Related papers: Remarks on q-Virasoro and qKdV
A new three-dimensional second-order nonlinear wave equation is introduced which passes the Painleve test for integrability and possesses KdV-type multisoliton solutions. Lax integrability of this equation remains unknown.
An algorithm for generating a class of closed form solutions to the Navier-Stokes equations is suggested, with examples. Of particular interest are those exact solutions that exhibit intermittency, tertiary Hopf bifurcations, flow reversal,…
We consider Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions. We prove that under some conditions the solution of KZ system is rational too. This assertion confirms…
We overview the main ideas and techniques of the functional-analytical approach to some extremal problems of convex geometry that stem from the Queen Dido problem.
We study Virasoro constraints for Gromov-Witten theory of a product variety when one factor has semi-simple quantum cohomology.
Ordinary and partial differential equation for unknown functions defined on the Cantor dyadic group are studied. We consider two types of equations: related to the Gibbs derivatives and to the fractional modified Gibbs derivatives (or…
The work concerns a type of backward multivalued McKean-Vlasov stochastic differential equations. First, we prove the existence and uniqueness of solutions for backward multivalued McKean-Vlasov stochastic differential equations. Then, it…
The discrete equations of motion for the quantum mappings of KdV type are given in terms of the Sklyanin variables (which are also known as quantum separated variables). Both temporal (discrete-time) evolutions and spatial (along the…
A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.
We derive a Liouville type result for special Lagrangian equations with certain "convexity" and restricted linear growth assumptions on the solutions.
Hirota's discrete KdV equation is a well-known integrable two-dimensional partial difference equation regarded as a discrete analogue of the KdV equation. In this paper, we show that a variation of Hirota's discrete KdV equation with an…
In this note we obtain the solutions of four $q$-functional equations and express the solutions in $q$-operator forms. These equations give sufficient conditions for $q$-operator methods.
The role of R in the solutions of the Ginsparg-Wilson relation is discussed.
A noncommutative KdV-type equation is introduced extending the Baecklund chart in [S. Carillo, M. Lo Schiavo, and C. Schiebold, SIGMA 12 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two…
We propose the functions defined by the maximum of a discrete quadratic form and satisfying the ultradiscrete KdV equation. These functions includes not only soliton solutions but also pseudo-periodic solutions. In the proof, we employ some…
An overview of recent theoretical progress on Non-Relativistic QCD and related effective theories is provided.
We consider wave models with lower order terms and recollect some recent results on energy and dispersive estimates for their solution based on symbolic type estimates for coefficients and partly stabilisation conditions. The exposition is…
It is well-known that solutions to the string equation are generated by elements of Sato's Grassmannian which are invariant under action of some differential operator. Here it is shown that this operator is nothing else than the…
The generalized Drinfeld-Sokolov construction of KdV systems is reviewed in the case of an arbitrary affine Lie algebra paying particular attention to Hamiltonian aspects and $\W$-algebras. Some extensions of known results as well as a new…
Weak solutions of incompressible Navier-Stokes Equations re-obtained variationally