• Publications
  • Influence
Solitary wave and other solutions for nonlinear heat equations
A number of explicit solutions for the heat equation with a polynomial non-linearity and for the Fisher equation is presented. An extended class of non-linear heat equations admitting solitary waveExpand
  • 36
  • 3
  • PDF
Symmetry and Exact Solutions for Systems of Nonlinear Reaction-Diffusion Equations
where u1 and u2 are functions dependent on t and x; a11, a12, a21, a22 are constant parameters and a11a22 − a21a12 = 0. In [1] a constructive algorithm was proposed for investigation of conditionalExpand
  • 20
  • 1
  • PDF
On hidden symmetries and solutions of the nonlinear d'Alembert equation
TLDR
Non-Lie symmetries of nonlinear d’Alembert equation in pseudo-Euclidean space R 2 , 2 are studied and new classes of exact solutions are constructed. Expand
  • 3
Solitary Wave Solutions for Heat Equations
A great number of mathematical models in thermomechanics, chemistry, biology, ecology, etc.,areformulatedusingnonlinearheatequations. Someofthesemodelsadmitexactsolutionswhichplay fundamental roleExpand
  • 5
  • PDF
Conditional Symmetry and Exact Solutions of a Multidimensional Diffusion Equation
We investigate the conditional symmetry of a multidimensional nonlinear reaction–diffusion equation by its reduction to a radial equation. We construct exact solutions of this equation and infiniteExpand
  • 3
Exact Solutions of the Nonlinear Equation utt=atuuxx+btux2+ctu$$ {u}_{tt}=a(t){uu}_{xx}+b(t){u}_x^2+c(t)u $$
We determine ansätzes that reduce the equation utt=atuuxx+btux2+ctu$$ {u}_{tt}=a(t){uu}_{xx}+b(t){u}_x^2+c(t)u $$ to a system of two ordinary differential equations. It is also shown that the problemExpand
  • 1
Generalized procedure of separation of variables and reduction of nonlinear wave equations
We propose a generalized procedure of separation of variables for nonlinear wave equations and construct broad classes of exact solutions of these equations that cannot be obtained by the classicalExpand
  • 2
  • PDF
Generalized separation of variables and exact solutions of nonlinear equations
We consider a generalized procedure of separation of variables in nonlinear hyperbolic-type equations and Korteweg–de-Vries-type equations. We construct a broad class of exact solutions of theseExpand
  • 2