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Publications Influence

Solitary wave and other solutions for nonlinear heat equations

- A. Nikitin, T. Barannyk
- Mathematics, Physics
- 2 March 2003

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 wave… Expand

36 3- PDF

Symmetry and Exact Solutions for Systems of Nonlinear Reaction-Diffusion Equations

- T. Barannyk
- Mathematics
- 2002

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 conditional… Expand

20 1- PDF

On hidden symmetries and solutions of the nonlinear d'Alembert equation

- A. Barannyk, T. Barannyk, I. Yuryk
- Mathematics, Computer Science
- Commun. Nonlinear Sci. Numer. Simul.
- 1 July 2013

TLDR

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Solitary Wave Solutions for Heat Equations

- T. Barannyk, A. Nikitin
- Mathematics
- 2004

A great number of mathematical models in thermomechanics, chemistry, biology, ecology, etc.,areformulatedusingnonlinearheatequations. Someofthesemodelsadmitexactsolutionswhichplay fundamental role… Expand

5- PDF

Conditional Symmetry and Exact Solutions of a Multidimensional Diffusion Equation

- T. Barannyk
- Mathematics
- 1 October 2002

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 infinite… Expand

3

Exact Solutions of the Nonlinear Equation utt=atuuxx+btux2+ctu$$ {u}_{tt}=a(t){uu}_{xx}+b(t){u}_x^2+c(t)u $$

- A. Barannyk, T. Barannyk, I. Yuryk
- Mathematics
- 22 February 2018

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 problem… Expand

1

The classification of the Galilei-invariant systems of nonlinear reaction-diffusion equations

- T. Barannyk
- Physics
- 25 July 2015

Generalized procedure of separation of variables and reduction of nonlinear wave equations

- A. Barannyk, T. Barannyk, I. Yuryk
- Mathematics
- 3 December 2009

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 classical… Expand

2- PDF

Generalized separation of variables and exact solutions of nonlinear equations

- A. Barannyk, T. Barannyk, I. Yuryk
- Mathematics
- 7 June 2011

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 these… Expand

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