The solitary wave solution of the two-dimensional regularized long-wave equation in fluids and plasmas

2011 ◽  
Vol 182 (12) ◽  
pp. 2540-2549 ◽  
Author(s):  
Mehdi Dehghan ◽  
Rezvan Salehi
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Two Dimensional ◽  
Long Wave ◽  
Regularized Long Wave Equation

scholarly journals A Modified Equation Approach to Selecting a Nonstandard Finite Difference Scheme Applied to the Regularized Long Wave Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
E. Momoniat
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Solitary Wave ◽  
Nonlinear Term ◽  
Solitary Wave Solution ◽  
Finite Difference Schemes ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Modified Equation ◽  
Nonstandard Finite Difference

Two nonstandard finite difference schemes are derived to solve the regularized long wave equation. The criteria for choosing the “best” nonstandard approximation to the nonlinear term in the regularized long wave equation come from considering the modified equation. The two “best” nonstandard numerical schemes are shown to preserve conserved quantities when compared to an implicit scheme in which the nonlinear term is approximated in the usual way. Comparisons to the single solitary wave solution show significantly better results, measured in theL2andL∞norms, when compared to results obtained using a Petrov-Galerkin finite element method and a splitted quadratic B-spline collocation method. The growth in the error when simulating the single solitary wave solution using the two “best” nonstandard numerical schemes is shown to be linear implying the nonstandard finite difference schemes are conservative. The formation of an undular bore for both steep and shallow initial profiles is captured without the formation of numerical instabilities.

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

Sign in / Sign up

Export Citation Format

Share Document