Local Geometric Invariants of Integrable Evolution EquationsThe integrable hierarchy of commuting vector fields for the localized induction equation of 3D hydrodynamics, and its associated recursion operator, are used to generate families of integrable…Joel Langer, Ron Perline·Jan 6, 1994SaveLearn
Continuous vacua in bilinear soliton equationsWe discuss the freedom in the background field (vacuum) on top of which the solitons are built. If the Hirota bilinear form of a soliton equation is given by $A(D x) GF=0,\, B(D…J. Hietarinta, A. Ramani, B. Grammaticos·Nov 24, 1993SaveLearn
Linearization And Solutions Of The Discrete Painlevé-III EquationWe present particular solutions of the discrete Painlevé III (d-PIII) equation of rational and special function (Bessel) type. These solutions allow us to establish a close parallel between…B. Grammaticos, F. W. Nijhoff, V. Papageorgiou et al.·Nov 3, 1993SaveLearn
Casorati Determinant Solutions for the Discrete Painlevé-II EquationWe present a class of solutions to the discrete Painlevé-II equation for particular values of its parameters. It is shown that these solutions can be expressed in terms of Casorati determinants whose…Kenji Kajiwara, Yasuhiro Ohta, Junkichi Satsuma et al.·Oct 20, 1993SaveLearn
Deformations of Calogero-Moser SystemsRecent results are surveyed pertaining to the complete integrability of some novel n-particle models in dimension one. These models generalize the Calogero-Moser systems related to classical root…J. F. van Diejen·Oct 18, 1993SaveLearn
Invariant Integrability Criterion for the Equations of Hydrodynamical TypeInvariant integrability criterion for the equations of hydrodynamical type is found. This criterion is written in the form of vanishing for some tensor which is derived from the velocities matrix of…M. V. Pavlov, R. A. Sharipov, S. I. Svinolupov·Jul 18, 1993SaveLearn
Solutions of the Kpi Equation with Smooth Initial DataThe solution u(t,x,y) of the Kadomtsev--Petviashvili I (KPI) equation with given initial data u(0,x,y) belonging to the Schwartz space is considered. No additional special constraints, usually…M. Boiti, F. Pempinelli, A. Pogrebkov·Jun 30, 1993SaveLearn
A note on the motion of surfacesWe study the motion of surfaces in an intrinsic formulation in which the surface is described by its metric and curvature tensors. The evolution equations for the six quantities contained in these…Robert I. McLachlan, Harvey Segur·Jun 23, 1993SaveLearn
Symmetry Reductions and Exact Solutions of a class of Nonlinear Heat EquationsClassical and nonclassical symmetries of the nonlinear heat equation ut=uxx+f(u),(1) are considered. The method of differential Gröbner bases is used both to find the conditions on…Peter A. Clarkson, Elizabeth L. Mansfield·Jun 16, 1993SaveLearn
The upper triangular solutions to the three-state constant quantum Yang-Baxter equationIn this article we present all nonsingular upper triangular solutions to the constant quantum Yang-Baxter equation $Rj1j2k1k2Rk1j3l1k3Rk2k3l2l3=…Jarmo Hietarinta·Jun 14, 1993SaveLearn
Lattice Virasoro from Lattice Kac-MoodyA new version of quantum Miura transformation on the lattice is proposed, based on the lattice Kac-Moody algebra. A possibility of existence of the Sugawara construction on the lattice is discussed.Aleksander A. Belov, Karen D. Chaltikian·May 31, 1993SaveLearn
On exact solution for some integrable nonlinear equations of the Schrödinger typeThe outlook of a simple method to generate localized (soliton-like) potentials of time-dependent Schrodinger type equations is given. The conditions are discussed for the potentials to be real and…V. G. Makhankov·May 28, 1993SaveLearn
Bäcklund Transformations of MKdV and Painlevé EquationsFor N 3 there are SN and DN actions on the space of solutions of the first nontrivial equation in the SL(N) MKdV hierarchy, generalizing the two Z2$ actions on the space of solutions of…Jeremy Schiff·May 19, 1993SaveLearn
The Super W3 Conformal Algebra and the Boussinesq HierarchyThe bihamiltonian structure of the N=2 Supersymmetric Boussinesq equation is found. It is not reduced to the corresponding classical structure and hence it describes the pure supersymmetric effect.…Ziemowit Popowicz·May 13, 1993SaveLearn
Integrable four-dimensional symplectic maps of standard typeWe search for rational, four-dimensional maps of standard type (xn+1 - 2xn + xn-1 = eps f(x,eps)) possessing one or two polynomial integrals. There are no non-trivial maps corresponding to…Robert I. McLachlan·Apr 28, 1993SaveLearn
Casorati Determinant Solution for the Relativistic Toda Lattice EquationThe relativistic Toda lattice equation is decomposed into three Toda systems, the Toda lattice itself, Bäcklund transformation of Toda lattice and discrete time Toda lattice. It is shown that the…Yasuhiro Ohta, Kenji Kajiwara, Junkichi Satsuma·Apr 22, 1993SaveLearn
Problem of Metrizability for the Dynamical Systems Accepting the Normal ShiftThe problem of metrizability for the dynamical systems accepting the normal shift is formulated and solved. The explicit formula for the force field of metrizable Newtonian dynamical system…R. A. Sharipov·Apr 18, 1993SaveLearn
q-Discrete Toda Molecule EquationA q-discrete version of the two-dimensional Toda molecule equation is proposed through the direct method. Its solution, Bäcklund transformation and Lax pair are discussed. The reduction to the…Kenji Kajiwara, Yasuhiro Ohta, Junkichi Satsuma·Apr 16, 1993SaveLearn
Dynamical Systems Accepting the Normal ShiftNewtonian dynamical systems accepting the normal shift on an arbitrary Riemannian manifold are considered. Partial differential equations forming the weak and additional normality conditions for them…R. A. Sharipov·Apr 7, 1993SaveLearn