Open AccessON SOLUTIONS OF TRAVELING WAVE TYPE FOR A NONLINEAR PARABOLIC EQUATION
Author(s) -
С. В. Пикулин
Publication year - 2015
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2015-21-6-110-116
Subject(s) - mathematics , nonlinear system , mathematical analysis , representation (politics) , type (biology) , function (biology) , continuation , range (aeronautics) , physics , computer science , ecology , materials science , quantum mechanics , evolutionary biology , politics , political science , law , composite material , biology , programming language
We consider the Kolmogorov — Petrovsky — Piskunov equation which isa quasilinear parabolic equation of second order appearing in the flame propagationtheory and in modeling of certain biological processes. An analyticalconstruction of self-similar solutions of traveling wave kind is presented for thespecial case when the nonlinear term of the equation is the product of theargument and a linear function of a positive power of the argument. The approachto the construction of solutions is based on the study of singular pointsof analytic continuation of the solution to the complex domain and on applyingthe Fuchs — Kovalevskaya — Painlev´e test. The resulting representation of thesolution allows an efficient numerical implementation.