Journal of Non-linear Mathematical Physics

ISSN: 1402-9251
Volume 15, Issue supplement 3, October 2008

Nonlinear Evolution Equations and Dynamical Systems 2007

Papers resulting from the NEEDS-07 workshop held in L'Ametlla Mar, Spain

Foreword
V Aldaya, M Calixto, J Guerrero, F F Lopez-Ruiz
Pages: 1 - 12
We study the dynamics of a particle moving on the SU(2) group manifold. An exact quantization of this system is accomplished by finding the unitary and irreducible representations of a finite-dimensional Lie subalgebra of the whole Poisson algebra in phase space. In fact, the basic position and momentum...
Angel Ballesteros, Alberto Enciso, Francisco José Herranz, Orlando Ragnisco
Pages: 43 - 52
The maximal superintegrability of the intrinsic harmonic oscillator potential on N-dimensional spaces with constant curvature is revisited from the point of view of sl(2)-Poisson coalgebra symmetry. It is shown how this algebraic approach leads to a straightforward definition of a new large family...
Carl M. Bender, E. Ben-Naim
Pages: 73 - 80
The nonlinear integral equation P(x) = dyw(y)P(y)P(x + y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomial solutions Pn(x). For polynomial solutions, this nonlinear integral equation reduces to a finite set of coupled linear algebraic...
Jesus Cuevas, Guillaume James, Panayotis G. Kevrekidis, Boris A. Malomed, Bernardo Sanchez-Rey
Pages: 124 - 136
We study four different approximations for finding the profile of discrete solitons in the one- dimensional Discrete Nonlinear Schrödinger (DNLS) Equation. Three of them are discrete approximations (namely, a variational approach, an approximation to homoclinic orbits and a Green-function approach),...
T Dobrowolski, P. Tatrocki
Pages: 144 - 154
The purpose of this report is to show the influence of imperfections on creation and evolution of a kink network. Our main finding is a mechanism for reduction of the kinetic energy of kinks which works in both the overdamped and underdamped regimes. This mechanism reduces mobility of kinks and therefore...
A. Enisco, F. Finkel, A. Gonzalez-Lopez, M.A. Rodriguez
Pages: 155 - 165
In this paper we prove an extension of the usual freezing trick argument which can be applied to a number of quasi-exactly solvable spin models of Calogero­Sutherland type. In order to illustrate the application of this method we analyze a partially solvable spin chain presenting near-neighbors interactions...
Anestis Fotiadis
Pages: 176 - 184
We describe the problem of finding a harmonic map between noncompact manifold. Given some sufficient conditions on the domain, the target and the initial map, we prove the existence of a harmonic map that deforms the given map.
Georgi G. Grahovski, Marissa Condon
Pages: 197 - 208
The generalized Zakharov­Shabat systems with complex-valued Cartan elements and the systems studied A.V. Mikhailov, and later on by Caudrey, Beals and Coifman (CBC systems), and their gauge equivalent are studied. This includes: the properties of fundamental analytical solutions (FAS) for the gauge-equivalent...
Dan Grecu, Alexandru Tudor Grecu, Anca Visinescu, Renato Fedele, Sergio De Nicola
Pages: 209 - 219
Recently using a Madelung fluid description a connection between envelope-like solutions of NLS-type equations and soliton-like solutions of KdV-type equations was found and investigated by R. Fedele et al. (2002). A similar discussion is given for the class of derivative NLS-type equations. For a...
Jorge Sotomayor, Luis Fernando Mello, Denis de Carvalho Braga
Pages: 288 - 299
This paper pursues the study carried out in [10], focusing on the codimension one Hopf bifurcations in the hexagonal Watt governor system. Here are studied Hopf bifurcations of codimensions two, three and four and the pertinent Lyapunov stability coefficients and bifurcation diagrams. This allows to...
C. Muriel, J. L. Romero
Pages: 300 - 309
We investigate the relationship between integrating factors and -symmetries for ordinary differential equations of arbitrary order. Some results on the existence of -symmetries are used to prove an independent existence theorem for integrating factors. A new method to calculate integrating factors...
Gregorio Falqui, Giovanni Ortenzi
Pages: 310 - 322
We discuss how the Camassa-Holm hierarchy can be framed within the geometry of the Sato Grassmannian. We discuss the geometry of an extension of the negative flows of the CH hierarchy, recover the well-known CH equations, and frame the problem within the theory of pseudo-differential operators.
Rafael Hernandez Heredero, Decio Levi, Matteo Petrera, Christian Scimiterna
Pages: 323 - 333
We apply the discrete multiscale expansion to the Lax pair and to the first few symmetries of the lattice potential Korteweg-de Vries equation. From these calculations we show that, like the lowest order secularity conditions give a nonlinear Schr¨odinger equation, the Lax pair gives at the same...
Beatrice Pelloni, Dimitrios A. Pinotsis
Pages: 334 - 344
We solve an initial-boundary problem for the Klein-Gordon equation on the half line using the Riemann-Hilbert approach to solving linear boundary value problems advocated by Fokas. The approach we present can be also used to solve more complicated boundary value problems for this equation, such as...
M. Maldonado, J. Prada, M.J. Senosiain
Pages: 345 - 352
Two differential operators T1 and T2 on a space are said to be equivalent if there is an isomorphism S from onto such that ST1 = T2 S. The notion was first introduced by Delsarte in 1938 [2] where T1 and T2 are differential operators of second order and a space of functions of one variable defined...
Luigi Martina, Alexander Protogenov, Valery Verbus
Pages: 353 - 361
We consider universal statistical properties of systems that are characterized by phase states with macroscopic degeneracy of the ground state. A possible topological order in such systems is described by non-linear discrete equations. We focus on the discrete equations which take place in the case...
Ryu Sasaki
Pages: 373 - 384
Exact solvability of two typical examples of the discrete quantum mechanics, i.e. the dynamics of the Meixner-Pollaczek and the continuous Hahn polynomials with full parameters, is newly demonstrated both at the Schr¨odinger and Heisenberg picture levels. A new quasiexactly solvable difference equation...
James Robert Stirling, Maria Zakynthinaki
Pages: 396 - 406
We present a geometric analysis of the model of Stirling et al. [14]. In particular we analyze the curvature of a heart rate time series in response to a step like increment in the exercise intensity. We present solutions for the point of maximum curvature which can be used as a marker of physiological...
James Robert Stirling, Maria Zakynthinaki, Ignacio Refoyo, Javier Sampedro
Pages: 426 - 436
We present a mathematical model, in the form of two coupled ordinary differential equations, for the heart rate kinetics in response to exercise. Our heart rate model is an adaptation of the model of oxygen uptake kinetics of Stirling et al. [21]; a physiological justification for this adaptation,...