We establish a correspondence between Darboux’s special isothermic surfaces of type (A, 0, C, D) and the solutions of the second order p.d.e. Φ∆Φ − |∇Φ| + Φ = s, s ∈ R. We then use the classical Darboux transformation for isothermic surfaces to construct a Bäcklund transformation for this equation and prove a superposition formula for its solutions. As an application we discuss 1 and 2-soliton ...

We present a noncommutative generalization of Lax formalism of U(N) principal chiral model in terms of a one-parameter family of flat connections. The Lax formalism is further used to derive a set of parametric noncommutative Bäcklund transformation and an infinite set of conserved quantities. From the Lax pair, we derive a noncommutative version of the Darboux transformation of the model. PACS...

In this paper, we construct a Darboux transformation and the related Backlund for super-symmetric Sawada-Kotera (SSK) equation. The associated nonlinear superposition formula is ...

Abstract We connect certain continuous motions of discrete planar curves resulting in semi-discrete potential Korteweg–de Vries (mKdV) equation with Darboux transformations smooth curves. In doing so, we define infinitesimal that include the aforementioned motions, and also give an alternate geometric interpretation for establishing mKdV equation.