The integrability of the super-KdV hierarchy suggests that it can be written in Hirota bilinear form as the group orbit equation for some infinite-dimensional Lie algebra. We show how the first few equations in the hierarchy can be written in Hirota bilinear form. We also conjecture a bilinear...
A. Bilal, Multi-component KdV hierarchy, V -algebra and non-abelian Toda theory, Princeton University preprint PUPT-1446 (January 1994), hep-th@xxx/9401167.A. Bilal, Nucl. Phys. B422, 258 (1994); Multi-Component KdV Hierarchy, V Algebra and Non Abelian Toda Theory, Preprint PUPT-1446...
Local well-posedness for the KdV hierarchy at high regularity. Adv. Differential Equations, 21(9-10):801-836, 2016.C. E. Kenig and D. Pilod. Local well-posedness for the KdV hierarchy at high regu- larity. Adv. Differential Equations, 21(9-10):801-836, 2016....
Based on the matrix-resolvent approach, for an arbitrary solution to the discrete KdV hierarchy, we define the tau-function of the solution, and compare it with another tau-function of the solution defined via reduction of the Toda lattice hierarchy. Explicit formulae for generating series of ...
SL(n,R)KDVHIERARCHYANDITSNONPOLYNOMIALREALIZATION THROUGHKACMOODYCURRENTS SasankaGhosh 1 andSamirK.Paul 2 1.InstituteofMathematicalSciences C.I.T.Campus,Madras-600113,India 2.S.N.BoseNationalCentreForBasicSciences DB17,Sector1,SaltLake,Calcutta-700064,India ItisshownthatSL(n,R)KdVhierarchycanbeexpre...
This paper considers the relation between the periodic KdV hierarchy and the limit of the periodic Toda hierarchies. By choosing the initial data of the Toda flows in a canonical way, the behavior of a certain Toda flow can mimic KdV flows. Conjecturally, a method of deforming the KdV hierar...
limit of the N=2 α = 1 KdV-hierarchy was derived in [12], and its structure, un- derlining relevance of these Hamiltonians in the bosonic limit, gives a hint towards its supersymmetric generalization. The organisation of this paper is as follows. First the general notions fromthe mathemat...
Based on the study of the confocal Lax matrix, new confocal involutive systems and a new spectral problem are proposed from which a hierarchy of generalized coupled KdV equations is derived. The Abel–Jacobi coordinates are introduced to straighten out the associated flows. Algebro-geometric solutio...
C KdV Hierarchy Chapter VIII Psi-Functions and Frequencies D Construction of the Psi-Functions E ATraceFormula F Frequencies Chapter IX Birkhoff Normal Forms G TwO Resuits on Birkhoff Normal Forms H BirkhoffNormal Form oforder I Kramer'S Lemma J Nondegeneracy of the Second KdV Hamiltonian Chapter...