Variational approximation for wave propagation in continuum and discrete media

L. A

Abstract


We develop a variational approximation for wave propagation in continuum and discrete media based on the modulation of wave profiles described by appropriate trial functions. We illustrate the method by considering an application to the theory of dislocation of materials. We first consider the continuum approximation of the model and reproduce the exact traveling known solution. We then consider the fully discrete non integrable model and obtain an approximate solution based on trial functions with functional form similar to the exact solution of the continuum. The description of this discrete approximate solution is in terms of a discrete nonlinear dispersion relation between the wave parameters. In this last situation we compare the numerical and variational solutions at the stationary case. We thus illustrate the usage of a variational asymptotic approximation to study nonlinear problems and we contrast the differences and difficulties between continuum and discrete problems.

Keywords


Modulation theory; average Lagrangian; trial function

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REVISTA MEXICANA DE FÍSICA E, year 18, issue 1, January-June 2021. Semiannual Journal published by Sociedad Mexicana de Física, A. C. Departamento de Física, 2º Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Apartado Postal 70-348. Tel. (+52)55-5622-4946, https://rmf.smf.mx/ojs/rmf-e, rmf@ciencias.unam.mx. Chief Editor: José Alejandro Ayala Mercado.  INDAUTOR Certificate of Reserve: 04-2019-080216402500-203, ISSN: 2683-2216 (on line), 1870-3542 (print), both granted by Instituto Nacional del Derecho de Autor.  Responsible for the last update of this issue, Technical Staff of Sociedad Mexicana de Física, A. C., Fís. Efraín Garrido Román, 2º. Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Date of last modification, January 04, 2021.

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