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

Abstract

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.

References in corpus (4)

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• On the Classification of Automorphic Lie Algebras
• Twisted hierarchies associated with the generalized sine-Gordon equation

Cited by in corpus (8)

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• Drinfel'd-Sokolov construction and exact solutions of vector modified KdV hierarchy
• Dressing method and quadratic bundles related to symmetric spaces. Vanishing boundary conditions
• Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl(n,C)
• New Reductions of a Matrix Generalized Heisenberg Ferromagnet Equation
• The Generalised Zakharov-Shabat System and the Gauge Group Action
• Integrable systems on symmetric spaces from a quadratic pencil of Lax operators
• Real Hamiltonian forms of affine Toda field theories: spectral aspects