∂¯ -dressing method for the complex modified KdV equation

Abstract

AbstractThe dressing method based on the 2 × 2 matrix∂¯-problem is generalized to study the complex modified KdV equation (cmKdV). Through two linear constraint equations, the spatial and time spectral problems related to the cmKdV equation are derived. The gauge equivalence between the cmKdV equation and the Heisenberg chain equation is obtained. Using a recursive operator, a hierarchy of cmKdV with source is proposed. On the basis of the∂¯-equation, theN-solition solutions of the cmKdV equation are obtained by selecting the appropriate spectral transformation matrix. Furthermore, we get explicit one-soliton and two-soliton solutions.