Bäcklund transformation and CRE solvability for the negative-order modified KdV equation

The residual symmetry is obtained for the negative-order modified KdV (nmKdV) equation from the truncated Painleve expansion by using symbolic computation. The multiple residual symmetries are presented and localized by introducing auxiliary variables, and then, nth Backlund transformation in terms of determinant is derived. By using the consistent Riccati expansion (CRE) method, the nmKdV equation is proved to be CRE solvable and exact soliton–Weierstrass elliptic function interaction solutions are constructed from the final consistent equation.