Bilinear form and soliton solutions for a higher order wave equation

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Under investigation in this paper is a higher order wave equation of the Korteweg–de Vries type, which describes the propagation of more complex wave in the shallow water. Bilinear form is derived based on the binary Bell polynomials. One-soliton solutions are constructed via the Hirota method. Two-soliton solutions are tried to be constructed, but it degenerates to the one-soliton solutions. Influences of the coefficients α and β on the soliton velocity and amplitude are analyzed through the characteristic line.