Related papers: Higher-Dimensional Integrable Systems from Multili…
We present the new extended supersymmetrization of the Nonlinear Schrodinger Equation by introducing two superbosons fields with the different gradation. Our model is different from this considered by Toppan and in the reduced case…
A very natural construction of integrable extensions of soliton systems is presented. The extension is made on the level of evolution equations by a modification of the algebra of dynamical fields. The paper is motivated by recent works of…
The structure of solutions is studied for the Lax equation $D_t(G)=[F,G]$ for formal power series with respect to the shift operator. It is proved that if the equation with a given series $F$ of degree $m$ admits a solution $G$ of degree…
We consider discrete one dimensional nonlinear equations and present the procedure of lifting them to Z-graded graphs. We identify conditions which allow one to lift one dimensional solutions to solutions on graphs. In particular, we prove…
A geometric approach to immersion formulas for soliton surfaces is provided through new cohomologies on spaces of special types of $\mathfrak{g}$-valued differential forms. This leads us to introduce Poincar\'e-type lemmas for these…
We formulate a dynamical system based on many-index objects. These objects yield a generalization of the Heisenberg's equation. Systems describing harmonic oscillators are given.
A Lax pair for the 2D Euler equation is found.
The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a…
The Darboux--Dressing Transformations are applied to the Lax pair associated to the system of nonlinear equations describing the resonant interaction of three waves in 1+1 dimensions. We display explicit solutions featuring localized waves…
Integrable boundary conditions in 1+1 and 2+1 dimensions are discussed from the higher symmetries point of view. Boundary conditions consistent with the discrete Landau-Lifshitz model and infinite 2D Toda lattice are represented.
We use a recently proposed scheme of matrix extension of dispersionless integrable systems for the Abelian case, in which it leads to linear equations, connected with the initial dispersionless system. In the examples considered, these…
Lax pairs are a useful tool in finding conserved quantities of some dynamical systems. In this expository article, we give a motivated introduction to the idea of a Lax pair of matrices $(L,A)$, first for mechanical systems such as the…
The N-dimensional generalization of Bertrand spaces as families of Maximally superintegrable systems on spaces with nonconstant curvature is analyzed. Considering the classification of two dimensional radial systems admitting 3 constants of…
Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian…
Using the point fusion procedure we obtain the new integrable systems from the Elliptic Schlesinger system (ESS). These new systems have the pole orders higher than one in the matrix of the Lax operator. Quadratic Poisson algebras on the…
We consider an integrable generalization of the nonlinear Schr\"odinger (NLS) equation that was recently derived by one of the authors using bi-Hamiltonian methods. This equation is related to the NLS equation in the same way that the…
We consider some natural connections which arise between right-flat (p, q) paraconformal structures and integrable systems. We find that such systems may be formulated in Lax form, with a "Lax p-tuple" of linear differential operators,…
A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
We present a simple novel construction of recursion operators for integrable multidimensional dispersionless systems that admit a Lax pair whose operators are linear in the spectral parameter and do not involve the derivatives with respect…