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Nonlinear Summation of Power Series and Exact Solutions of Evolution Equations

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Abstract

The technique of quadratic and cubic summation of power series in the perturbation method was first used for finding exact solutions to nonlinear evolution equations. The series were construction with the use of exponential partial solutions to linearized equations. The solution of both classic and modified nonintegrable Korteweg-de Vries equations, the modified Burgers equation, and the Fisher one allows one to demonstrate specific features of the mentioned method. We obtain exact solitary wave solutions to the mentioned equations in the form of a wave impulse and a wave front and show that summation parameters depend on the pole orders of the desired solutions.

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Authors and Affiliations

  1. Yuri Gagarin State Technical University of Saratov, ul. Politechnicheskaya 77, Saratov, 410054, Russia

    A. I. Zemlyanukhin & A. V. Bochkarev

Authors
  1. A. I. Zemlyanukhin
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  2. A. V. Bochkarev
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Corresponding author

Correspondence to A. I. Zemlyanukhin.

Additional information

Original Russian Text © A.I. Zemlyanukhin, A.V. Bochkarev, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 1, pp. 34–41.

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Zemlyanukhin, A.I., Bochkarev, A.V. Nonlinear Summation of Power Series and Exact Solutions of Evolution Equations. Russ Math. 62, 29–35 (2018). https://doi.org/10.3103/S1066369X1801005X

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  • DOI: https://doi.org/10.3103/S1066369X1801005X

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