Painlevé-integrability of a (2+1)-dimensional reaction-diffusion equation: exact solutions and their interactions.
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 '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.
Victor
Kuetche Kamgang
KK
Ecole Nationale Supérieure Polytechnique, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box. 812, Cameroon. vkuetche@yahoo.fr
Thomas
Bouetou Bouetou
BB
Kofane
Timoleon Crepin
TC