标题： 多项式丛与可积方程在A.III型对称空间上的广义傅里叶变换 显示英文标题

标题： Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces

摘要： 与A.III型对称空间相关并具有附加约化的可积非线性微分方程的一个特殊类通过逆散射方法（ISM）进行分析。 利用配饰方法，构造了与Lax算子相关的两类孤子解。 接下来，通过Wronskian关系，构建了势函数与散射数据最小集合之间的映射。 此外，推导了“平方解”（广义指数）的完备性关系。 接下来，得到了势函数及其变化的展开式。 这表明将逆散射方法解释为广义傅里叶变换是正确的。 最后，简要分析了这些广义多组分海森堡铁磁（MHF）类型可积模型在A.III型对称空间上的哈密顿结构。 显示英文摘要

摘要： A special class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions are analyzed via the inverse scattering method (ISM). Using the dressing method we construct two classes of soliton solutions associated with the Lax operator. Next, by using the Wronskian relations, the mapping between the potential and the minimal sets of scattering data is constructed. Furthermore, completeness relations for the 'squared solutions' (generalized exponentials) are derived. Next, expansions of the potential and its variation are obtained. This demonstrates that the interpretation of the inverse scattering method as a generalized Fourier transform holds true. Finally, the Hamiltonian structures of these generalized multi-component Heisenberg ferromagnetic (MHF) type integrable models on A.III-type symmetric spaces are briefly analyzed.