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Exact solutions of reaction-diffusion systems and nonlinear wave equations

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Abstract

We propose a general method to find exact travelling and standing wave solutions of reaction-diffusion systems and nonlinear wave equations. The method is applied to several well-known reaction-diffusion systems such as a competition-diffusion system of Lotka-Volterra type, the Gray-Scott model, a simplification of the Noyes-Field model for the Belousov-Zhabotinskii reaction, and two- and three-component models for quadratic solitons. We also find exact solutions of several generalized nonlinear dispersive equations occurring in mathematical physics.

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Authors and Affiliations

  1. Department of Mathematical and Life Sciences, Institute for Nonlinear Sciences and Applied Mathematics, Graduate School of Science, Hiroshima University, 739-8526, Higashi-Hiroshima, Japan

    M. Rodrigo & M. Mimura

Authors
  1. M. Rodrigo
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  2. M. Mimura
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Corresponding author

Correspondence to M. Rodrigo.

Additional information

M. R. is supported by a Postdoctoral Fellowship from the Japan Society for the Promotion of Science. M. M. acknowledges the support of Grant-in-Aid for Scientific Research (A) 08404005 and 09354001.

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Rodrigo, M., Mimura, M. Exact solutions of reaction-diffusion systems and nonlinear wave equations. Japan J. Indust. Appl. Math. 18, 657–696 (2001). https://doi.org/10.1007/BF03167410

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  • DOI: https://doi.org/10.1007/BF03167410

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