A non-standard Lax formulation of the Harry Dym hierarchy and its supersymmetric extension
نویسندگان
چکیده
منابع مشابه
Supersymmetric Harry Dym Type Equations
A supersymmetric version is proposed for the well known Harry Dym system. A general class super Lax operator which leads to consistent equations is considered.
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Abstract An extended Harry Dym hierarchy is constructed by using eigenfunctions and adjoint eigenfunctions of the spectral problems of the Harry Dym hierarchy associated with the pseudo-differential operator L = u∂ +u0 +u1∂−1 + · · ·. The corresponding Lax presentation possesses a self-consistent source involving squared eigenfunctions. The resulting extended Harry Dym hierarchy is reduced to t...
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We study the Harry Dym hierarchy of nonlinear evolution equations from the bi-Hamiltonian view point. This is done by using the concept of an S-hierarchy, which permits us to define a matrix Harry Dym hierarchy. We conclude by showing that the conserved densities of the matrix Harry Dym equation can be found by means of a Riccati-type equation.
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A debarapproach is adopted to study the dispersionless Harry-Dym (dHD) hierarchy. Moreover, this formulism is applied to construct some explicit solutions of the dHD hierarchy.
متن کاملConstruction of coupled Harry Dym hierarchy and its solutions from Stackel systems
In this paper we show how to construct the coupled (multicomponent) Harry Dym (cHD) hierarchy from classical Stäckel separable systems. Both nonlocal and purely di¤erential parts of hierarchies are obtained. We also construct various classes of solutions of cHD hierarchy from solutions of corresponding Stäckel systems.
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2012
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/45/12/122001