Solitary wave solution of nonlinear Benjamin–Bona–Mahony–Burgers equation using a high-order difference scheme

2015 ◽  
Vol 36 (2) ◽  
pp. 915-927 ◽  
Author(s):  
Akbar Mohebbi ◽  
Zahra Faraz
Keyword(s):  
Solitary Wave ◽  
Difference Scheme ◽  
Wave Solution ◽  
Burgers Equation ◽  
Solitary Wave Solution ◽  
High Order ◽  
Order Difference

scholarly journals The Mass Calculation of Solitary Wave Solution of the One-Dimensional Burgers Equation

POSITRON ◽  
2012 ◽  
Vol 2 (1) ◽  
Author(s):  
Teguh B. Prayitno
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Lagrangian Density ◽  
Burgers Equation ◽  
Solitary Wave Solution ◽  
Classical Field Theory ◽  
Classical Field ◽  
Hamiltonian Density ◽  
One Dimensional ◽  
The One

We have calculated the mass of the solitary wave solution of the one-dimensional Burgers equation by integrating the Hamiltonian density of its equation based on the formulation of the classical field theory. To use this method, we first construct the Lagrangian density in order to obtain the Hamiltonian density by initially introducing the ansatz function of the appropriate field. In this paper, we have obtained that the mass of the solitary of the one-dimensional of Burgers equation is literally divergent.

The novel multi-solitary wave solution to the fifth-order KdV equation

2004 ◽  
Vol 13 (10) ◽  
pp. 1606-1610 ◽  
Author(s):  
Zhang Yi ◽  
Chen Deng-Yuan
Keyword(s):  
Solitary Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Kdv Equation ◽  
The Novel ◽  
Fifth Order

scholarly journals Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaoxiao Zheng ◽  
Yadong Shang ◽  
Yong Huang
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Constant Coefficient ◽  
Wave Solution ◽  
Integral Method ◽  
Solitary Wave Solution ◽  
First Integral ◽  
Mkdv Equation ◽  
Variable Coefficients ◽  
First Integral Method

This paper is concerned with the variable coefficients mKdV (VC-mKdV) equation. First, through some transformation we convert VC-mKdV equation into the constant coefficient mKdV equation. Then, using the first integral method we obtain the exact solutions of VC-mKdV equation, such as rational function solutions, periodic wave solutions of triangle function, bell-shape solitary wave solution, kink-shape solitary wave solution, Jacobi elliptic function solutions, and Weierstrass elliptic function solution. Furthermore, with the aid of Mathematica, the extended hyperbolic functions method is used to establish abundant exact explicit solution of VC-mKdV equation. By the results of the equation, the first integral method and the extended hyperbolic function method are extended from the constant coefficient nonlinear evolution equations to the variable coefficients nonlinear partial differential equation.

A regularized model for strongly nonlinear internal solitary waves

2009 ◽  
Vol 629 ◽  
pp. 73-85 ◽  
Author(s):  
WOOYOUNG CHOI ◽  
RICARDO BARROS ◽  
TAE-CHANG JO
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Wave Solution ◽  
Wave Amplitude ◽  
Solitary Wave Solution ◽  
Shear Instability ◽  
Internal Solitary Waves ◽  
Strongly Nonlinear ◽  
Regularized Model

The strongly nonlinear long-wave model for large amplitude internal waves in a two-layer system is regularized to eliminate shear instability due to the wave-induced velocity jump across the interface. The model is written in terms of the horizontal velocities evaluated at the top and bottom boundaries instead of the depth-averaged velocities, and it is shown through local stability analysis that internal solitary waves are locally stable to perturbations of arbitrary wavelengths if the wave amplitudes are smaller than a critical value. For a wide range of depth and density ratios pertinent to oceanic conditions, the critical wave amplitude is close to the maximum wave amplitude and the regularized model is therefore expected to be applicable to the strongly nonlinear regime. The regularized model is solved numerically using a finite-difference method and its numerical solutions support the results of our linear stability analysis. It is also shown that the solitary wave solution of the regularized model, found numerically using a time-dependent numerical model, is close to the solitary wave solution of the original model, confirming that the two models are asymptotically equivalent.

New Solitary Wave Solution for the Boussinesq Wave Equation Using the Semi-Inverse Method and the Exp-Function Method

2009 ◽  
Vol 64 (11) ◽  
pp. 709-712 ◽  
Author(s):  
Wenjun Liu
Keyword(s):  
Wave Equation ◽  
Variational Principle ◽  
Solitary Wave ◽  
Wave Solution ◽  
Variational Formulation ◽  
Function Method ◽  
Inverse Method ◽  
Solitary Wave Solution ◽  
Solitary Solutions

Using the semi-inverse method, a variational formulation is established for the Boussinesq wave equation. Based on the obtained variational principle, solitary solutions in the sech-function and expfunction forms are obtained

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