Related papers: Remarks on q-Virasoro and qKdV
A new construction, with more visible canonical features, of a qKdV equation in a q-Virasoro context is exhibited.
The method for solving the KdV are considered.
We construct non-Abelian analogs for some KdV type equations, including the (rational form of) exponential Calogero--Degasperis equation and generalizations of the Schwarzian KdV equation. Equations and differential substitutions under…
We investigate the structure of representations of the (positive half of the) Virasoro algebra and situations in which they decompose as a tensor product of Lie algebra representations. As an illustration, we apply these results to the…
Virasoro-type symmetries and their roles in solvable models are reviewed. These symmetries are described by the two-parameter Virasoro-type algebra $Vir_{p,q}$ by choosing the parameters p and q suitably.
Relations between differential calculi, quantum groups, integrable systems, and q-analysis are studied. Some new Hirota type formulas are established for qKP along with variations on classical Hirota formulas.
A collection of miscellaneous continuous, semi-discrete, and discrete integrable systems can be associated with each integrable evolution equation of the KdV type. We give them for the Schwarz-KdV equation and generalize to the vector case.…
This article gives a short sketch of the origins of Virasoro cocycle, both in algebra and quantum field theory.
By imposing special compatible similarity constraints on a class of integrable partial $q$-difference equations of KdV-type we derive a hierarchy of second-degree ordinary $q$-difference equations. The lowest (non-trivial) member of this…
The main object of this paper is to produce a deformation of the KdV hierarchy of partial differential equations. We construct this deformation by taking a certain limit of the Toda hierarchy. This construction also provides a deformation…
We propose the algebro-geometric mothod of construction of solutions of the discrete KP equation over a finite field. We also perform the corresponding reduction to the finite field version of the discrete KdV equation. We write down…
We give a simple geometric interpretation of the mapping of the negative KdV equation as proposed by Qiao and Li {arXiv:1101.1605 [math-ph], Europhys. Lett.,94 (2011) 50003} and the Fuchssteiner equation using geometry of projective…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
We obtain some new inequalities of Chebyshev Type.
Using a multicomponent version of the CKP hierarchy we construct the prepotential of the WDVV equations.
We show that the integrable subclassess of a class of third order non-autonomous equations are identical with the integrable subclassess of the autonomous ones.
We prove well-posedness of the Cauchy problem for a class of third order quasilinear evolution equations with variable coefficients in projective Gevrey spaces. The class considered is connected with several equations in Mathematical…
The KdV equation is the canonical example of an integrable non-linear partial differential equation supporting multi-soliton solutions. Seeking to understand the nature of this interaction, we investigate different ways to write the KdV…
Various aspects of q-differential equations are examined in the contexts of quantum groups and spaces, differential calculi, zero curvature, and Lax-Sato hierarchies. There are many explicit formulas and examples along with some survey…
A K-theoretic counterpart of quantum cohomology theory is discussed.