Backlund Transformations between the KdV Equation and a New Nonlinear Evolution Equation

摘要

We first give a Backlund transformation from the KdV equation to a new nonlinear evolution equation. We then derive two Backlund 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 Backlund transformations to known solutions, we construct some novel solutions to the new equation.