Related papers: Gauge-invariant description of some (2+1)-dimensio…
By explicitly eliminating all gauge degrees of freedom in the $3+1$-gauge description of a classical relativistic (open) membrane moving in $\Real^3$ we derive a $2+1$-dimensional nonlinear wave equation of Born-Infeld type for the graph…
Most evolution equations %or wave equations are partially integrable and, in order to explicitly integrate all possible cases, there exist several methods of complex analysis, but none is optimal. The theory of Nevanlinna and Wiman-Valiron…
We show that the nonlinear 2+1--dimensional Three--Wave Resonant Interaction equations, describing several important physical phenomena, can be generated starting from incomplete Lie algebras in the framework of multidimensional…
The evolution of an initial perturbation in Vlasov plasma is studied in the intrinsically nonlinear long-time limit dominated by the effects of particle trapping. After the possible transient linear exponential Landau damping, the evolution…
We generalize the Giveon-Kutasov duality by adding possible Chern-Simons interactions for the $U(N)$ gauge group. Some of the generalized dualities are known in the literature and many others are new to the best of our knowledge. The…
We discuss the constraints imposed on the nonlinear evolution of the Large Scale Structure (LSS) of the universe by galilean invariance, the symmetry relevant on subhorizon scales. Using Ward identities associated to the invariance, we…
In the model of extended non-Abelian tensor gauge fields we have found new metric-independent densities: the exact (2n+3)-forms and their secondary characteristics, the (2n+2)-forms as well as the exact 6n-forms and the corresponding…
We discuss gravity-like formulations of massive Abelian and non-Abelian gauge field theories in four space-time dimensions with particular emphasis on the issue of gauge invariance. Alternative descriptions in terms of antisymmetric tensor…
We define fully non-perturbative generalizations of the uniform density and comoving curvature perturbations, which are known, in the linear theory, to be conserved on sufficiently large scales for adiabatic perturbations. Our non-linear…
Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
A method is proposed of obtaining (2+1)-dimensional non- linear equations with non-analytic dispersion relations. Bilocal formalism is shown to make it possible to represent these equations in a form close to that for their counterparts in…
We investigate symmetry properties of vector-valued diffusion and Schr\"odinger equations. For a separable Hilbert space $H$ we characterize the subspaces of $L^2(\Omega, H)$ that are local (i.e., defined pointwise) and discuss the issue of…
First we introduce and analyze a convergent numerical method for a large class of nonlinear nonlocal possibly degenerate convection diffusion equations. Secondly we develop a new Kuznetsov type theory and obtain general and possibly optimal…
This paper is part of a research project on relations between differential-difference matrix Lax representations (MLRs) with the action of gauge transformations and discrete Miura-type transformations (MTs) for (nonlinear) integrable…
The role of the gauge invariance in noncommutative field theory is discussed. A basic introduction to noncommutative geometry and noncommutative field theory is given. Background invariant formulation of Wilson lines is proposed. Duality…
A non-isospectral (2+1) dimensional integrable spin equation is investigated. It is shown that its geometrical and gauge equivalent counterparts is the (2+1) dimensional nonlinear Schr\"odinger equation introduced by Zakharov and studied…
We study a class of noncommutative gauge theory models on 2-dimensional Moyal space from the viewpoint of matrix models and explore some related properties. Expanding the action around symmetric vacua generates non local matrix models with…
We study the elliptic version of doubly nonlinear diffusion equations on a complete Riemannian manifold $(M,g)$. Through the combination of a special nonlinear transformation and the standard Nash-Moser iteration procedure, some Cheng-Yau…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…