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.
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