Nonlinear Evolution Equations Invariant Under Schroedinger Group in three-dimensional Space-timeA classification of all possible realizations of the Galilei, Galilei-similitude and Schroedinger Lie algebras in three-dimensional space-time in terms of vector fields under the action of the group…Faruk Gungor·Nov 21, 1998SaveLearn
Finite gap integration of a discrete Euler topIn [1] new discretizations of the Euler top have been found. They can be discribed with a Lax pair with a spectral parameter on an elliptic curve. This is used in this paper to perform a finite gap…Boris Lorbeer·Nov 21, 1998SaveLearn
Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approachThe second Painlevé hierarchy is defined as the hierarchy of ordinary differential equations obtained by similarity reduction from the modified Korteweg-de Vries hierarchy. Its first member is the…Peter A. Clarkson, Nalini Joshi, Andrew Pickering·Nov 20, 1998SaveLearn
Integrable KdV Systems: Recursion Operators of Degree FourThe recursion operator and bi-Hamiltonian formulation of the Drinfeld- Sokolov system are givenMetin Gurses, Atalay Karasu·Nov 19, 1998SaveLearn
Two Integrable Systems Related to Hyperbolic MonopolesMonopoles on hyperbolic 3-space were introduced by Atiyah in 1984. This article describes two integrable systems which are closely related to hyperbolic monopoles: a one-dimensional lattice equation…R S Ward·Nov 17, 1998SaveLearn
Darboux Transformations and solutions for an equation in 2+1 dimensionsPainleve analysis and the singular manifold method are the tools used in this paper to perform a complete study of an equation in 2+1 dimensions. This procedure has allowed us to obtain the Lax pair,…Pilar Garcia Estevez·Nov 16, 1998SaveLearn
Q-deformed KP hierarchy: Its additional symmetries and infinitesimal Bäcklund transformationsWe study the additional symmetries associated with the q-deformed Kadomtsev-Petviashvili (q-KP) hierarchy. After identifying the resolvent operator as the generator of the additional symmetries,…Ming-Hsien Tu·Nov 15, 1998SaveLearn
Spectral Difference Equations Satisfied by KP Soliton WavefunctionsThe Baker-Akhiezer (wave) functions corresponding to soliton solutions of the KP hierarchy are shown to satisfy eigenvalue equations for a commutative ring of translational operators in the spectral…Alex Kasman·Nov 11, 1998SaveLearn
Bi-Hamiltonian manifolds, quasi-bi-Hamiltonian systems and separation variablesWe discuss from a bi-Hamiltonian point of view the Hamilton-Jacobi separability of a few dynamical systems. They are shown to admit, in their natural phase space, a quasi-bi-Hamiltonian formulation…G. Tondo, C. Morosi·Nov 10, 1998SaveLearn
On a class of dynamical systems both quasi-bi-Hamiltonian and bi-HamiltonianIt is shown that a class of dynamical systems (encompassing the one recently considered by F. Calogero [J. Math. Phys. 37 (1996) 1735]) is both quasi-bi-Hamiltonian and bi-Hamiltonian. The first…C. Morosi, G. Tondo·Nov 10, 1998SaveLearn
A unified treatment of cubic invariants at fixed and arbitrary energyCubic invariants for two-dimensional Hamiltonian systems are investigated using the Jacobi geometrization procedure. This approach allows for a unified treatment of invariants at both fixed and…Max Karlovini, Kjell Rosquist·Nov 9, 1998SaveLearn
Canonical variables for multiphase solutions of the KP equationThe KP equation has a large family of quasiperiodic multiphase solutions. These solutions can be expressed in terms of Riemann-theta functions. In this paper, a finite-dimensional canonical…Bernard Deconinck·Nov 9, 1998SaveLearn
On Darboux-Bäcklund Transformations for the Q-Deformed Korteweg-de Vries HierarchyWe study Darboux-Bäcklund transformations (DBTs) for the q-deformed Korteweg-de Vries hierarchy by using the q-deformed pseudodifferential operators. We identify the elementary DBTs which are…Ming-Hsien Tu, Jiin-Chang Shaw, Chin-Rong Lee·Nov 6, 1998SaveLearn
Quantum 2+1 evolution modelA quantum evolution model in 2+1 discrete space - time, connected with 3D fundamental map R, is investigated. Map R is derived as a map providing a zero curvature of a two dimensional lattice system…S. M. Sergeev·Oct 31, 1998SaveLearn
Bethe ansatz solution of the anisotropic correlated electron model associated with the Temperley-Lieb algebraA recently proposed strongly correlated electron system associated with the Temperley-Lieb algebra is solved by means of the coordinate Bethe ansatz for periodic and closed boundary conditions.A. Lima-Santos, I. Roditi, A. Foerster·Oct 30, 1998SaveLearn
Hirota bilinear forms with 2-toroidal symmetryIn this note, we compute Hirota bilinear forms arising from both homogeneous and principal realization of vertex representations of 2-toroidal Lie algebras of type Al, Dl, El.K. Iohara, Y. Saito, M. Wakimoto·Oct 30, 1998SaveLearn
Exact Solutions of a (2+1)-Dimensional Nonlinear Klein-Gordon EquationThe purpose of this paper is to present a class of particular solutions of a C(2,1) conformally invariant nonlinear Klein-Gordon equation by symmetry reduction. Using the subgroups of similitude…F. Gungor·Oct 29, 1998SaveLearn
On Integrability and Chaos in Discrete SystemsThe scalar nonlinear Schrodinger (NLS) equation and a suitable discretization are well known integrable systems which exhibit the phenomena of ``effective'' chaos. Vector generalizations of…M. J. Ablowitz, Y. Ohta, A. D. Trubatch·Oct 29, 1998SaveLearn
Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange topWe develop the theory of discrete time Lagrangian mechanics on Lie groups, originated in the work of Veselov and Moser, and the theory of Lagrangian reduction in the discrete time setting. The…A. I. Bobenko, Yu. B. Suris·Oct 28, 1998SaveLearn
Algebraic Exact Solvability of trigonometric-type Hamiltonians associated to root systemsIn this article, we study and settle several structural questions concerning the exact solvability of the Olshanetsky-Perelomov quantum Hamiltonians corresponding to an arbitrary root system. We show…N. Kamran, R. Milson·Oct 27, 1998SaveLearn
Asymptotics of the Fredholm determinant associated with the correlation functions of the quantum Nonlinear Schrodinger equationThe correlation functions of the quantum nonlinear Schrodinger equation can be presented in terms of a Fredholm determinant. The explicit expression for this determinant is found for the large time…N. A. Slavnov·Oct 23, 1998SaveLearn
The Lax operators L of the Benney type equations bound with the circleThe Lax operators of the Benney type equations are studied on the circle. The vectors fields of the Lax operators are showed to commute with each otherAntoine Balan·Oct 22, 1998SaveLearn
On Discretizations of the Vector Nonlinear Schrodinger EquationTwo discretizations of the vector nonlinear Schrodinger (NLS) equation are studied. One of these discretizations, referred to as the symmetric system, is a natural vector extension of the scalar…M. J. Ablowitz, Y. Ohta, A. D. Trubatch·Oct 19, 1998SaveLearn
Stochastic Soliton LatticesWe introduce a new concept, Stochastic Soliton Lattice, as a random process generated by a finite-gap potential of the Shroedinger operator. We study the basic properties of this stochastic process…Gennady A. El, Alexander L. Krylov·Oct 16, 1998SaveLearn
Lax pair tensors in arbitrary dimensionsA recipe is presented for obtaining Lax tensors for any n-dimensional Hamiltonian system admitting a Lax representation of dimension n. Our approach is to use the Jacobi geometry and…Martin Goliath, Max Karlovini, Kjell Rosquist·Oct 15, 1998SaveLearn