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Solitary waves for the generalized equal width (GEW) equation. (English) Zbl 1064.65114

Summary: The authors 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 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.

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:
65M70Spectral, collocation and related methods (IVP of PDE)
76B25Solitary waves (inviscid fluids)
76M25Other numerical methods (fluid mechanics)
65M12Stability and convergence of numerical methods (IVP of PDE)
35Q35PDEs in connection with fluid mechanics
35Q51Soliton-like equations