Abstract
In this paper we use stochastic semiclassical analysis and the logarithmic transformation to study the gradients of the approximate travelling wave solutions for the generalised KPP equations with Gaussian and Dirac delta initial distributions. We apply the logarithmic transformation to the nonlinear reaction diffusion equations and obtain a Maruyama–Girsanov–Cameron–Martin formula for the driftμ2∇loguμ,uμbeing a solution of a generalised KPP equation. We obtain thatμ2|∇ loguμ(t,x)| is bounded and the trough is flat. The difficult problem in this paper is to prove that the corresponding crest is flat. A probabilistic approach is used in this paper to treat this problem successfully.
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Schedule a callMore From: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
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