The modified Camassa–Holm equation: Bäcklund transformation and nonlinear superposition formula

This paper is concerned with the modified Camassa–Holm equation and its Bäcklund transformation. With the aid of reciprocal transformation and the associated modified Camassa–Holm equation, a Bäcklund transformation, which involves both dependent and independent variables, is constructed for the modified Camassa–Holm equation. The related nonlinear superposition formula is worked out and applications of both Bäcklund transformation and nonlinear superposition formula are considered.