Singularity structure, symmetries and integrability of generalized Fisher-type nonlinear diffusion equation

P S Bindu, M Senthilvelan, M Lakshmanan
2001 Journal of Physics A: Mathematical and General  
In this letter, the integrability aspects of a generalized Fisher type equation with modified diffusion in (1+1) and (2+1) dimensions are studied by carrying out a singularity structure and symmetry analysis. It is shown that the Painlevé property exists only for a special choice of the parameter (m=2). A Bäcklund transformation is shown to give rise to the linearizing transformation to the linear heat equation for this case (m=2). A Lie symmetry analysis also picks out the same case (m=2) as
more » ... e only system among this class as having nontrivial infinite dimensional Lie algebra of symmetries and that the similarity variables and similarity reductions lead in a natural way to the linearizing transformation and physically important classes of solutions (including known ones in the literature), thereby giving a group theoretical understanding of the system. For nonintegrable cases in (2+1) dimensions, associated Lie symmetries and similarity reductions are indicated.
doi:10.1088/0305-4470/34/49/101 fatcat:hmnmxbdn55awhlpuctynz5d6au