English

Darboux transformation and soliton solutions of the generalized Sasa-Satsuma equation

Exactly Solvable and Integrable Systems 2023-06-07 v1

Abstract

The Sasa-Satsuma equation, a higher-order nonlinear Schr\"{o}dinger equation, is an important integrable equation, which displays the propagation of femtosecond pulses in optical fibers. In this paper, we investigate a generalized Sasa-Satsuma(gSS) equation. The Darboux transformation(DT) for the focusing and defocusing gSS equation is constructed. By using the DT, various of soliton solutions for the generalized Sasa-Satsuma equation are derived, including hump-type, breather-type and periodic soliton. Dynamics properties and asymptotic behavior of these soliton solutions are analyzed. Infinite number conservation laws and conserved quantities for the gSS equation are obtained.

Keywords

Cite

@article{arxiv.2212.01646,
  title  = {Darboux transformation and soliton solutions of the generalized Sasa-Satsuma equation},
  author = {Hong-Qian Sun and Zuo-Nong Zhu},
  journal= {arXiv preprint arXiv:2212.01646},
  year   = {2023}
}