On the preservation of invariants in the simulation of solitary waves in some nonlinear dispersive equations |
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| Authors: | J. Á lvarez |
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| Affiliation: | a Departamento de Matemática Aplicada, E.T.S. de Ingenieros Industriales, Universidad de Valladolid, Paseo del Cauce s/n, E-47011 Valladolid, Spain
b Departamento de Matemática Aplicada, E.T.S.I. de Telecomunicación, Universidad de Valladolid, Campus Miguel Delibes, Camino del Cementerio s/n, E-47011 Valladolid, Spain |
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| Abstract: | In this paper we generalize some results in the literature concerning the structure of numerical approximations to solitary wave solutions of some nonlinear, dispersive equations is studied. We prove that those time discretizations with the property of preserving, exactly or approximately up to certain order, some invariants of the problems, have a better propagation of the error and provide a more suitable simulation of the solitary waves. The generalization involves the treatment of nonlocal operators and two different kinds of equations. |
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| Keywords: | Solitary waves Conservative numerical methods Conserved quantities |
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