Integrability and localized wave solutions of the (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation with variable coefficients

This paper focuses on a class of (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation with variable-coefficient, which has been used in the fields of fluid mechanics and plasma. The Lax pair derived from the Bell polynomials confirms the Lax integrability of the equation. Hirota’s bilinear form, Bäcklund transformation and the infinite conservation laws are also derived by using Bell polynomials. Furthermore, the ansatz method is utilized to study lump solutions and interaction solutions. The coordinates of the peak and valleys of the lump wave are obtained by calculation. Meanwhile, the displacements, trails and velocities of the lump wave are studied. The results can be used to describe the motion of nonlinear waves in shallow water under the influence of time. These localized wave solutions are useful for the study of nonlinear optics, engineering and optical fiber.