A generalized (2+1)-dimensional Hirota bilinear equation: integrability, solitons and invariant solutions

In this paper, we consider an extended form of generalized (2 + 1)-dimensional Hirota bilinear equation which demonstrates nonlinear wave phenomena in shallow water, oceanography and nonlinear optics. We have successfully studied the integrability characteristic of the nonlinear equation in different aspects. We have applied the Painleve analysis technique on the equation and found that it is not completely integrable in Painleve sense. The concept of Bell polynomial form is introduced and the Hirota bilinear form, Backlund transformations are obtained. By means of Cole-Hopf transformation, we have derived the Lax pairs by direct linearization of coupled system of binary Bell polynomials. We have also derived infinite conservation laws from two field condition of the generalized (2 + 1)-dimensional Hirota bilinear equation. We have exploited the expressions of one-soliton, two-soliton and three-soliton solutions directly from Hirota bilinear form and demonstrated them pictorially. Further, Lie symmetry approach is applied to analyze the Lie symmetries and vector fields of the considered problem. The symmetry reductions were then obtained using similarity variables and some closed-form solutions such as parabolic wave solutions and kink wave solutions are secured.