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Zbl 0759.65086
Gardner, L.R.T.; Gardner, G.A.
Solitary waves of the equal width wave equation. (English)
[J] J. Comput. Phys. 101, No.1, 218-223 (1992). ISSN 0021-9991

In 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.\par For small $\delta$ $(U\sb t+UU\sb x-\delta U\sb{xxt}=0)$ 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.
[L.G.Vulkov (Russe)]

MSC 2000:: *65Z05 Applications to physics
65M60 Finite numerical methods (IVP of PDE)
35Q53 KdV-like equations
35L75 Nonlinear hyperbolic PDE of higher $(>2)$ order

Keywords: regularized long wave equation; Galerkin method; $B$-spline finite elements; equal width equation; solitary waves; positive waves

Citations: Zbl 0717.65072

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