Related papers: Integrable geometry and Soliton equations in 2+1 d…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
The paper presents the bosonic and fermionic supersymmetric extensions of the structural equations describing conformally parametrized surfaces immersed in a Grasmann superspace, based on the authors' earlier results. A detailed analysis of…
Lie derivatives of various geometrical and physical quantities define symmetries and conformal symmetries in general relativity. Thus we obtain motions, collineations, conformal motions and conformal collineations. These symmetries are used…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
Two integrable differential-difference equations are derived from a (2+1)-dimensional modified Heisenberg ferromagnetic equation and a resonant nonlinear Schr\"oinger equation respectively. Multi-soliton solutions of the resulted…
In this letter, we construct new meshy soliton structures by using two concrete (2+1)-dimensional integrable systems. The explicit expressions based on corresponding Cole-Hopf type transformations are obtained. Constraint equation…
A hierarchy of differential equations on a Banach Lie-Poisson space related to the restricted Grassmannian is studied. Flows on the groupoid of partial isometries and on the restricted Grassmannian are described, and a momentum map picture…
The notion of multidimensional quadrilateral lattice is introduced. It is shown that such a lattice is characterized by a system of integrable discrete nonlinear equations. Different useful formulations of the system are given. The…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…
Integrable models of 1+1 dimensional gravity coupled to scalar and vector fields are briefly reviewed. A new class of integrable models with nonminimal coupling to scalar fields is constructed and discussed.
Interactions of noncommutative solitons in a modified U(n) sigma model in 2+1 dimensions can be analyzed exactly. Using an extension of the dressing method, we construct explicit time-dependent solutions of its noncommutative field equation…
In two space-time dimensions a class of classical multicomponent scalar field theories with discrete, in general non-Abelian global symmetry is considered. The corresponding soliton solutions are given for the cases of 2, 3, and 4…
The solubility of a general two dimensional model, which reduces to various models in different limits, is studied within the path integral formalism. Various subtleties and interesting features are pointed out.
The peculiar intergrability of the Davey-Stewartson equation allows us to find analytically solutions describing the simultaneous formation and interaction of one-dimensional and two-dimensional localized coherent structures. The predicted…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
We give a self-contained introduction to the relations between Integrable Systems and the Geometry of Riemann Surfaces. We start from a historical introduction to the topic of integrable systems. Afterwards, we study the polynomial…
We consider 2+1-dimensional classical noncommutative scalar field theory. The general ansatz for a radially symmetric solution is obtained. Some exact solutions are presented. Their possible physical meaning is discussed. The case of the…
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…
Inspired by the well known sine-Gordon equation, we present a symmetric coupled system of two real scalar fields in $1+1$ dimensions. There are three different topological soliton solutions which be labelled according to their topological…
This paper is devoted to a study of the connections between three different analytic descriptions for the immersion functions of 2D-surfaces corresponding to the following three types of symmetries: gauge symmetries of the linear spectral…