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Exact solution for a two-dimensional KDV-Burgers-type equation with nonlinear terms of any order

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  • In this paper, we study a two-dimensional Burgers--Korteweg-de Vries-type equation with higher-order nonlinearities. A class of solitary wave solution is obtained by means of the Divisor Theorem which is based on the ring theory of commutative algebra. Our result indicates that the presentation of traveling wave solution in [J. Phys. A (Math. Gen.) 35 (2002) 8253--8265] is incorrect; an explanation as to why this is so is given.
    Mathematics Subject Classification: Primary: 13P10, 35Q53; Secondary: 34C05.


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