Integrability Analysis of the Generalized (2+1)-dimensional Hirota-Satsuma-Ito Equation Based on Bell Polynomial Method

In this paper, based on the Bell polynomial method, we study the integrability and solutions of the generalized (2+1)-dimensional Hirota-Satsuma-Ito(HSI) equation. Firstly, the bilinear form of the equation is constructed by using Bell polynomial method. Secondly, the double Bell polynomial Bäcklund transformation and Lax pair of the equation are obtained by using the bilinear form and the symbolic calculation system Mathematica. Then, the conservation laws of the equation and nonlinear superposition formula of solution are constructed. Finally, the Weierstrass elliptic function solutions and N-soliton solutions are obtained, and their physical properties are studied. The integrability and exact solution of the generalized (2+1)-dimensional HSI equation are studied by the Bell polynomial method. It is found that the velocity and shape of solitons remain constant during the motion, and the interaction between solitons plays an important role in the discussion of the physical phenomena of nonlinear waves.