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Symmetry analysis and exact explicit solutions for Kadomtsev-Petviashvili-Burgers equation

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Abstract

We apply the group theory to Kadomtsev-Petviashvili-Burgers (KPBII) equation which is a natural model for the propagation of the two-dimensional damped waves. In correspondence with the generators of the symmetry group allowed by the equation, new types of symmetry reductions are performed. Some new exact solutions are obtained, which can be in the form of solitary waves and periodic waves. Specially, our solutions indicate that the equation may have time-dependent nonlinear shears. Such exact explicit solutions and symmetry reductions are important in both applications and the theory of nonlinear science.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Engineering Computations, Hangzhou Dianzi University, Zhejiang, 310018, China

    Long Wei

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  1. Long Wei
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Correspondence to Long Wei.

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Original Russian Text © Long Wei, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 8, pp. 1467–1475.

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Wei, L. Symmetry analysis and exact explicit solutions for Kadomtsev-Petviashvili-Burgers equation. Comput. Math. and Math. Phys. 51, 1369–1376 (2011). https://doi.org/10.1134/S0965542511080148

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  • DOI: https://doi.org/10.1134/S0965542511080148

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