A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. II. Exact One- and Two-Periodic Wave Solution of the Coupled Bilinear Equations

1980 ◽  
Vol 48 (4) ◽  
pp. 1365-1370 ◽  
Author(s):  
Akira Nakamura
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Direct Method ◽  
Periodic Wave ◽  
Nonlinear Evolution Equations ◽  
Periodic Wave Solution ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
A Direct Method ◽  
Bilinear Equations

The Periodic Wave Solutions for Two Nonlinear Evolution Equations

2003 ◽  
Vol 40 (2) ◽  
pp. 129-132 ◽  
Author(s):  
Zhang Jin-Liang ◽  
Wang Ming-Liang ◽  
Cheng Dong-Ming ◽  
Fang Zong-De
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Periodic Wave ◽  
Nonlinear Evolution Equations ◽  
Periodic Wave Solutions ◽  
Wave Solutions

scholarly journals Traveling Wave Solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zhengyong Ouyang
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Nonlinear Evolution Equations ◽  
Periodic Waves ◽  
Bifurcation Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions

We use bifurcation method of dynamical systems to study exact traveling wave solutions of a nonlinear evolution equation. We obtain exact explicit expressions of bell-shaped solitary wave solutions involving more free parameters, and some existing results are corrected and improved. Also, we get some new exact periodic wave solutions in parameter forms of the Jacobian elliptic function. Further, we find that the bell-shaped waves are limits of the periodic waves in some sense. The results imply that we can deduce bell-shaped waves from periodic waves for some nonlinear evolution equations.

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