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Exact travelling annular waves in generalized reaction-diffusion equations

Authors
Journal
Physics Letters A
0375-9601
Publisher
Elsevier
Publication Date
Volume
232
Identifiers
DOI: 10.1016/s0375-9601(97)00360-5
Keywords
  • Nonlinear Science

Abstract

Abstract We have recently introduced a semi-inverse method which renders exact static solutions of one-component, one-dimensional reaction-diffusion (RD) equations with variable diffusion coefficient D( φ), 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) Schrödinger 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 Schrödinger potential which is a close relative to the Pöschl-Teller potential, to exhibit a highly non-trivial solution which describes outgoing radial waves.

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