scholarly journals Global Continuation of Homoclinic Solutions

2018 ◽  
Vol 37 (2) ◽  
pp. 159-187 ◽  
Author(s):  
Christian Pötzsche ◽  
Robert Skiba
Keyword(s):  
Homoclinic Solutions ◽  
Global Continuation

The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wei Tan ◽  
Zhao-Yang Yin
Keyword(s):  
Differential Equations ◽  
Wave Equations ◽  
Rogue Wave ◽  
Nonlinear Partial Differential Equations ◽  
Rogue Waves ◽  
Homoclinic Solutions ◽  
Nonlinear Wave Equations ◽  
Bilinear Method ◽  
Wave Solutions ◽  
Rogue Wave Solutions

Abstract The parameter limit method on the basis of Hirota’s bilinear method is proposed to construct the rogue wave solutions for nonlinear partial differential equations (NLPDEs). Some real and complex differential equations are used as concrete examples to illustrate the effectiveness and correctness of the described method. The rogue waves and homoclinic solutions of different structures are obtained and simulated by three-dimensional graphics, respectively. More importantly, we find that rogue wave solutions and homoclinic solutions appear in pairs. That is to say, for some NLPDEs, if there is a homoclinic solution, then there must be a rogue wave solution. The twin phenomenon of rogue wave solutions and homoclinic solutions of a class of NLPDEs is discussed.

Homoclinic solutions for ordinary p-Laplacian systems

2012 ◽  
Vol 218 (9) ◽  
pp. 5682-5692 ◽  
Author(s):  
Xiang Lv ◽  
Shiping Lu
Keyword(s):  
Homoclinic Solutions
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