Abstract
The residual symmetry is obtained for the negative-order modified KdV (nmKdV) equation from the truncated Painlevé expansion by using symbolic computation. The multiple residual symmetries are presented and localized by introducing auxiliary variables, and then, nth Bäcklund 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.
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Acknowledgements
This work was supported by the Zhejiang Province Natural Science Foundation of China (Grant No. LY14A010005), the Scientific Research Foundation of the First-Class Discipline of Zhejiang Province(B) (No.201601) and the Science and Technology Plan Project of Lishui (No. 2016GYX04).
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Song, JF., Hu, YH. & Ma, ZY. Bäcklund transformation and CRE solvability for the negative-order modified KdV equation. Nonlinear Dyn 90, 575–580 (2017). https://doi.org/10.1007/s11071-017-3682-z
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DOI: https://doi.org/10.1007/s11071-017-3682-z