The exact travelling wave solutions of a KPP equation
Eugene Kogan
TL;DR
This paper derives exact traveling wave solutions for the KPP equation and the generalized Burgers-Huxley equation, providing analytical insights into wave behaviors for specific wave speeds.
Contribution
It presents new exact analytical solutions for the KPP and Burgers-Huxley equations at particular wave speeds, expanding the understanding of these nonlinear PDEs.
Findings
Exact solutions for KPP equation at specific wave speeds
Analytical solutions for generalized Burgers-Huxley equation
Enhanced understanding of wave propagation in reaction-diffusion systems
Abstract
We obtain the exact analytical traveling wave solutions of the Kolmogorov-Petrovskii-Piskunov equation with the reaction term belonging to the class of functions, which includes that of the (generalized) Fisher equation, for the particular values of the waves speed. Additionally we obtain the the exact analytical traveling wave solutions of the generalized Burgers-Huxley equation.
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Taxonomy
TopicsNonlinear Waves and Solitons