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Finite element approximation to two-dimensional sine-Gordon solitons. (English) Zbl 0762.65073

This is a well-grounded and exhaustive numerical investigation of the two-dimensional sine-Gordon equation undertaken in the framework of the finite element methodology. From technical point of view the authors use a semidiscrete Galerkin approach based on simple four-noded bilinear finite elements in combination with a generalized Newmark integration scheme. The paper does not contain the strong convergence proof, but comparisons with finite difference solutions exhibit a very good accuracy of the developed algorithm.
The solutions are presented for interaction of circular ring solitons, symmetric perturbation of static line solitons, superposition of two orthogonal solitons, line and elliptic solitons in an inhomogeneous medium etc. The text is concluded with a series of beautiful pictures that undoubtedly will fascinate every reader of this paper.
Reviewer: O.Titow (Berlin)

MSC:

65Z05 Applications to the sciences
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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