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

被引：9

作者：

Pikulin, S. V. ^{[1
]}

机构：

[1] Russian Acad Sci, Dorodnicyn Comp Ctr, Fed Res Ctr Comp Sci & Control, Moscow 119333, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2018年 / 58卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

Kolmogorov-Petrovskii-Piskunov equation; generalized Fisher equation; Abel's equation of the second kind; Fuchs-Kowalewski-Painleve test; self-similar solutions; traveling waves; intermediate asymptotic regime; MODELS;

D O I：

10.1134/S0965542518020124

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：230 / 237

页数：8

共 50 条

[41] Kolmogorov-Petrovskii-Piskunov方程行波系统的无穷远奇点
李向正
张卫国
原三领
[J]. 系统科学与数学, 2013, 33 (02) : 231 - 235
[42] Kolmogorov-Petrovskii-Piskunov方程和Zhiber-Shabat方程的行波解
李玉梅
李宝毅
宋媛媛
[J]. 天津师范大学学报(自然科学版), 2015, 35 (02) : 10 - 12
[43] FACTORIZATION AS A METHOD OF FINDING EXACT INVARIANT SOLUTIONS OF THE KOLMOGOROV-PETROVSKII-PISKUNOV EQUATION AND THE RELATED SEMENOV AND ZELDOVICH EQUATIONS (VOL 322, PG 823, 1992)
BERKOVICH, LM
[J]. DOKLADY AKADEMII NAUK, 1993, 329 (05) : U685 - U685
[44] Numerical methods for the generalized Fisher-Kolmogorov-Petrovskii-Piskunov equation
Branco, J. R.
Ferreira, J. A.
de Oliveira, P.
[J]. APPLIED NUMERICAL MATHEMATICS, 2007, 57 (01) : 89 - 102
[45] On semi analytical and numerical simulations for a mathematical biological model; the time-fractional nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation
Khater, Mostafa M. A.
Mohamed, Mohamed S.
Attia, Raghda A. M.
[J]. CHAOS SOLITONS & FRACTALS, 2021, 144
[46] THE MARKOV BRANCHING RANDOM-WALK AND SYSTEMS OF REACTION-DIFFUSION (KOLMOGOROV-PETROVSKII-PISKUNOV) EQUATIONS
KELBERT, MY
SUHOV, YM
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1995, 167 (03) : 607 - 634
[47] Approximate Solutions of the One-Dimensional Fisher–Kolmogorov–Petrovskii– Piskunov Equation with Quasilocal Competitive Losses
A. V. Shapovalov
[J]. Russian Physics Journal, 2018, 60 : 1461 - 1468
[48] Travelling wave solutions of the degenerate Kolmogorov-Petrovski-Piskunov equation
Medvedev, GS
Ono, K
Holmes, PJ
[J]. EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2003, 14 : 343 - 367
[49] Symmetry Operators of the Nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov Equation with a Quadratic Operator
E. A. Levchenko
A. Yu. Trifonov
A. V. Shapovalov
[J]. Russian Physics Journal, 2014, 56 : 1415 - 1426
[50] Approximate Solutions of Nonlinear Fractional Kolmogorov-Petrovskii-Piskunov Equations Using an Enhanced Algorithm of the Generalized Two-Dimensional Differential Transform Method
Song Li-Na
Wang Wei-Guo
[J]. COMMUNICATIONS IN THEORETICAL PHYSICS, 2012, 58 (02) : 182 - 188

← 1 2 3 4 5 →