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Bilinear Form and N-Shock-Wave Solutions for a (2+1)-Dimensional Breaking Soliton Equation in Certain Fluids with the Bell Polynomials and Auxiliary Function

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Abstract

In this paper, we will investigate a (2+1)-dimensional breaking soliton (BS) equation for the (2+1)-dimensional collision of a Riemann wave with a long wave in certain fluids. Using the Bell polynomials and an auxiliary function, we derive a new bilinear form for the (2+1)-dimensional BS equation, which is different from those in the previous literatures. One-, two- and N-shock-wave solutions are obtained with the Hirota method and symbolic computation. One shock wave is found to be able to stably propagate. Two shock waves are observed to have the parallel collision, oblique collision, and stable propagation of the V-type structure. In addition, we present the collision between one shock wave and V-type structure, and the collision between two V-type structures.

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