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

Phys Rev E Stat Nonlin Soft Matter Phys. 2009 May;79(5 Pt 2):056605. doi: 10.1103/PhysRevE.79.056605. Epub 2009 May 11.


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.