Bell polynomials approach applied to \((2+1)\)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation (Q1724321)

Summary: The bilinear form, bilinear Bäcklund transformation, and Lax pair of a \((2+1)\)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation are derived through Bell polynomials. The integrable constraint conditions on variable coefficients can be naturally obtained in the procedure of applying the Bell polynomials approach. Moreover, the \(N\)-soliton solutions of the equation are constructed with the help of the Hirota bilinear method. Finally, the infinite conservation laws of this equation are obtained by decoupling binary Bell polynomials. All conserved densities and fluxes are illustrated with explicit recursion formulae.