Related papers: Symmetry classification of variable coefficient cu…
We start developing a formalism which allows to construct supersymmetric theories systematically across space-time signatures. Our construction uses a complex form of the supersymmetry algebra, which is obtained by doubling the spinor…
We develop efficient group-theoretical approach to the problem of classification of evolution equations that admit non-local transformation groups (quasi-local symmetries), i.e., groups involving integrals of the dependent variable. We…
The symmetry SU(2) and its geometric Bloch Sphere rendering are familiar for a qubit (spin-1/2) but extension of symmetries and geometries have been investigated far less for multiple qubits, even just a pair of them, that are central to…
We establish sharp-in-time kernel and dispersive estimates for the Schr\"odinger equation on non-compact Riemannian symmetric spaces of any rank. Due to the particular geometry at infinity and the Kunze-Stein phenomenon, these properties…
A detailed study is made of the noncommutative geometry of $R^3_q$, the quantum space covariant under the quantum group $SO_q(3)$. For each of its two $SO_q(3)$-covariant differential calculi we find its metric, the corresponding frame and…
We discuss the asymptotic symmetry algebra of the Schrodinger-invariant metrics in d+3 dimensions and its realization on finite temperature solutions of gravity coupled to matter fields. These solutions have been proposed as gravity…
In this paper we develop a systematic and self consistent procedure based on a set of compatibility conditions for identifying all maximal (eight parameter) and non-maximal (one and two parameter) symmetry groups associated with the mixed…
We study space-time symmetries in scalar quantum field theory (including interacting theories) on static space-times. We first consider Euclidean quantum field theory on a static Riemannian manifold, and show that the isometry group is…
We use a change of variables that turns the critical nonlinear Schroedinger equation into the critical nonlinear Schroedinger equation with isotropic harmonic potential, in any space dimension. This change of variables is isometric on…
We associate to any Riemannian symmetric space (of finite or infinite dimension) a L$^*$-algebra, under the assumption that the curvature operator has a fixed sign. L$^*$-algebras are Lie algebras with a pleasant Hilbert space structure.…
We consider discrete nonlinear hyperbolic equations on quad-graphs, in particular on the square lattice. The fields are associated to the vertices and an equation Q(x_1,x_2,x_3,x_4)=0 relates four fields at one quad. Integrability of…
We consider the defocusing quintic nonlinear Schr\"odinger equation in four space dimensions. We prove that any solution that remains bounded in the critical Sobolev space must be global and scatter. We employ a space-localized interaction…
An integrable two-component nonlinear Schr\"odinger equation in $2+1$ dimensions is presented. The singular manifold method is applied in order to obtain a three-component Lax pair. The Lie point symmetries of this Lax pair are calculated…
We carry out group analysis of a class of generalized fifth-order Korteweg-de Vries equations with time dependent coefficients. Admissible transformations, Lie symmetries and similarity reductions of equations from the class are classified…
We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schr\"odinger equations driven by additive It\^o noise. The class of nonlinearities of interest includes nonlocal…
For the Schr\"odinger equation with a cubic-quintic, focusing-focusing nonlinearity in one space dimension, this article proves the local asymptotic completeness of the family of small standing solitary waves under even perturbations in the…
The quantum lens spaces form a natural and well-studied class of noncommutative spaces which can be subjected to classification using algebraic invariants by drawing on the fully developed classification theory of unital graph…
The Kucha\v{r} canonical transformation for vacuum geometrodynamics in the presence of cylindrical symmetry is applied to a general non-vacuum case. The resulting constraints are highly non-linear and non-local in the momenta conjugate to…
The present paper solves completely the problem of the group classification of nonlinear heat-conductivity equations of the form\ $u_{t}=F(t,x,u,u_{x})u_{xx} + G(t,x,u,u_{x})$. We have proved, in particular, that the above class contains no…
The results from J. Stat. Phys. 159:668-712 & 163:1350-1393, on a quadratic kinetic equation in the analysis of the long time asymptotics of weak turbulence theory for the nonlinear Schr\"odinger equation, are summarized and placed in…