta conditions. Particularly, we analyze some representative reflectionless potentials containing the triple-pole multi-dark-anti-dark solitons and breathers. The idea can also be extended to the whole mKdV hierarchy (e.g. the fifth-order mKdV equation, and third-fifth-order mKdV equation) with NZBCs and triple zeros of analytical scattering coefficients. Moreover, these obtained triple-pole solutions can also be degenerated to the triple-pole soliton solutions with zero boundary conditions.

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Ltd

Subject

Condensed Matter Physics,Statistical and Nonlinear Physics

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