scholarly journals Rogue Wave for the (3+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hanlin Chen ◽  
Zhenhui Xu ◽  
Zhengde Dai
Keyword(s):  
Nonlinear Evolution Equation ◽  
Wave Solution ◽  
Nonlinear Evolution ◽  
Rogue Wave ◽  
Test Method ◽  
Wave Fields ◽  
New Family ◽  
Rogue Wave Solution ◽  
Extreme Behavior ◽  
Ytsf Equation

A new method, homoclinic (heteroclinic) breather limit method (HBLM), for seeking rogue wave solution to nonlinear evolution equation (NEE) is proposed. (3+1)-dimensional Yu-Toda-Sasa-Fukuyama (YTSF) equation is used as an example to illustrate the effectiveness of the suggested method. A new family of two-wave solution, rational breather wave solution, is obtained by extended homoclinic test method, and it is just a rogue wave solution. This result shows rogue wave can come from extreme behavior of breather solitary wave for (3+1)-dimensional nonlinear wave fields.

scholarly journals New Rational Homoclinic and Rogue Waves for Davey-Stewartson Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Changfu Liu ◽  
Chuanjian Wang ◽  
Zhengde Dai ◽  
Jun Liu
Keyword(s):  
Wave Solution ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Periodic Wave ◽  
Homoclinic Solution ◽  
Test Method ◽  
New Family ◽  
Higher Dimensional ◽  
Rogue Wave Solution ◽  
Extreme Behavior

A new method, homoclinic breather limit method (HBLM), for seeking rogue wave solution of nonlinear evolution equation is proposed. A new family of homoclinic breather wave solution, and rational homoclinic solution (homoclinic rogue wave) for DSI and DSII equations are obtained using the extended homoclinic test method and homoclinic breather limit method (HBLM), respectively. Moreover, rogue wave solution is exhibited as period of periodic wave in homoclinic breather wave approaches to infinite. This result shows that rogue wave can be generated by extreme behavior of homoclinic breather wave for higher dimensional nonlinear wave fields.

Characteristics of the lump, lumpoff and rouge wave solutions in a (3+1)-dimensional generalized potential Yu–Toda–Sasa–Fukuyama equation

2019 ◽  
Vol 33 (24) ◽  
pp. 1950291 ◽  
Author(s):  
Zhi-Qiang Li ◽  
Shou-Fu Tian ◽  
Hui Wang ◽  
Jin-Jie Yang ◽  
Tian-Tian Zhang
Keyword(s):  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Rogue Wave ◽  
Graphical Analysis ◽  
Propagation Path ◽  
Wave Solutions ◽  
Generalized Potential ◽  
Ytsf Equation ◽  
Lump Wave ◽  
Rouge Wave

In this work, we consider a (3[Formula: see text]+[Formula: see text]1)-dimensional generalized nonlinear evolution equation, which can be reduced to the potential Yu–Toda–Sasa–Fukuyama (YTSF) equation. We establish the more general lump solutions of the equation and discover its propagation path. It is interesting that we study the case where the lump wave is cut by one stripe wave. In this case, we obtain the lumpoff solution. Furthermore, the special rogue wave is generated by the collision of the lump wave and a couple of stripe soliton waves. The time and position it generates can be determined by tracking the propagation path of the lump wave. Finally, some graphical analysis of the solutions are presented to better understand the dynamic behavior of these waves.

Characteristics of the breathers, rogue waves and soliton waves in a (2 + 1)-dimensional generalized Nizhnik–Novikov–Veselov equation

2019 ◽  
Vol 33 (03) ◽  
pp. 1950014 ◽  
Author(s):  
Xiu-Bin Wang ◽  
Bo Han
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Rogue Wave ◽  
Solitary Wave Solution ◽  
Dynamical Behavior ◽  
Rogue Waves ◽  
Bilinear Forms ◽  
Wave Fields ◽  
Rogue Wave Solution ◽  
Bell’S Polynomials

In this work, a (2 + 1)-dimensional generalized Nizhnik–Novikov–Veselov (GNNV) equation, which can be reduced to several integrable equations, is under investigation. By virtue of Bell’s polynomials, an effective and straightforward way is presented to succinctly construct its two bilinear forms. Furthermore, based on the bilinear formalism and the extended homoclinic test, the breather wave solution, rogue-wave solution and solitary-wave solution of the equation are well constructed. The results can be used to enrich the dynamical behavior of the (2 + 1)-dimensional nonlinear wave fields.

New Rational Homoclinic Solution and Rogue Wave Solution for the Coupled Nonlinear Schrödinger Equation

2014 ◽  
Vol 69 (8-9) ◽  
pp. 441-445 ◽  
Author(s):  
Long-Xing Li ◽  
Jun Liu ◽  
Zheng-De Dai ◽  
Ren-Lang Liu
Keyword(s):  
Schrödinger Equation ◽  
Wave Solution ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Homoclinic Solution ◽  
Nonlinear Schrodinger Equation ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Coupled Nonlinear Schrödinger Equation ◽  
Rogue Wave Solution

In this work, the rational homoclinic solution (rogue wave solution) can be obtained via the classical homoclinic solution for the nonlinear Schrödinger (NLS) equation and the coupled nonlinear Schrödinger (CNLS) equation, respectively. This is a new way for generating rogue wave comparing with direct constructing method and Darboux dressing technique

The rogue wave of the nonlinear Schrödinger equation with self-consistent sources

2018 ◽  
Vol 32 (30) ◽  
pp. 1850367 ◽  
Author(s):  
Yehui Huang ◽  
Hongqing Jing ◽  
Runliang Lin ◽  
Yuqin Yao
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Wave Solution ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Breather Solution ◽  
Rogue Wave Solution ◽  
Self Consistent

In this paper, we study the nonlinear Schrödinger equation with self-consistent sources, and obtain the rogue wave solution, the breather solution and their interactions by the generalized Darboux transformation. The dynamics of the rogue wave solution, the breather solution and their interactions are analyzed.

scholarly journals On the rogue wave solution in the framework of a Korteweg–de Vries equation

2021 ◽  
Vol 30 ◽  
pp. 104847
Author(s):  
Wedad Albalawi ◽  
S.A. El-Tantawy ◽  
Alvaro H. Salas
Keyword(s):  
Wave Solution ◽  
Vries Equation ◽  
Rogue Wave ◽  
Rogue Wave Solution ◽  
De Vries
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