# 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

### General rogue wave solutions to the Sasa-Satsuma equation

- Mathematics
- 2022

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

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

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

- MathematicsAnalysis and Mathematical Physics
- 2022

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.

- PhysicsPhysical review. E
- 2022

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.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

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

- Mathematics
- 2016

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

- Physics
- 2010

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

- MathematicsProceedings 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

- PhysicsThe European Physical Journal Plus
- 2021

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

- MathematicsProceedings 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

- Mathematics, PhysicsNonlinearity
- 2018

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

- MathematicsJournal of Differential Equations
- 2018

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

- Mathematics, PhysicsStudies in Applied Mathematics
- 2020

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…