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.

Solitary Wave Solutions of High Order Scalar Fields and Coupled Scalar Fields

1999 ◽  
Vol 54 (3-4) ◽  
pp. 195-203 ◽  
Author(s):  
Jian-song Yang ◽  
Sen-yue Lou
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
General Solution ◽  
Solitary Wave ◽  
Arbitrary Function ◽  
Scalar Fields ◽  
High Order ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Klein Gordon

An arbitrary Klein-Gordon field with a quite general constrained condition (which contains an arbitrary function) can be used as an auxilialy field such that some special types of solutions of high order scalar fields can be obtain by solving an ordinary differential equation (ODE). For a special type of constraint, the general solution of the ODE can be obtained by twice integrating. The solitary wave solutions of the model ф5 are treated in an alternative simple way. The obtained solutions of the ф5 model can be changed to those of the ф8 field and coupled scalar fields.

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.

scholarly journals Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1601
Author(s):  
Zakieh Avazzadeh ◽  
Omid Nikan ◽  
José A. Tenreiro Machado
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Solitary Wave ◽  
Wave Equations ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Ode System ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
De Vries

This paper investigates the solitary wave solutions of the generalized Rosenau–Korteweg-de Vries-regularized-long wave equation. This model is obtained by coupling the Rosenau–Korteweg-de Vries and Rosenau-regularized-long wave equations. The solution of the equation is approximated by a local meshless technique called radial basis function (RBF) and the finite-difference (FD) method. The association of the two techniques leads to a meshless algorithm that does not requires the linearization of the nonlinear terms. First, the partial differential equation is transformed into a system of ordinary differential equations (ODEs) using radial kernels. Then, the ODE system is solved by means of an ODE solver of higher-order. It is shown that the proposed method is stable. In order to illustrate the validity and the efficiency of the technique, five problems are tested and the results compared with those provided by other schemes.

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
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