Geometric phase effects for wavepacket revivalsThe study of wavepacket revivals is extended to the case of Hamiltonians which are made time-dependent through the adiabatic cycling of some parameters. It is shown that the quantal geometric phase…Christopher Jarzynski·Feb 2, 1995SaveLearn
Integrable nonlinear field equations and loop algebra structuresWe apply the (direct and inverse) prolongation method to a couple of nonlinear Schrödinger equations. These are taken as a laboratory field model for analyzing the existence of a connection between…E. Alfinito, M. Leo, R. A. Leo et al.·Jan 30, 1995SaveLearn
Lattice and q-difference Darboux-Zakharov-Manakov systems via ∂-dressing methodA general scheme is proposed for introduction of lattice and q-difference variables to integrable hierarchies in frame of ∂-dressing method . Using this scheme, lattice and…L. V. Bogdanov, B. G. Konopelchenko·Jan 28, 1995SaveLearn
Nonselfintersecting magnetic orbits on the plane. Proof of Principle of the Overthrowing of the Cycles.Beginning from 1981 one of the present authors (S.Novikov) published a series of papers, (some of them in collaboration with I.Schmelzer and I.Taimanov) dedicated to the development of the analog of…P. G. Grinevich, S. P. Novikov·Jan 18, 1995SaveLearn
Bilinearization of a Generalized Derivative Nonlinear Schrödinger equationA generalized derivative nonlinear Schrödinger equation, qt + qxx + 2 γ|q|2 qx + 2 (γ-1)q2 q*x + (γ-1)(γ-2)|q|4 q = 0 , is studied by means of Hirota's bilinear formalism.…Saburo Kakei, Narimasa Sasa, Junkichi Satsuma·Jan 17, 1995SaveLearn
String equation--2. Physical solutionThis paper is a continuation of the paper by S.P.Novikov in Funct.Anal.Appl., v.24(1990), No 4, pp 196-206. String equation is by definition the equation [L,A]=1 for the coefficients of two linear…P. G. Grinevich, S. P. Novikov·Jan 11, 1995SaveLearn
Conservation Laws in Field Dynamics or Why Boundary Motion is Exactly Integrable?An infinite number of conserved quantities in the field dynamics ϕt = L U(ϕ) + ρ for a linear Hermitian (or anti-Hermitian) operator L, an arbitrary function U and a given source ρ are…Mark B. Mineev-Weinstein·Jan 11, 1995SaveLearn
Dual Field Approach to Correlation Functions in the Heisenberg Xxz Spin ChainWe study zero temperature correlation functions of the spin-1 2 Heisenberg XXZ model in the critical regime -1< Δ≤ 1 in a magnetic field by means of the Dual Field Approach. We…Fabian H. L. Essler, Vladimir E. Korepin·Jan 11, 1995SaveLearn
The Integrable Dynamics of Discrete and Continuous CurvesWe show that the following geometric properties of the motion of discrete and continuous curves select integrable dynamics: i) the motion of the curve takes place in the N dimensional sphere of…Adam Doliwa, Paolo Maria Santini·Dec 30, 1994SaveLearn
Bilinear Discrete Painleve-II and its Particular SolutionsBy analogy to the continuous Painlevé II equation, we present particular solutions of the discrete Painlevé II (d-PII) equation. These solutions are of rational and special function (Airy)…J. Satsuma, K. Kajiwara, B. Grammaticos et al.·Dec 23, 1994SaveLearn
Integrable systems and Riemann surfaces of infinite genusTo the spectral curves of smooth periodic solutions of the n-wave equation the points with infinite energy are added. The resulting spaces are considered as generalized Riemann surfcae. In general…Martin U. Schmidt·Dec 21, 1994SaveLearn
Period preserving nonisospectral flows and the moduli space of periodic solutions of soliton equationsFlows on the moduli space of the algebraic Riemann surfaces, preserving the periods of the corresponding solutions of the soliton equations are studied. We show that these flows are gradient with…P. G. Grinevich, M. U. Schmidt·Dec 15, 1994SaveLearn
Casorati Determinant Solutions for the Discrete Painlevé III EquationThe discrete Painlevé III equation is investigated based on the bilinear formalism. It is shown that it admits the solutions expressed by the Casorati determinant whose entries are given by the…Kenji Kajiwara, Yasuhiro Ohta, Junkichi Satsuma·Dec 15, 1994SaveLearn
Symmetries and Exact Solutions of a 2+1-dimensional Sine-Gordon SystemWe investigate the classical and nonclassical reductions of the 2+1-dimensional sine-Gordon system of Konopelchenko and Rogers, which is a strong generalisation of the sine-Gordon equation. A…P. A. Clarkson, E. L. Mansfield, A. E. Milne·Dec 9, 1994SaveLearn
Backlund Transformations and Hierarchies of Exact Solutions for the Fourth Painleve Equation and their Application to Discrete EquationsIn this paper we describe Bäcklund transformations and hierarchies of exact solutions for the fourth Painlevé equation (PIV) 2 w z2=12w( w z)2 +…Peter A. Clarkson, Andrew P. Bassom·Dec 9, 1994SaveLearn
Bäcklund transformation and the construction of the integrable boundary-value problem for the equation uxx-utt=eu-e-2uBäcklund transformation for the Bullough-Dodd-Jiber-Shabat equation uxx-utt=eu-e-2u is found. The construction of integrable boundary condition for this equation together with the…R. A. Sharipov, R. I. Yamilov·Dec 5, 1994SaveLearn
Bilinear Structure and Exact Solutions of the Discrete Painlevé I EquationBilinear structure for the discrete Painlevé I equation is investigated. The solution on semi-infinite lattice is given in terms of the Casorati determinant of discrete Airy function. Based on this…Y. Ohta, K. Kajiwara, J. Satsuma·Nov 30, 1994SaveLearn
Limits to Extensions of Burgers EquationThe vector Burgers equation is extended to include pressure gradients and gravity. It is shown that within the framework of the Cole-Hopf transformation there are no physical solutions to this…Steven Nerney, Edward J. Schmahl, Z. E. Musielak·Nov 17, 1994SaveLearn
Variable Coefficient Third Order KdV Type of EquationsWe show that the integrable subclassess of a class of third order non-autonomous equations are identical with the integrable subclassess of the autonomous ones.Metin Gurses, Atalay Karasu·Nov 16, 1994SaveLearn
Integrable Trilinear PDE'sIn a recent publication we proposed an extension of Hirota's bilinear formalism to arbitrary multilinearities. The trilinear (and higher) operators were constructed from the requirement of gauge…J. Hietarinta, B. Grammaticos, A. Ramani·Nov 16, 1994SaveLearn
On the Existence of Localized Excitations in Nonlinear Hamiltonian LatticesWe consider time-periodic nonlinear localized excitations (NLEs) on one-dimensional translationally invariant Hamiltonian lattices with arbitrary finite interaction range and arbitrary finite number…S. Flach·Nov 14, 1994SaveLearn
Boundary Value Problems For Integrable Equations Compatible With The Symmetry AlgebraBoundary value problems for integrable nonlinear partial differential equations are considered from the symmetry point of view. Families of boundary conditions compatible with the Harry-Dym, KdV and…Burak Gurel, Metin Gurses, Ismagil Habibullin·Nov 9, 1994SaveLearn
Analytic Solutions of the Vector Burgers' EquationThe well-known analytical solution of Burgers' equation is extended to curvilinear coordinate systems in three-dimensions by a method which is much simpler and more suitable to practical…Steven Nerney, Edward J. Schmahl, Z. E. Musielak·Nov 1, 1994SaveLearn
Transparent Potentials at Fixed Energy in Dimension Two. Fixed-Energy Dispersion Relations for the Fast Decaying PotentialsFor the two-dimensional Schrödinger equation [- Δ+v(x)]ψ=Eψ,\ x∈ 2,\ E=Efixed>0 \ \ \ \ \ (*) at a fixed positive energy with a fast decaying at infinity potential v(x) dispersion…Piotr G. Grinevich, Roman G. Novikov·Oct 26, 1994SaveLearn
Maps, PDE's and Solitary WavesWe describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of…Troy Shinbrot, J. M. Ottino·Oct 13, 1994SaveLearn