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Exactly Solvable and Integrable Systems papers — page 23

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Lagrangian Description, Symplectic Structure, and Invariants of 3D Fluid Flow
Three dimensional unsteady flow of fluids in the Lagrangian description is considered as an autonomous dynamical system in four dimensions. The condition for the existence of a symplectic structure…
H. GumralMar 24, 1997
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Non-standard Construction of Hamiltonian Structures
Examples of the construction of Hamiltonian structures for dynamical systems in field theory (including one reputedly non-Hamiltonian problem) without using Lagrangians, are presented. The recently…
Andres Gomberoff, Sergio A. HojmanMar 20, 1997
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Some eigenstates for a model associated with solutions of tetrahedron equation. III. Tetrahedral Zamolodchikov algebras and perturbed strings
This paper continues the series begun with works solv-int/9701016 and solv-int/9702004. Here we show how to construct eigenstates for a model based on tetrahedron equation using the tetrahedral…
I. G. KorepanovMar 20, 1997
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Linearizability of the Perturbed Burgers Equation
We show in this letter that the perturbed Burgers equation ut = 2uux + uxx + ε( 3 α1 u2 ux + 3α2 uuxx + 3α3 ux2 + α4 uxxx ) is equivalent, through a near-identity transformation…
R. A. Kraenkel, J. G. Pereira, E. C. de Rey NetoMar 19, 1997
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Inelastic Collision and Switching of Coupled Bright Solitons in Optical Fibers
By constructing the general six-parameter bright two-soliton solution of the integrable coupled nonlinear Schrodinger equation (Manakov model) using the Hirota method, we find that the solitons…
R. Radhakrishnan, M. Lakshmanan, J. HietarintaMar 12, 1997
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Non-autonomous Hénon-Heiles Systems
Scaling similarity solutions of three integrable PDEs, namely the Sawada-Kotera, fifth order KdV and Kaup-Kupershmidt equations, are considered. It is shown that the resulting ODEs may be written as…
Andrew N. W. HoneMar 12, 1997
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Raman Solitons and Raman spikes
Stimulated Raman scattering of a laser pump pulse seeded by a Stokes pulse generically leaves a two-level medium initially at rest in an excited state constituted of static solitons and radiation.…
J. Leon, A. V. MikhailovMar 10, 1997
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Modified Korteweg-de Vries Hierachies in Multiple-Times Variables and the Solutions of Modified Boussinesq Equations
We study solitary-wave and kink-wave solutions of a modified Boussinesq equation through a multiple-time reductive perturbation method. We use appropriated modified Korteweg-de Vries hierarchies to…
M. A. Manna, V. MerleMar 10, 1997
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A collection of integrable systems of the Toda type in continuous and discrete time, with 2x2 Lax representations
A fairly complete list of Toda-like integrable lattice systems, both in the continuous and discrete time, is given. For each system the Newtonian, Lagrangian and Hamiltonian formulations are…
Yuri B. SurisMar 6, 1997
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On the point transformations for the second order differential equations. I
Point transformations for the ordinary differential equations of the form y''=P(x,y)+3 Q(x,y) y'+3 R(x,y) (y')2+S(x,y) (y')3 are considered. Some classical results are…
V. V. Dmitrieva, R. A. SharipovMar 6, 1997
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An analog of the variational derivative and constructive necessary integrability condition for hyperbolic equation
An algorithm is constructed which allows to express conserved flows of hyperbolic equations in terms of corresponding conserved densities and to eliminate these flows from conservation laws of…
S. Ya. StartsevMar 4, 1997
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Poisson brackets with divergence terms in field theories: two examples
In field theories one often works with the functionals which are integrals of some densities. These densities are defined up to divergence terms (boundary terms). A Poisson bracket of two functionals…
L. A. DickeyMar 1, 1997
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Symbolic Computation of Conserved Densities for Systems of Nonlinear Evolution Equations
A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented. The algorithm is implemented in Mathematica. The program…
Unal Goktas, Willy HeremanFeb 27, 1997
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An Integral Operator Solution to the Matrix Toda Equations
In previous work the author found solutions to the Toda equations that were expressed in terms of determinants of integral operators. Here it is observed that a simple variant yields solutions to the…
Harold WidomFeb 26, 1997
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Quasi-BiHamiltonian Systems and Separability
Two quasi--biHamiltonian systems with three and four degrees of freedom are presented. These systems are shown to be separable in terms of Nijenhuis coordinates. Moreover the most general Pfaffian…
C. Morosi, G. TondoFeb 24, 1997
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Asymptotics for Solution to the Cauchy Problem for Volterra Lattice with Step-Like Initial Values
The connection between modulated Riemann surface of genus one and solution to Volterra lattice that tends to constants at infinity is studied. The main term of asymptotics for large time of solution…
V. L. VereschaginFeb 20, 1997
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Some eigenstates for a model associated with solutions of tetrahedron equation. II. A bit of algebraization
This paper adds two observations to the work solv-int/9701016 where some eigenstates for a model based on tetrahedron equation have been constructed. The first observation is that there exists a more…
I. G. KorepanovFeb 19, 1997
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On an integrable discretization of the modified Korteweg-de Vries equation
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…
Yuri B. SurisFeb 17, 1997
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Fully Supersymmetric Hierarchies From A Energy Dependent Super Hill Operator
A super Hill operator with energy dependent potentials is proposed and the associated integrable hierarchy is constructed explicitly. It is shown that in the general case, the resulted hierarchy is…
Q. P. LiuFeb 13, 1997
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Rational Solutions for the Discrete Painlevé II Equation
The rational solutions for the discrete Painlevé II equation are constructed based on the bilinear formalism. It is shown that they are expressed by the determinant whose entries are given by the…
Kenji Kajiwara, Kazushi Yamamoto, Yasuhiro OhtaFeb 10, 1997
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Coupled Nonlinear Schrödinger equation and Toda equation (the Root of Integrability)
We consider the relation between the discrete coupled nonlinear Schrödinger equation and Toda equation. Introducing complex times we can show the intergability of the discrete coupled nonlinear…
Masato HisakadoJan 31, 1997
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Is the classical Bukhvostov-Lipatov model integrable? A Painlevé analysis
In this work we apply the Weiss, Tabor and Carnevale integrability criterion (Painlevé analysis) to the classical version of the two dimensional Bukhvostov-Lipatov model. We are led to the conclusion…
Marco Ameduri, Costas J. EfthimiouJan 29, 1997
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The Discrete Symmetries of the N=2 Supersymmetric GNLS Hierarchies
The discrete symmetry transformations of the N=2 supersymmetric (n,m)-GNLS hierarchy are constructed. Their bosonic limit is analyzed and new discrete symmetries of the modified GNLS hierarchy are…
A. SorinJan 29, 1997
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The Solution of the N=2 Supersymmetric f-Toda Chain with Fixed Ends
The integrability of the recently introduced N=2 supersymmetric f-Toda chain, under appropriate boundary conditions, is proven. The recurrent formulae for its general solutions are derived. As an…
A. N. Leznov, A. SorinJan 29, 1997
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Symplectic Structures and Volume Elements in the Function Space for the Cubic Schrodinger Equation
We consider various trace formulas for the cubic Schrodinger equation in the space of infinitely smooth functions subject to periodic boundary conditions. The formulas relate conventional integrals…
K. L. VaninskyJan 28, 1997
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