Exact travelling annular waves in generalized reaction-diffusion equations

MAURICIO BELLINI; ROBERTO DEZA; NICOLAS GIOVAMBATTISTA

PHYSICS LETTERS A

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 1997 vol. 232 p. 200 - 206

0375-9601

We have recently introduced a semi-inverse method which renders exact static solutions of one-component, onedimensional reaction-diffusion (RD) equations with variable diffusion coefficient D(4), requiring at most qualitative information on the spatial dependence D(X) of the latter. Through a simple ansatz the RD equations can be mapped onto (stationary) Schrodinger equations, having the form of the potential still at our disposal. In this work we show that the method also applies to two- and three-dimensional static cases with angular symmetry, as well as to (steady) non-static cases. As an illustration we exploit the knowledge of the ground state solutions of a spatially periodic, quasi-exactly solvable Schrodinger potential which is a close relative to the Poschl-Teller potential, to exhibit a highly non-trivial solution which describes outgoing radial waves.