Six-dimensional heavenly equation. Dressing scheme and the hierarchy
نویسندگان
چکیده
منابع مشابه
On the ∂̄-dressing method applicable to heavenly equation
The ∂̄-dressing scheme based on local nonlinear vector ∂̄-problem is developed. It is applicable to multidimensional nonlinear equations for vector fields, and, after Hamiltonian reduction, to heavenly equation. Hamiltonian reduction is described explicitely in terms of the ∂̄-data. An analogue of Hirota bilinear identity for heavenly equation hierarchy is introduced, τ -function for the hierarchy...
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Second heavenly equation hierarchy is considered using the framework of hyper-Kähler hierarchy developed by Takasaki [1, 2]. Generating equations for the hierarchy are introduced, they are used to construct generating equations for reduced hierarchies. General N reductions, logarithmic reduction and rational reduction for one of the Lax-Sato functions are discussed. It is demonstrated that rati...
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A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undres...
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ژورنال
عنوان ژورنال: Physics Letters A
سال: 2019
ISSN: 0375-9601
DOI: 10.1016/j.physleta.2018.09.037