Solitary waves of the equal width wave equation.

*(English)*Zbl 0759.65086In a recent paper of the authors [ibid. 91, No. 2, 441-459 (1990; Zbl 0717.65072)] a Galerkin method with cubic $B$-spline finite elements was proposed to obtain accurate and efficient numerical solutions to the regularized long wave (RLW) equation. Here, the same method is applied to the equal width equation and to simulate the migration and interaction of solitary waves and evolution of a Maxwellian initial condition.

For small $\delta $ $({U}_{t}+U{U}_{x}-\delta {U}_{xxt}=0)$ only positive waves are formed and the behaviour mimics that of the KdV and RLW equations. For larger values of $\delta $ both positive and negative solitary waves are generated.

Reviewer: L.G.Vulkov (Russe)

##### MSC:

65Z05 | Applications of numerical analysis to physics |

65M60 | Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE) |

35Q53 | KdV-like (Korteweg-de Vries) equations |

35L75 | Nonlinear hyperbolic PDE of higher $(>2)$ order |