Abelian Toda solitons revisited

Abstract

We present a systematic and detailed review of the application of the method of Hirota and the rational dressing method to abelian Toda systems associated with the untwisted loop groups of complex general linear groups. Emphasizing the rational dressing method, we compare the soliton solutions constructed within these two approaches, and show that the solutions obtained by the Hirota's method are a subset of those obtained by the rational dressing method.

minor corrections (mostly stylistic), version to appear in Rev. Math. Phys

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Cited by in corpus (6)

• On the universal R-matrix for the Izergin-Korepin model
• The rational dressing for abelian twisted loop Toda systems
• More non-Abelian loop Toda solitons
• Darboux transformations for two dimensional elliptic affine Toda equations
• Solving non-abelian loop Toda equations
• Finite dimensional Hamiltonian system related to Lax pair with symplectic and cyclic symmetries