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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 ${u}_{t}+\epsilon {u}^{p}{u}_{x}-\delta {u}_{xxt}=0$. 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.

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:
 65M70 Spectral, collocation and related methods (IVP of PDE) 76B25 Solitary waves (inviscid fluids) 76M25 Other numerical methods (fluid mechanics) 65M12 Stability and convergence of numerical methods (IVP of PDE) 35Q35 PDEs in connection with fluid mechanics 35Q51 Soliton-like equations