Solitary wave solutions of two-dimensional nonlinear Kadomtsev–Petviashvili dynamic equation in dust-acoustic plasmas

Pramana ◽  
2017 ◽  
Vol 89 (3) ◽  
Author(s):  
Aly R Seadawy
Keyword(s):  
Solitary Wave ◽  
Dynamic Equation ◽  
Two Dimensional ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Dust Acoustic

scholarly journals Mixed Rational Lump-Solitary Wave Solutions to an Extended (2+1)-Dimensional KdV Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhigang Yao ◽  
Huayong Xie ◽  
Hui Jie
Keyword(s):  
Solitary Wave ◽  
Rogue Wave ◽  
Kdv Equation ◽  
Auxiliary Function ◽  
Mixed Solution ◽  
Two Dimensional ◽  
Solitary Wave Solutions ◽  
Bilinear Method ◽  
Trilinear Form ◽  
Wave Solutions

Based on the bilinear method, rational lump and mixed lump-solitary wave solutions to an extended (2+1)-dimensional KdV equation are constructed through the different assumptions of the auxiliary function in the trilinear form. It is found that the rational lump decays algebraically in all directions in the space plane and its amplitude possesses one maximum and two minima. One kind of the mixed solution describes the interaction between one lump and one line solitary wave, which exhibits fission and fusion phenomena under the different parameters. The other kind of the mixed solution shows one lump interacting with two paralleled line solitary waves, in which the evolution of the lump gives rise to a two-dimensional rogue wave. This shows that these three interesting phenomena exist in the corresponding physical model.

Solitary wave solutions for variant two-dimensional Zakharov-Kuznetsov equation

2017 ◽  
Vol 11 ◽  
pp. 347-352
Author(s):  
Juan Carlos Hernandez R. ◽  
Martha Cecilia Moreno ◽  
German Preciado L.
Keyword(s):  
Solitary Wave ◽  
Two Dimensional ◽  
Solitary Wave Solutions ◽  
Wave Solutions

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 .

Sign in / Sign up

Export Citation Format

Share Document