New peaked solitary wave solutions of the generalized Camassa–Holm equation

2004 ◽  
Vol 19 (3) ◽  
pp. 621-637 ◽  
Author(s):  
Lixin Tian ◽  
Xiuying Song
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Holm Equation

scholarly journals A Note on Solitary Wave Solutions of the Nonlinear Generalized Camassa-Holm Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Lei Zhang ◽  
Xing Tao Wang
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Solitary Wave ◽  
Numerical Simulations ◽  
Solitary Wave Solutions ◽  
Simple Method ◽  
Wave Solutions ◽  
Holm Equation

We give a simple method for applying ordinary differential equation to solve the nonlinear generalized Camassa-Holm equation ut+2kux−uxxt+aumux−2uxuxx+uuxxx=0. Furthermore we give a new ansätz. In the cases where m=1,2,3, the numerical simulations demonstrate the results.

scholarly journals Diverse approaches to search for solitary wave solutions of the fractional modified Camassa–Holm equation

2021 ◽  
pp. 104882
Author(s):  
Asim Zafar ◽  
M. Raheel ◽  
Kamyar Hosseini ◽  
Mohammad Mirzazadeh ◽  
Soheil Salahshour ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Holm Equation

scholarly journals Cusped and Smooth Solitons for the Generalized Camassa-Holm Equation on the Nonzero Constant Pedestal

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Dong Li ◽  
Yongan Xie ◽  
Shengqiang Tang
Keyword(s):  
Solitary Wave ◽  
Numerical Simulations ◽  
Mathematical Analysis ◽  
Soliton Solutions ◽  
Explicit Solutions ◽  
Solitary Wave Solutions ◽  
Nonzero Constant ◽  
Wave Solutions ◽  
Holm Equation

We investigate the traveling solitary wave solutions of the generalized Camassa-Holm equationut - uxxt + 3u2ux=2uxuxx + uuxxxon the nonzero constant pedestallimξ→±∞⁡uξ=A. Our procedure shows that the generalized Camassa-Holm equation with nonzero constant boundary has cusped and smooth soliton solutions. Mathematical analysis and numerical simulations are provided for these traveling soliton solutions of the generalized Camassa-Holm equation. Some exact explicit solutions are obtained. We show some graphs to explain our these solutions.

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