对与多维Delsarte变换算子相关的De Rham-Hodge-Skrypnik理论的谱和微分几何方面及其在谱和孤子问题中的应用进行了综述。第2部分
A survey of the spectral and differential geometric aspects of the De Rham-Hodge-Skrypnik theory related with Delsarte transmutation operators in multidimension and its applications to spectral and soliton problems. Part 2
摘要：
利用De Rham-Hodge-Skrypnik微分复形，研究了Delsarte变换算子及其对应的Gelfand-Levitan-Marchenko型方程的微分几何和拓扑结构.阐述了Delsarte变换算子与谱理论及特殊Berezansky型同余性质的关系。给出了与自对偶Yang-Mills方程相关的多维微分算子的一些应用，包括三维Laplace算子、二维经典Dirac算子及其多维仿射扩张。讨论了相关非线性动力系统的类孤子解。
英文摘要：
The differential-geometric and topological structure of Delsarte transmutation operators and associated with them Gelfand-Levitan-Marchenko type eqautions are studied making use of the De Rham-Hodge-Skrypnik differential complex. The relationships with spectral theory and special Berezansky type congruence properties of Delsarte transmuted operators are stated. Some applications to multidimensional differential operators are done including three-dimensional Laplace operator, two-dimensional classical Dirac operator and its multidimensional affine extension, related with self-dual Yang-Mills eqautions. The soliton like solutions to the related set of nonlinear dynamical systemare discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
