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The solitary waves, breather waves and rogue waves for a generalized nonlinear equation

Under investigation in this work is a generalized nonlinear equation, which can be widely applied to describe various phenomena in nonlinear physical science field. The equation can be reduced to Kadomtsev–Petviashvili-type equations and Jimbo–Miwa-type equations as its special cases. By using Bell’s polynomial, its bilinear representation is well constructed. Based on the obtained bilinear formalism, we derive the solitary wave solutions of the equation. We also consider its kinky breather wave, rational breather wave and rogue wave solutions by employing the extended homoclinic test method, respectively. Moreover, the dynamic behaviors of these solutions are given by graphical analysis. It is hoped that our works can be helpful to understand dynamical behavior of the nonlinear equation.