Traveling-Wave Solutions of the Kolmogorov–Petrovskii–Piskunov Equation

被引：0
|
作者：
S. V. Pikulin
机构：
[1] Russian Academy of Sciences,Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,”
来源：
Computational Mathematics and Mathematical Physics | 2018年 / 58卷
关键词：
Kolmogorov–Petrovskii–Piskunov equation; generalized Fisher equation; Abel’s equation of the second kind; Fuchs–Kowalewski–Painlevé test; self-similar solutions; traveling waves; intermediate asymptotic regime;
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摘要：
We consider quasi-stationary solutions of a problem without initial conditions for the Kolmogorov–Petrovskii–Piskunov (KPP) equation, which is a quasilinear parabolic one arising in the modeling of certain reaction–diffusion processes in the theory of combustion, mathematical biology, and other areas of natural sciences. A new efficiently numerically implementable analytical representation is constructed for self-similar plane traveling-wave solutions of the KPP equation with a special right-hand side. Sufficient conditions for an auxiliary function involved in this representation to be analytical for all values of its argument, including the endpoints, are obtained. Numerical results are obtained for model examples.
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页码：230 / 237
页数：7
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