Recursion Operator and Bäcklund Transformation for Super mKdV Hierarchy

Abstract

In this paper we consider the N = 1 supersymmetric mKdV hierarchy composed of positive odd flows embedded within an affineŝl(2, 1) algebra. Its Bäcklund transformations are constructed in terms of a gauge transformation preserving the zero curvature representation. The recursion operator relating consecutive flows is derived and shown to relate their Backlund transformations.

Bäcklund Transformations for Liouville Equations with Exponential Nonlinearity

“…Bäcklund transformations are a differential relationship of two equations. Recently, this approach has made it possible to solve many interesting problems [8][9][10][11]14,[17][18][19].…”

“…Taking into account equalities (7), (8), we have ∂F 1 ∂v η = 0, ∂F 2 ∂v ξ = 0 and then ∂ 2 F 1 ∂z∂v η = 0, and equality remains…”

“…Due to the complexity of various nonlinear equations, there is no single method for solving them. For integrable systems, effective methods have been developed, such as the inverse scattering method [1,2], the Hirota method [3][4][5], the Painleve method [6,7], Bäcklund transformations [8][9][10][11] and the mapping and deformation method [2]. Bäcklund transformations are an example of differential geometric structures generated by differential equations.…”