The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems) then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.
Painleve analysis, Backlund transformation, Lax pair and periodic wave solutions for a generalized (2+1)-dimensional Hirota-Satsuma-Ito equation in fluid mechanics
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。
