3,313 research outputs found

    Nonlinear Schrodinger Equations and N=1 Superconformal Algebra

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    By using AKNS scheme and soliton connection taking values in N=1 superconformal algebra we obtain new coupled super Nonlinear Schrodinger equations.Comment: 12 pages, no figures, LaTex fil

    On the dynamics of rational solutions for 1-D generalized Volterra system

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    The Hirota bilinear formalism and soliton solutions for a generalized Volterra system is presented. Also, starting from the soliton solutions, we obtain a class of nonsingular rational solutions using the "long wave" limit procedure of Ablowitz and Satsuma, and appropriate "gauge" transformations. Their properties are also discussed and it is shown that these solutions interact elastically with no phase shift.Comment: 9 pages, Late

    On an integrable discretization of the modified Korteweg-de Vries equation

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    We find time discretizations for the two ''second flows'' of the Ablowitz-Ladik hierachy. These discretizations are described by local equations of motion, as opposed to the previously known ones, due to Taha and Ablowitz. Certain superpositions of our maps allow a one-field reduction and serve therefore as valid space-time discretizations of the modified Korteweg-de Vries equation. We expect the performance of these discretizations to be much better then that of the Taha-Ablowitz scheme. The way of finding interpolating Hamiltonians for our maps is also indicated, as well as the solution of an initial value problem in terms of matrix factorizations.Comment: 23 pages, LaTe

    On the equivalence of the discrete nonlinear Schr\"odinger equation and the discrete isotropic Heisenberg magnet

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    The equivalence of the discrete isotropic Heisenberg magnet (IHM) model and the discrete nonlinear Schr\"odinger equation (NLSE) given by Ablowitz and Ladik is shown. This is used to derive the equivalence of their discretization with the one by Izergin and Korepin. Moreover a doubly discrete IHM is presented that is equivalent to Ablowitz' and Ladiks doubly discrete NLSE.Comment: 9 pages, LaTeX2

    A Bi-Hamiltonian Structure for the Integrable, Discrete Non-Linear Schrodinger System

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    This paper shows that the Ablowitz-Ladik hierarchy of equations (a well-known integrable discretization of the Non-linear Schrodinger system) can be explicitly viewed as a hierarchy of commuting flows which: (a) are Hamiltonian with respect to both a standard, local Poisson operator J and a new non-local, skew, almost Poisson operator K, on the appropriate space; (b) can be recursively generated from a recursion operator R (obtained by composing K and the inverse of J.) In addition, the proof of these facts relies upon two new pivotal resolvent identities which suggest a general method for uncovering bi-Hamiltonian structures for other families of discrete, integrable equations.Comment: 33 page

    Transformations of ordinary differential equations via Darboux transformation technique

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    A new approach for obtaining the transformations of solutions of nonlinear ordinary differential equations representable as the compatibility condition of the overdetermined linear systems is proposed. The corresponding transformations of the solutions of the overdetermined linear systems are derived in the frameworks of the Darboux transformation technique.Comment: 7 pages, LaTeX2

    Computation of conservation laws for nonlinear lattices

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    An algorithm to compute polynomial conserved densities of polynomial nonlinear lattices is presented. The algorithm is implemented in Mathematica and can be used as an automated integrability test. With the code diffdens.m, conserved densities are obtained for several well-known lattice equations. For systems with parameters, the code allows one to determine the conditions on these parameters so that a sequence of conservation laws exist.Comment: To appear in Physica D, 17 pages, Latex, uses the style files elsart.sty and elsart12.st

    Computation of conserved densities for systems of nonlinear differential-difference equations

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    A new method for the computation of conserved densities of nonlinear differential-difference equations is applied to Toda lattices and discretizations of the Korteweg-de Vries and nonlinear Schrodinger equations. The algorithm, which can be implemented in computer algebra languages such as Mathematica, can be used as an indicator of integrability.Comment: submitted to Phys. Lett A, 10 pages, late

    New symmetries for the Ablowitz-Ladik hierarchies

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    In the letter we give new symmetries for the isospectral and non-isospectral Ablowitz-Ladik hierarchies by means of the zero curvature representations of evolution equations related to the Ablowitz-Ladik spectral problem. Lie algebras constructed by symmetries are further obtained. We also discuss the relations between the recursion operator and isospectral and non-isospectral flows. Our method can be generalized to other systems to construct symmetries for non-isospectral equations.Comment: 11 page
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