Multi-breather solutions to the Sasa–Satsuma equation

@article{Wu2021MultibreatherST,
  title={Multi-breather solutions to the Sasa–Satsuma equation},
  author={Chengfa Wu and Bo Wei and Changyan Shi and Bao-Feng Feng},
  journal={Proceedings of the Royal Society A},
  year={2021},
  volume={478}
}
General breather solution to the Sasa–Satsuma equation (SSE) is systematically investigated in this paper. We firstly transform the SSE into a set of three Hirota bilinear equations under a proper plane wave boundary condition. Starting from a specially arranged tau-function of the Kadomtsev–Petviashvili hierarchy and a set of 11 bilinear equations satisfied, we implement a series steps of reduction procedure, i.e. C-type reduction, dimension reduction and complex conjugate reduction, and… 
4 Citations

Figures from this paper

General rogue wave solutions to the Sasa-Satsuma equation

General rogue wave solutions to the Sasa-Satsuma equation are constructed by the Kadomtsev-Petviashvili (KP) hierarchy reduction method. These solutions are presented in three different forms. The

Higher-order rogue wave solutions of the Sasa–Satsuma equation

Up to the third-order rogue wave solutions of the Sasa–Satsuma (SS) equation are derived based on the Hirota’s bilinear method and Kadomtsev–Petviashvili hierarchy reduction method. They are

The initial-boundary value problems of the new two-component generalized Sasa–Satsuma equation with a $$4\times 4$$ matrix Lax pair

In this paper, we consider a new two-component Sasa–Satsuma equation, which can simulate the propagation and interaction of ultrashort pulses and describe the propagation of femtosecond pulses in

Phase characters of optical dark solitons with third-order dispersion and delayed nonlinear response.

Dark soliton is usually seen as one of the simplest topological solitons, due to phase shift across its intensity dip. We investigate phase characters of single-valley dark soliton (SVDS) and

References

SHOWING 1-10 OF 52 REFERENCES

Sasa-Satsuma higher-order nonlinear Schrödinger equation and its bilinearization and multisoliton solutions.

The correct bilinearization is given based on the interpretation of the Sasa-Satsuma equation as a reduction of the three-component Kadomtsev-Petviashvili hierarchy and multisoliton formulas are obtained.

The algebraic representation for high order solution of Sasa-Satsuma equation

In this paper, we reestablish the elementary Darboux transformation for Sasa-Satsuma equation with the aid of loop group method. Furthermore, the generalized Darboux transformation is given with the

Dark soliton solution of Sasa-Satsuma equation

The Sasa‐Satsuma equation is a higher order nonlinear Schrodinger type equation which admits bright soliton solutions with internal freedom. We present the dark soliton solutions for the equation by

The n-component nonlinear Schrödinger equations: dark–bright mixed N- and high-order solitons and breathers, and dynamics

  • Guoqiang ZhangZhenya Yan
  • Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2018
The general n-component nonlinear Schrödinger equations are systematically investigated with the aid of the Darboux transformation method and its extension. Firstly, we explore the condition of the

Penrose instabilities and the emergence of rogue waves in Sasa–Satsuma equation

In this paper, we calculate the region of emergence of rogue waves in the Sasa–Satsuma equation by performing Penrose stability analysis. We consider Wigner-transformed Sasa–Satsuma equation and

The unified transform method for the Sasa–Satsuma equation on the half-line

  • Jian XuE. Fan
  • Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2013
The unified transform method is implemented to the initial-boundary value (IBV) problem of the Sasa–Satsuma equation on the half line and the associated general Dirichlet to Neumann map is analysed using the so-called global relation.

General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions

General soliton solutions to a nonlocal nonlinear Schrödinger (NLS) equation with PT-symmetry for both zero and nonzero boundary conditions are considered via the combination of Hirota’s bilinear

The Deift–Zhou steepest descent method to long-time asymptotics for the Sasa–Satsuma equation

General soliton and (semi‐)rational solutions to the nonlocal Mel'nikov equation on the periodic background

In this paper, the Hirota's bilinear method and Kadomtsev‐Petviashvili hierarchy reduction method are applied to construct soliton, line breather and (semi‐)rational solutions to the nonlocal
...