Homoclinic Solutions of Differential Equations

2001 ◽  
pp. 207-264
Author(s):  
Maria do Rosário Grossinho ◽  
Stepan Agop Tersian
Keyword(s):  
Differential Equations ◽  
Homoclinic Solutions

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.

A new method for homoclinic solutions of ordinary differential equations

2009 ◽  
Vol 39 (3) ◽  
pp. 1073-1082 ◽  
Author(s):  
F. Talay Akyildiz ◽  
K. Vajravelu ◽  
S.-J. Liao
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Homoclinic Solutions ◽  
New Method
Sign in / Sign up

Export Citation Format

Share Document