Solitary waves for the generalized equal width (GEW) equation
- 1 April 2005
- journal article
- other
- Published by Informa UK Limited in International Journal of Computer Mathematics
- Vol. 82 (4), 445-455
- https://doi.org/10.1080/0020716042000272539
Abstract
We consider solitary wave solutions of the generalized equal width (GEW) wave equation u t + ϵu p u x − δu xxt = 0. This paper presents a collocation method for the GEW equation, which is classified as a nonlinear PDE using quadratic B-splines at midpoints as element shape functions. In this research, the scheme of the equation under investigation is found to be unconditionally stable. Test problems including the single soliton and the interaction of solitons are used to validate the suggested methods that is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Finally, a Maxwellian initial condition pulse is then studied.Keywords
This publication has 12 references indexed in Scilit:
- A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equationApplied Mathematics and Computation, 2004
- A computational method for the equal width equationInternational Journal of Computer Mathematics, 2004
- An application of the decomposition method for the generalized KdV and RLW equationsChaos, Solitons, and Fractals, 2003
- Solitary waves induced by the boundary forced EW equationComputer Methods in Applied Mechanics and Engineering, 2001
- A least-squares finite element scheme for the EW equationComputer Methods in Applied Mechanics and Engineering, 2000
- The Boundary Forced MKdV EquationJournal of Computational Physics, 1994
- Solitary waves of the equal width wave equationJournal of Computational Physics, 1992
- Model equations for long waves in nonlinear dispersive systemsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1972
- Long waves on a beachJournal of Fluid Mechanics, 1967
- Calculations of the development of an undular boreJournal of Fluid Mechanics, 1966