English

Coherent structure of Alice-Bob modified Korteweg de-Vries Equation

Exactly Solvable and Integrable Systems 2024-06-04 v1 Mathematical Physics math.MP Pattern Formation and Solitons

Abstract

To describe two-place events, Alice-Bob systems have been established by means of the shifted parity and delayed time reversal in Ref. [1]. In this paper, we mainly study exact solutions of the integrable Alice-Bob modified Korteweg de-Vries (AB-mKdV) system. The general Nth Darboux transformation for the AB-mKdV equation are constructed. By using the Darboux transformation, some types of shifted parity and time reversal symmetry breaking solutions including one-soliton, two-soliton and rogue wave solutions are explicitly obtained. In addition to the similar solutions of the mKdV equation (group invariant solutions), there are abundant new localized structures for the AB-mKdV systems.

Keywords

Cite

@article{arxiv.1706.08178,
  title  = {Coherent structure of Alice-Bob modified Korteweg de-Vries Equation},
  author = {Congcong Li and S. Y. Lou and Man Jia},
  journal= {arXiv preprint arXiv:1706.08178},
  year   = {2024}
}

Comments

19 pages; 8 Figs