Integrability and exact solutions of the (2+1)-dimensional variable coefficient Ito equation

This paper focuses on the study of the (2+1)-dimensional Ito equation with spatially variable coefficients. The Lax integrability of the equation is confirmed by the Lax pair derived from the Bell polynomials. In addition, the Hirota bilinear form, the Bäcklund transformation and infinite conservation laws of the equation are obtained by the Bell polynomials. More importantly, the ansatz method is utilized to construct lump solutions and interaction solutions between one line soliton and one lump, and the Hirota bilinear method is employed to construct different types of N-soliton solutions and interaction solutions for the (2+1)-dimensional Ito equation with different coefficient functions. All these solutions are presented graphically.