Related papers: Geometric transformations and soliton equations
The structure properties of multidimensional Delsarte transmutation operators in parametirc functional spaces are studied by means of differential-geometric tools. It is shown that kernels of the corresponding integral operator expressions…
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…
This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at…
Lagrangian multiforms provide a variational framework for describing integrable hierarchies. This thesis presents two approaches for systematically constructing Lagrangian one-forms, which cover the case of finite-dimensional integrable…
After recalling the construction of a graded Lie bracket on the space of cyclic multilinear forms on a vector space V, due to Georges Pinczon and Rosane Ushirobira, we prove this construction gives a structure of quadratic associative…
The $\hat B_n^{(1)}$-hierarchy is constructed from the standard splitting of the affine Kac-Moody algebra $\hat B_n^{(1)}$, the Drinfeld-Sokolov $\hat B_n^{(1)}$-KdV hierarchy is obtained by pushing down the $\hat B_n^{(1)}$-flows along…
A hierarchy of integrable hamiltonian nonlinear ODEs is associated with any decomposition of the Lie algebra of Laurent series with coefficients being elements of a semi-simple Lie algebra into a sum of the subalgebra consisting of the…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
We examine the reductions of the order of certain third- and second-order nonlinear equations with arbitrary nonlinearity through their symmetries and some appropriate transformations. We use the folding transformation which enables one to…
We generalize to noncommutative cylinder the solution generation technique, originally suggested for gauge theories on noncommutative plane. For this purpose we construct partial isometry operators and complete set of orthogonal projectors…
We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order…
The forced soliton equation is the starting point for semiclassical computations with solitons away from the small momentum transfer regime. This paper develops necessary analytical and numerical tools for analyzing solutions to the forced…
In this paper, we firstly establish the multi-Hamiltonian structure and infinite many conservation laws for the vector Kaup-Newell hierarchy of the positive and negative orders. The first nontrivial negative flow corresponds to a coupled…
The paper surveys some new results and open problems connected with such fundamental combinatorial concepts as polytopes, simplicial complexes, cubical complexes, and subspace arrangements. Particular attention is paid to the case of…
An integrable hierarchies connected with linear stationary Schr\"odinger equation with energy dependent potentials (in general case) are considered. Galilei-like and scaling invariance transformations are constructed. A symmetry method is…
This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…
A systematic construction of St\"{a}ckel systems in separated coordinates and its relation to bi-Hamiltonian formalism are considered. A general form of related hydrodynamic systems, integrable by the Hamilton-Jacobi method, is derived. One…
We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is…
A set of integral relations for rotational and translational zero modes in the vicinity of the classical soliton solution are derived from the particle-like properties of the latter. The validity of these all relations is considered for a…
Preliminary results toward the analysis of the Hamiltonian structure of multifield theories describing complex materials are mustered: we involve the invariance under the action of a general Lie group of the balance of substructural…