相关论文: Lax pairs for string Newton Cartan geometry

We find a Polyakov-type action for strings moving in a torsional Newton-Cartan geometry. This is obtained by starting with the relativistic Polyakov action and fixing the momentum of the string along a non-compact null isometry. For a flat…

We review the relation between Chern-Simons gauge theory and topological string theory on noncompact Calabi-Yau spaces. This relation has made possible to give an exact solution of topological string theory on these spaces to all orders in…

We provide a formal definition of p-brane Newton--Cartan (pNC) geometry and establish some foundational results. Our approach is the same followed in the literature for foundations of Newton--Cartan Gravity. Our results provide control of…

We find a Lax pair for the geometrically exact discrete Hamiltonian equations for the discrete elastic rod. This is paper III of a series.

Differential-difference integrable exponential type systems are studied corresponding to the Cartan matrices of semi-simple or affine Lie algebras. For the systems corresponding to the algebras $A_2$, $B_2$, $C_2$, $G_2$ the complete sets…

We investigate the possible existence of non-topological solitons in string-like theories, or in other completions of Einstein theory, by examining a simple extension of standard theory that describes a non-linear scalar field interacting…

The important unsolved problem in theory of integrable systems is to find conditions guaranteeing existence of a Lax representation for a given PDE. The use of the exotic cohomology of the symmetry algebras opens a way to formulate such…

A family of integrable $GL(NM)$ models is described. On the one hand it generalizes the classical spin Ruijsenaars--Schneider systems (the case $N=1$), and on the other hand it generalizes the relativistic integrable tops on $GL(N)$ Lie…

We describe the structure of string vacuum states in the supersymmetric matrix model for M theory compactified on a circle in the large-N limit. We show that the theory admits topological instanton field configurations which at…

We show that the (torsional) nonrelativistic string sigma models on $ R\times S^2 $ can be mapped into \emph{deformed} Rosochatius like integrable models in one dimension. We also explore the associated Hamiltonian constrained structure by…

We show that the Nonlinear Schr\"odinger Equation and the related Lax pair in 1+1 dimensions can be derived from 2+1 dimensional Chern-Simons Topological Gauge Theory. The spectral parameter, a main object for the Loop algebra structure and…

Nonrelativistic string theory is a self-contained corner of string theory, with its string spectrum enjoying a Galilean-invariant dispersion relation. This theory is unitary and ultraviolet complete, and can be studied from first…

We show that there is a series of topological string theories whose integrable structure is described by the Toda lattice hierarchy. The monodromy group of the Frobenius manifold for the matter sector is an extension of the affine Weyl…

In this paper, based on simple analytic techniques, we explore the integrability conditions for classical stringy configurations defined over $ \eta $ as well as $ \lambda $- deformed backgrounds. We perform our analysis considering…

We find the Hamiltonian for physical excitations of the classical bosonic string propagating in the AdS_5 x S^5 space-time. The Hamiltonian is obtained in a so-called uniform gauge which is related to the static gauge by a 2d duality…

The correspondence between Matrix String Theory in the strong coupling limit and IIA superstring theory can be shown by means of the instanton solutions of the former. We construct the general instanton solutions of Matrix String Theory…

We propose a method for constructing the Lax connection of two-dimensional relativistic integrable sigma models on coset spaces by means of exponentiation of a suitable operator. We derive a simple quadratic relation that this operator must…

We give a Lax description for the system of polytropic gas equations. The special structure of the Lax function naturally leads to the two infinite sets of conserved charges associated with this system. We obtain closed form expressions for…

Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete…

In this letter, we study systematically the general properties of the $B$-extension of any integrable model. In addition to discussing the general properties of Hamiltonians, Hamiltonian structures etc, we also clarify the origin of…