We first give a Bäcklund transformation from the KdV equation to a new nonlinear evolution equation. We then derive two Bäcklund transformations with two pseudopotentials, one of which is from the KdV equation to the new equation and the other from the new equation to itself. As applications, by applying our Bäcklund transformations to known solutions, we construct some novel solutions to the new equation.
Abstract
Exact solutions of a new (2+1)-dimensional nonlinear evolution equation are studied. Through the Hirota bilinear method, the test function method and the improved tanh-coth and tah-cot method, with the assisstance of symbolic operations, one can obtain the lump solutions, multi lump solutions and more soliton solutions. Finally, by determining different parameters, we draw the three-dimensional plots and density plots at different times.
Bilinear derivative method is widely used in calculating multi-soliton solutions of some nonlinear evolution equation. The paper proves some frequently used properties of bilinear derivative from the perspective of the definition of bilinear derivative, hoping to be useful for learning and teaching in nonlinear science.
Bäcklund Transformations between the KdV Equation and a New Nonlinear Evolution Equation