We study supersymmetric structure of the self-isospectral crystalline chains formed by N copies of the mutually displaced one-gap Lame systems. It is generated by the N(N-1) integrals of motion which are the first order matrix differential operators, by the same number of the nontrivial second order integrals, and by the N third order Lax integrals. We show that the structure admits distinct alternatives for a grading operator, and in dependence on its choice one of the third order matrix integrals plays either the role of the bosonic central charge or the role of the fermionic supercharge to be a square root of the spectral polynomial. Yet another peculiarity is that the set of all the second order integrals of motion generates a nonlinear sub-superalgebra. We also investigate the associated self-isospectral soliton chains, and discuss possible physical applications of the unusual extended supersymmetry.
Factorization of nonlinear supersymmetry in one-dimensional Quantum Mechanics. I: general classification of reducibility and analysis of the third-order algebra
Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
我们研究了一种特殊的超对称性的对无反射量子力学系统所描述的n-孤子的一般形式，取决于n标度和n平移参数的潜力。证明了如果子系统的离散能级不同，则超代数对平移参数不敏感，是由两个2n阶微分超荷、两个2n+1阶超荷和两个由子系统的Lax积分组成的2n+1阶玻色积分生成的.当一个子系统的r个离散能级与另一个子系统的任意r个离散能级重合时，奇异超对称性发生了约化，两个相互独立的纠缠生成元的总阶数降为4 n-2 r +1，非线性超代数结构获得了对r个相对平移的依赖性.对于一个完整的成对符合的比例参数控制的束缚态的能量和传输散射振幅，新兴的isospectrality检测到的一个蜕变的Lax积分到玻色子中心荷。在等谱类，我们揭示了一个特殊的情况下，给一个新的家庭的有限间隙一阶Bogoliubov-德Gennes系统相关的AKNS可积族。
