scholarly journals Blow up and instability of solitary-wave solutions to a generalized Kadomtsev-Petviashvili equation

2000 ◽  
Vol 353 (1) ◽  
pp. 191-208 ◽  
Author(s):  
Yue Liu
Keyword(s):  
Solitary Wave ◽  
Blow Up ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation

Blow up and instability of solitary wave solutions to a generalized Kadomtsev–Petviashvili equation and two-dimensional Benjamin–Ono equations

2007 ◽  
Vol 464 (2089) ◽  
pp. 49-64 ◽  
Author(s):  
Jianqing Chen ◽  
Boling Guo ◽  
Yongqian Han
Keyword(s):  
Initial Data ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Blow Up ◽  
Positive Energy ◽  
Two Dimensional ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Special Case

Let with p being the ratio of an even to an odd integer. For the generalized Kadomtsev–Petviashvili equation, coupled with Benjamin–Ono equations, in the form it is proved that the solutions blow up in finite time even for those initial data with positive energy. As a by-product, it is proved that for all , the solitary waves are strongly unstable if . This result, even in a special case , improves a previous work by Liu (Liu 2001 Trans. AMS 353 , 191–208) where the instability of solitary waves was proved only in the case of .

scholarly journals Periodic Wave Solutions and Their Limits for the Generalized KP-BBM Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Ming Song ◽  
Zhengrong Liu
Keyword(s):  
Dynamical Systems ◽  
Solitary Wave ◽  
Blow Up ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Bifurcation Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Kink Wave ◽  
Bbm Equation

We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. A number of explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain periodic wave solutions, kink wave solutions, unbounded wave solutions, blow-up wave solutions, and solitary wave solutions.

scholarly journals Traveling Wave Solutions for the Generalized Zakharov Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Ming Song ◽  
Zhengrong Liu
Keyword(s):  
Dynamical Systems ◽  
Solitary Wave ◽  
Traveling Wave ◽  
Blow Up ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Bifurcation Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions

We use the bifurcation method of dynamical systems to study the traveling wave solutions for the generalized Zakharov equations. A number of traveling wave solutions are obtained. Those solutions contain explicit periodic wave solutions, periodic blow-up wave solutions, unbounded wave solutions, kink profile solitary wave solutions, and solitary wave solutions. Relations of the traveling wave solutions are given. Some previous results are extended.

Solitary wave solutions for the modified Kadomtsev–Petviashvili equation

2007 ◽  
Vol 34 (2) ◽  
pp. 465-475 ◽  
Author(s):  
Xiaoshan Zhao ◽  
Wei Xu ◽  
Huabing Jia ◽  
Hongxian Zhou
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation
Sign in / Sign up

Export Citation Format

Share Document