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Painlevé-integrability of a (2+1)-dimensional reaction-diffusion equation: Exact solutions and their interactions

Kuetche Kamgang Victor1,2,*, Bouetou Bouetou Thomas1,2,3,†, and Timoleon Crepin Kofane2,3,‡

  • 1Ecole Nationale Supérieure Polytechnique, University of Yaounde I, P.O. Box. 8390, Cameroon
  • 2Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box. 812, Cameroon
  • 3The Abdus Salam International Centre for Theoretical Physics, P.O. Box 586, Strada Costiera, II-34014 Trieste, Italy

  • *vkuetche@yahoo.fr
  • †tbouetou@yahoo.fr
  • ‡tckofane@yahoo.com
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Phys. Rev. E 79, 056605 – Published 11 May, 2009

DOI: https://doi.org/10.1103/PhysRevE.79.056605

Abstract

We investigate the singularity structure analysis of a (2+1)-dimensional coupled nonlinear extension of the reaction-diffusion (NLERD) equation by means of the Painlevé (P) test. Following the Weiss et al.’s formalism [J. Math. Phys. 24, 522 (1983)], we prove the arbitrariness of the expansion coefficients of the observables. Thus, without the use of the Kruskal’s simplification, we obtain a Bäcklund transformation of the coupled NLERD equation via a consistent truncation procedure stemming from the Weiss et al.’s methodology [J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 25, 13 (1984)]. In the wake of such results, we unveil a typical spectrum of localized and periodic coherent patterns. We also investigate the scattering properties of such structures and we unearth two peculiar soliton phenomena, namely, the fusion and the fission.

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Phys. Rev. E 79, 056605– Published 11 May, 2009
  • Received 28 July 2008

© 2009 American Physical Society

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