Riccati-Ermakov systems and explicit solutions for variable coefficient reaction-diffusion equations

被引：10
作者：
Pereira, Enrique [1 ,2 ]
Suazo, Erwin [3 ]
Trespalacios, Jessica [4 ]
机构：
[1] Southern Methodist Univ, Dept Math Sci, POB 750100, Dallas, TX 75275 USA
[2] Univ Cartagena, Dept Matemat, Cra 6 36-100, Cartagena, Bolivar, Colombia
[3] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, 1201 West Univ Dr, Edinburg, TX 78539 USA
[4] Univ Santiago de Cali, Dept Ciencias Basicas, Cra 73 2a-80, Cali, Valle Del Cauca, Colombia
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 329卷
基金：
美国国家科学基金会;
关键词：
Similarity transformations; Variable coefficient Burgers equation; Variable coefficient Fisher-KPP equation; Riccati-Ermakov systems of ODEs; Exact solutions; Multiparameters; PARTIAL-DIFFERENTIAL-EQUATIONS; SEMILINEAR PARABOLIC EQUATION; BLOW-UP; SYMBOLIC COMPUTATION; BURGERS-EQUATION; WAVE-FUNCTIONS; TRANSFORMATION; BEHAVIOR;
D O I：
10.1016/j.amc.2018.01.047
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present several families of nonlinear reaction-diffusion equations with variable coefficients including generalizations of Fisher-KPP and Burgers type equations. Special exact solutions such as traveling wave, rational, triangular wave and N-wave type solutions are shown. By means of similarity transformations the variable coefficients are conditioned to satisfy Riccati or Ermakov systems of equations. When the Riccati system is used, conditions are established so that finite-time singularities might occur. We explore solution dynamics across multi-parameters. In the supplementary material, we provide a computer algebra verification of the solutions and exemplify nontrivial dynamics of the solutions. Published by Elsevier Inc.
引用
收藏
页码：278 / 296
页数：19
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