Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Zemlyanukhin A. I., Bochkarev A. V. Exact Solitary-wave Solutions of the Burgers – Huxley and Bradley – Harper Equations. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2017, vol. 17, iss. 1, pp. 62-70. DOI: 10.18500/1816-9791-2017-17-1-62-70, EDN: YNBYBV

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
22.02.2017
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Russian
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517.958:53
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YNBYBV

Exact Solitary-wave Solutions of the Burgers – Huxley and Bradley – Harper Equations

Autors: 
Zemlyanukhin Alexandr Isaevich, Yuri Gagarin State Technical University of Saratov
Bochkarev Andrey Vladimirovich, Yuri Gagarin State Technical University of Saratov
Abstract: 

It is shown that the exact soliton-like solutions of nonlinear wave mechanics evolution equations can be obtained by direct perturbation method based on the solution of a linearized equation. The sought solutions are sums of the perturbation series which can be found using the requirement that the series are to be geometric. This requirement leads to the conditions for the coefficients of the equations and parameters of the sought solutions. The exact solitary-wave solutions of the nonlinear non-integrable Burgers–Huxley equation and the generalized Bradley–Harper equation are obtained. The conditions are formulated under which these solutions have the form of a wave front. It is shown that these solutions can also be found from the system of Riccati equations, that is equivalent to the original equation. By utilizing the Cole–Hopf transformation, the generalized Bradley–Harper equation is reduced to a second-order linear differential equation with constant coefficients.

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Received: 
24.09.2016
Accepted: 
22.01.2017
Published: 
28.02.2017