Journal of Non-linear Mathematical Physics

ISSN: 1402-9251
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905 articles
Joseph BERNSTEIN, Ossip SCHWARZMAN
Pages: 323 - 351
We prove that, for the irreducible complex crystallographic Coxeter group W, the following conditions are equivalent: a) W is generated by reflections; b) the analytic variety X/W is isomorphic to a weighted projective space. The result is of interest, for example, in application to topological conformal...
Hailiang LIU
Pages: 441 - 466
The Korteweg de Vries (KdV) equation is well known as an approximation model for small amplitude and long waves in different physical contexts, but wave breaking phenomena related to short wavelengths are not captured in. In this work we consider a class of nonlocal dispersive wave equations which...
C. BURDIK, S. POSTA, O NAVRATIL
Pages: 27 - 36
We study the exact solvable 3 × 3 matrix model of the type G2. We apply the construction similar to that one, which give the 2 × 2 matrix model. But in the studied case the construction does not give symmetric matrix potential. We conceive that the exact solvable 3 × 3 matrix potential model of...
Tatjana GRAMUSHNJAK, Peeter PUUSEMP
Pages: 55 - 65
Let n be an integer such that n 3 and Cm denote a cyclic group of order m . It is proved that there exist exactly 17 non-isomorphic groups of order 22n+1 which can be represented as a semidirect product (C2n × C2n ) C2. These groups are given by generators and defining relations.
Maido RAHULA, Vitali RETSNOI
Pages: 102 - 109
Total differentiation operators as linear vector fields, their flows, invariants and symmetries form the geometry of jet space. In the jet space the dragging of tensor fields obeys the exponential law. The composition of smooth maps induces a composition of jets in corresponding jet spaces....
F CALOGERO, J-P FRANCOISE
Pages: 231 - 254
We revisit an integrable (indeed, superintegrable and solvable) many-body model itroduced almost two decades ago by Gibbons and Hermsen and by Wojciechowski, and we modify it so that its generic solutions are all isochronous (namely, completely periodic with fixed period). We then show how this model...
A S HEGAZI, M MANSOUR
Pages: 9 - 18
In this paper, we define a new q-analogy of the Bernoulli polynomials and the Bernoulli numbers and we deduced some important relations of them. Also, we dduced a q-analogy of the Euler-Maclaurin formulas. Finally, we present a relation between the q-gamma function and the q-Bernoulli polynomials.
Misha FEIGIN
Pages: 95 - 136
We prove bispectral duality for the generalized Calogero­Moser­Sutherland systems related to configurations An,2(m), Cn(l, m). The trigonometric axiomatics of the Baker­Akhiezer function is modified, the dual difference operators of rational Madonald type and the Baker­Akhiezer functions related to...
Fabio MUSSO, Matteo PETRERA, Orlando RAGNISCO, Giovanni SATTA
Pages: 240 - 252
We consider a long­range homogeneous chain where the local variables are the geerators of the direct sum of N e(3) interacting Lagrange tops. We call this classical integrable model rational "Lagrange chain" showing how one can obtain it starting from su(2) rational Gaudin models. Moreover we construct...
A Raouf CHOUIKHA
Pages: 162 - 169
In this paper we are interested in developments of the elliptic functions of Jacobi. In particular a trigonometric expansion of the classical theta functions introduced by the author (Algebraic methods and q-special functions, C.R.M. Proceedings and Lectures Notes, A.M.S., vol 22, Providence, 1999,...
K SOKALSKI, T WIETECHA, D SOKALSKA
Pages: 31 - 52
A concept of strong necessary conditions for extremum of functional has been aplied for analysis an existence of dual equations for a system of two nonlinear Partial Differential Equations (PDE) in 1+1 dimensions. We consider two types of the dual equations: the Bäcklund transformations and the Bogomolny...
J-P FRANCOISE
Pages: 315 - 326
This article displays examples of planar isochronous systems and discuss the new techniques found by F. Calogero with these examples. A sufficient condition is found to keep track of some periodic orbits for perturbations of isochronous systems.
V K CHANDRASEKAR, M SENTHILVELAN, M LAKSHMANAN
Pages: 184 - 201
We discuss a method of solving nth order scalar ordinary differential equations by extending the ideas based on the Prelle-Singer (PS) procedure for second order ordnary differential equations. We also introduce a novel way of generating additional integrals of motion from a single integral. We illustrate...
Adam DOLIWA
Pages: 244 - 252
We study a potential introduced by Darboux to describe conjugate nets, which within the modern theory of integrable systems can be interpreted as a -function. We investigate the potential using the nonlocal ¯-dressing method of Manakov and Zkharov and we show that it can be interpreted as the Fredholm...
Robert CONTE, Micheline MUSETTE, Caroline VERHOEVEN
Pages: 212 - 227
We consider the cubic and quartic Hénon-Heiles Hamiltonians with additional inverse square terms, which pass the Painlevé test for only seven sets of coefficients. For all the not yet integrated cases we prove the singlevaluedness of the general solution. The seven Hamiltonians enjoy two properties:...
J FERNANDEZ-NUNEZ, W GARCIA-FUERTES, A M PERELOMOV
Pages: 280 - 301
We re-express the quantum Calogero-Sutherland model for the Lie algebra E6 and the particular value of the coupling constant = 1 by using the fundamental irreducible characters of the algebra as dynamical variables. For that, we need to develop a systematic procedure to obtain all the Clebsch-Gordan...
P GROZMAN, D LEITES
Pages: 372 - 379
Berger and Stassen reviewed skein relations for link invariants coming from the simple Lie algebras g. They related the invariants with decomposition of the tensor square of the g-module V of minimal dimension into irreducible components. (If V V , one should also consider the decompositions of...
Vasyl V GAFIYCHUK, Anatoliy K PRYKARPATSKY
Pages: 350 - 360
We consider the general properties of the quasispecies dynamical system from the standpoint of its evolution and stability. Vector field analysis as well as spectral properties of such system have been studied. Mathematical modeling of the system under consideration has been performed.
David Mumo MALONZA
Pages: 376 - 398
The set of systems of differential equations that are in normal form with respect to a particular linear part has the structure of a module of equivariants, and is best described by giving a Stanley decomposition of that module. In this paper Groebner basis methods are used to determine a Groebner...
Min Ho LEE
Pages: 199 - 207
A solution of the KP-hierarchy can be given by the -function or the Baker function associated to an element of the Grassmannian Gr(L2 (S1 )) consisting of some subspaces of the space L2 (S1 ) of square-integrable functions on the unit circle S1 . The Krichever map associates an element W Gr(L2 (S1 ))...
Hiêú D NGUYÊÑ
Pages: 180 - 198
This paper investigates the nature of particle collisions for three-soliton solutions of the Korteweg-de Vries (KdV) equation by describing mathematically the interaction of soliton particles and generation of ghost particle radiation. In particular, it is proven that a collision between any two soliton...
PGL LEACH, J MIRITZIS
Pages: 123 - 133
We examine the classical model of two competing species for integrability in terms of analytic functions by means of the Painlevé analysis. We find that the governing equations are integrable for certain values of the essential parameters of the system. We find that, for all integrable cases with...
A. RAMANI, T. TAMIZHMANI, B. GRAMMATICOS, K. M. TAMIZHMANI
Pages: 149 - 165
We present an extension of a family of second-order integrable mappings to the case where the variables do not commute. In every case we introduce a commutation rule which is consistent with the mapping evolution. Through the proper ordering of variables we ensure the existence of an invariant in...
Runliang Lin, Xiaojun Liu, Yunbo Zeng
Pages: 333 - 347
A method is proposed in this paper to construct a new extended q-deformed KP (q-KP) hiearchy and its Lax representation. This new extended q-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey hierarchy...