A Comprehensive Study of the Complex mKdV Equation through the Singular Manifold Method

Abstract

In this paper, we introduce a modification of the Singular Manifold Method in order to derive the associated spectral problem for a generalization of the complex version of the modified Korteweg–de Vries equation. This modification yields the right Lax pair and allows us to implement binary Darboux transformations, which can be used to construct an iterative method to obtain exact solutions.

Keywords

• integrability
• complex mKdV equation
• Singular Manifold Method
• Lax pair
• Darboux transformations
• soliton solutions