A super mKdV equation: bi-Hamiltonian structures and Darboux transformations

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作者：
Hanyu Zhou
Kai Tian
XiaoXia Yang
机构：
[1] North China Institute of Science and Technology,College of Science
[2] China University of Mining and Technology,School of Mathematical Sciences
[3] Capital Normal University,School of Mathematical Sciences
来源：
Pramana | / 98卷
关键词：
Hamiltonian structure; linear spectral problem; gauge transformation; reduction; 02.30.Ik; 02.30.Jr;
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摘要：
Under an appropriate Miura-type transformation, a super modified Korteweg–de Vries (mKdV) equation, introduced by Hu in 1997, is shown to be a modification of the generalised super Korteweg–de Vries (KdV) equation. By correspondingly changing bi-Hamiltonian formulations of the latter, bi-Hamiltonian structures are established for the super mKdV equation. Moreover, from an ansatz about gauge transformations of its linear spectral problem, elementary Darboux transformations are constructed, and suitably composing them yields a binary Darboux transformation, as well as the fourth one. As a reduction of the fourth Darboux transformation, a proper Darboux transformation is obtained for Kupershmidt’s super mKdV equation.
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