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Zbl 1064.65114
Evans, D.J.; Raslan, K.R.
Solitary waves for the generalized equal width (GEW) equation. (English)
[J] Int. J. Comput. Math. 82, No. 4, 445-455 (2005). ISSN 0020-7160; ISSN 1029-0265/e

Summary: The authors consider solitary wave solutions of the generalized equal width (GEW) wave equation $u_t+\varepsilon u^p u_x-\delta u_{xxt}= 0$. This paper presents a collocation method for the GEW equation, which is classified as a nonlinear partial differential equation 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.\par 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.

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
76B25 Solitary waves, etc. (inviscid fluids)
76M25 Other numerical methods
65M12 Stability and convergence of numerical methods (IVP of PDE)
35Q35 Other equations arising in fluid mechanics
35Q51 Solitons

Keywords: stability; numerical examples; solitons; generalized equal width wave equation; solitary wave solutions; collocation method; quadratic B-splines

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Zentralblatt MATH Berlin [Germany]