*(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 |