Related papers: Supersymmetric Two-Boson Equation: Bilinearization…
In this note we extend the Pasti-Sorokin-Tonin formalism for chiral bosons in two dimensions to $N=(1,1)$ and $N=(2,2)$ superspace. In the latter case the formalism is developed for chiral, twisted chiral and semi-chiral superfields.
It is shown that the method of the nonlinear realization of local supersymmetry previously developed in framework of supergravity being applied to the n=(2,2) superconformal symmetry allows one to get the new form of the exactly solvable…
We review self-duality of nonlinear electrodynamics and its extension to several Abelian gauge fields coupled to scalars. We then describe self-duality in supersymmetric models, both N = 1 and N = 2. The self-duality equations, which have…
We investigate the doubling inequality and nodal sets for the solutions of bi-Laplace equations. A polynomial upper bound for the nodal sets of solutions and their gradient is obtained based on the recent development of nodal sets for…
Given two infinite sequences with known binomial transforms, we compute the binomial transform of the product sequence. Various identities are obtained and numerous examples are given involving sequences of special numbers: Harmonic…
We review some general and recent results on the characterization and construction of timelike supersymmetric solutions of 4-dimensional supergravity theories.
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
We study Darboux transformations for a Boussinesq-type equations. The parasupersymmetric structure of link between Boussinesq and modified Boussinesq systems is revealed.
The classification problem is solved for some type of nonlinear lattices. These lattices are closely related to the lattices of Ruijsenaars-Toda type and define the Backlund auto-transformations for the class of two-component hyperbolic…
We study multivariable (bilateral) basic hypergeometric series associated with (type $A$) Macdonald polynomials. We derive several transformation and summation properties for such series including analogues of Heine's ${}_2\phi_1$…
In this paper we propose a subgradient algorithm for solving the equilibrium problem where the bifunction may be quasiconvex with respect to the second variable. The convergence of the algorithm is investigated. A numerical example for a…
Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical second order intertwining relations and…
A nonlinear equation in a Banach space is written as a linear equation with a linear operator depending on the unknown solution. This method, which we call a global linearization method, differs essentially from the local linearization…
Casorati determinant solution to the non-autonomous discrete KdV equation is constructed by using the bilinear formalism. We present three different bilinear formulations which have different origins.
Some special solutions to the multidimensional Lam\'e and Bourlet type equations are constructed in an explicit form.
In this paper we study systematically the question of supersymmetrization of the non-local gas equation. We obtain both the N=1 and the N=2 supersymmetric generalizations of the system which are integrable. We show that both the systems are…
We construct one soliton solutions for the nonlinear Schroedinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillators. The soliton wave…
A quantum superintegrable model with reflections on the 2-sphere is introduced. Its two algebraically independent constants of motion generate a central extension of the Bannai--Ito algebra. The Schrodinger equation separates in spherical…
We present the bilinear forms of the (continuous) Painlev\'e equations obtained from the continuous limit of the analogous expresssions for the discrete ones. The advantage of this method is that it leads to very symmetrical results. A new…
The Painleve expansion for the second Painleve equation (PII) and fourth Painleve equation (PIV) have two branches. The singular manifold method therefore requires two singular manifolds. The double singular manifold method is used to…