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Exactly Solvable and Integrable Systems papers — page 33

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Darboux Transformations from Reductions of the KP Hierarchy
The use of effective Darboux transformations for general classes Lax pairs is discussed. The general construction of ``binary'' Darboux transformations preserving certain properties of the…
J J C NIMMOOct 11, 1994
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On the Monge-Ampere equivalent of the sine-Gordon equation
Surfaces of constant negative curvature in Euclidean space can be described by either the sine-Gordon equation for the angle between asymptotic directions, or a Monge-Ampere equation for the graph of…
E. V. Ferapontov, Y. NutkuOct 3, 1994
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Symmetry Reductions and Exact Solutions of Shallow Water Wave Equations
In this paper we study symmetry reductions and exact solutions of the shallow water wave (SWW) equation uxxxt + αux uxt + βut uxx - uxt - uxx = 0,(1) where α and β are…
Peter A. Clarkson, Elizabeth L. MansfieldSep 23, 1994
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New exact solutions for the discrete fourth Painlevé equation
In this paper we derive a number of exact solutions of the discrete equation xn+1xn-1+xn(xn+1+xn-1)= -2znxn3+(η-3δ-2-zn2)xn2+μ2 (xn+zn+γ)(xn+zn-γ),(1)…
Andrew P. Bassom, Peter A. ClarksonSep 16, 1994
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Integrable Quantum Mappings
We discuss the canonical structure of a class of integrable quantum mappings, i.e. iterative canonical transformations that can be interpreted as a discrete dynamical system. As particular examples…
H. W. Capel, F. W. NijhoffSep 2, 1994
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Numerical investigation of iso-spectral cavities built from triangles
We present computational approaches as alternatives to the recent microwave cavity experiment by S. Sridhar and A. Kudrolli (Phys. Rev. Lett. 72, 2175 (1994)) on iso-spectral cavities built…
Hua Wu, D. W. L. Sprung, J. MartorellAug 17, 1994
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Integrable dynamics of a discrete curve and the Ablowitz-Ladik hierarchy
We show that the following elementary geometric properties of the motion of a discrete (i.e. piecewise linear) curve select the integrable dynamics of the Ablowitz-Ladik hierarchy of evolution…
Adam Doliwa, Paolo Maria SantiniJul 27, 1994
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Integrable deformations of a polygon
The new integrable mapping with a simple geometric interpretation is presented. This mapping arise from the nonlinear superposition principle for the Bäcklund transformations of some vector evolution…
V. E. AdlerJul 19, 1994
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Complete integrability of a modified vector derivative nonlinear Schroedinger equation
Oblique propagation of magnetohydrodynamic waves in warm plasmas is described by a modified vector derivative nonlinear Schroedinger equation, if charge separation in Poisson's equation and the…
Ralph Willox, Willy Hereman, Frank VerheestJul 14, 1994
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Helicity Conservation via the Noether Theorem
The conservation of helicity in ideal barotropic fluids is discussed from a group theoretical point of view. A new symmetry group is introduced i.e. the alpha group of translations. It is proven via…
Asher YahalomJul 1, 1994
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Non-integrability of the mixmaster universe
We comment on an analysis by Contopoulos et al. which demonstrates that the governing six-dimensional Einstein equations for the mixmaster space-time metric pass the ARS or reduced Painlevé test. We…
Freddy Christiansen, Hans Henrik Rugh, Svend Erik RughJun 13, 1994
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Localized induction equation and pseudospherical surfaces
We describe a close connection between the localized induction equation hierarchy of integrable evolution equations on space curves, and surfaces of constant negative Gauss curvature.
Ron PerlineJun 11, 1994
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Multilinear Operators: The Natural Extension Of Hirota's Bilinear Formalism
We introduce multilinear operators, that generalize Hirota's bilinear D operator, based on the principle of gauge invariance of the τ functions. We show that these operators can be…
B. Grammaticos, A. Ramani, J. HietarintaApr 26, 1994
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Non-Linear Evolution Equations with Non-Analytic Dispersion Relations in 2+1 Dimensions. Bilocal Approach
A method is proposed of obtaining (2+1)-dimensional non- linear equations with non-analytic dispersion relations. Bilocal formalism is shown to make it possible to represent these equations in a form…
Evgeny V. DoktorovApr 20, 1994
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Spatial Solitons in Media with Delayed-Response Optical Nonlinearities
Near-soliton scanning light-beam propagation in media with both delayed-response Kerr-type and thermal nonlinearities is analyzed. The delayed-response part of the Kerr nonlinearity is shown to be…
Evgeny V. Doktorov, Rafael A. VlasovApr 20, 1994
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Localized induction equation, Heisenberg chain, and nonlinear Schrodinger equation
The three equations named in the title are examples of infinite-dimensional completely integrable Hamiltonian systems, and are related to each other via simple geometric constructions. In this paper,…
Joel Langer, Ron PerlineApr 4, 1994
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The planar filament equation
The planar filament equation and its relation to the modified Korteweg-deVries equation are studied in the context of Poisson geometry. The structure of the planar filament equation is shown to be…
Joel Langer, Ron PerlineMar 25, 1994
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On UrKdV and UrKP
We present two extensions of Wilson's explanation of the Miura map from MKdV to KdV. In the first we explain the map of Svinolupov et al from a certain UrKdV-like equation to KdV, and in the…
Didier A Depireux, Jeremy Schiff, U de Montreal et al.Mar 1, 1994
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Integrable systems and symmetric products of curves
We show how there is associated to each non-constant polynomial F(x,y) a completely integrable system with polynomial invariants on and on 2d for each d≥1; in fact the invariants…
Pol VanhaeckeFeb 18, 1994
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Multi-Hamiltonian formulation for a class of degenerate completely integrable systems
Generalizing a construction of P. Vanhaecke, we introduce a large class of degenerate (i.e., associated to a degenerate Poisson bracket) completely integrable systems on (a dense subset of) the space…
Peter BuekenFeb 18, 1994
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Non Proliferation of Preimages in Integrable Mappings
We present an integrability criterion for rational mappings based on two requirements. First, that a given point should have a unique preimage under the mapping and, second, that the spontaneously…
B. Grammaticos, A. Ramani, K. M. TamizhmaniFeb 10, 1994
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A Novel Hierarchy of Integrable Lattices
In the framework of the reduction technique for Poisson-Nijenhuis structures, we derive a new hierarchy of integrable lattice, whose continuum limit is the AKNS hierarchy. In contrast with other…
I. Merola, O. Ragnisco, Tu Gui ZhangJan 25, 1994
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Nonlinear integrable systems related to arbitrary space-time dependence of the spectral transform
We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an…
Jerome LeonJan 14, 1994
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On a Shallow Water Wave Equation
In this paper we study a shallow water equation derivable using the Boussinesq approximation, which includes as two special cases, one equation discussed by Ablowitz et. al. [Stud. Appl. Math., 53…
Peter A. Clarkson, Elizabeth L. MansfieldJan 13, 1994
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Algorithms for the Nonclassical Method of Symmetry Reductions
In this article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Cole) for…
Peter A. Clarkson, Elizabeth L. MansfieldJan 12, 1994
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