Journal of Nonlinear Mathematical Physics

Volume 23, Issue 1, January 2016
Research Article

1. Automorphisms of the q-deformed algebra suq(1, 1) and d-Orthogonal polynomials of q-Meixner type

Ali Zaghouani
Pages: 1 - 20
Starting from an operator given as a product of q-exponential functions in irreducible representations of the positive discrete series of the q-deformed algebra suq(1, 1), we express the associated matrix elements in terms of d-orthogonal polynomials. An algebraic setting allows to establish some properties...
Research Article

2. On the dynamics of a class of rational Kolmogorov systems

Rachid Boukoucha, Ahmed Bendjeddou
Pages: 21 - 27
In this paper we are intersted in studying the existence of a First integral and the non-existence of limit cycles of rational Kolmogorov systems of the form {x′=x(P(x,y)+R(x,y)S(x,y)),y′=y(Q(x,y)+R(x,y)S(x,y)), where P (x, y) , Q (x, y) , R (x, y) , S (x, y) are homogeneous polynomials of degree...
Research Article

3. A new solvable many-body problem of goldfish type

Oksana Bihun, Francesco Calogero
Pages: 28 - 46
A new solvable many-body problem of goldfish type is introduced and the behavior of its solutions is tersely discussed.
Research Article

4. Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties

Mahouton Norbert Hounkonnou, Partha Guha, Tudor Ratiu
Pages: 47 - 73
Motivated by the work of Kupershmidt (J. Nonlin. Math. Phys. 6 (1998), 222 –245) we discuss the occurrence of left symmetry in a generalized Virasoro algebra. The multiplication rule is defined, which is necessary and sufficient for this algebra to be quasi-associative. Its link to geometry and nonlinear...
Research Article

5. Geometry of Real Forms of the Complex Neumann System

Tina Novak
Pages: 74 - 91
In the paper, we study real forms of the complex generic Neumann system. We prove that the real forms are completely integrable Hamiltonian systems. The complex Neumann system is an example of the more general Mumford system. The Mumford system is characterized by the Lax pair (Lℂ(λ), Mℂ(λ)) of 2 × 2...
Research Article

6. The Ablowitz–Ladik hierarchy integrability analysis revisited: the vertex operator solution representation structure

Yarema A. Prykarpatskyy
Pages: 92 - 107
A regular gradient-holonomic approach to studying the Lax type integrability of the Ablowitz–Ladik hierarchy of nonlinear Lax type integrable discrete dynamical systems in the vertex operator representation is presented. The relationship to the Lie-algebraic integrability scheme is analyzed and the connection...
Research Article

7. Ermakov-Modulated Nonlinear Schrödinger Models. Integrable Reduction

Colin Rogers, Giuseppe Saccomandi, Luigi Vergori
Pages: 108 - 126
Nonlinear Schrödinger equations with spatial modulation associated with integrable Hamiltonian systems of Ermakov-Ray-Reid type are introduced. An algorithmic procedure is presented which exploits invariants of motion to construct exact wave packet representations with potential applications in a wide...
Research Article

8. The Elliptic Sinh-Gordon Equation in the Quarter Plane

Guenbo Hwang
Pages: 127 - 140
We study the elliptic sinh-Gordon equation formulated in the quarter plane by using the so-called Fokas method, which is a significant extension of the inverse scattering transform for the boundary value problems. The method is based on the simultaneous spectral analysis for both parts of the Lax pair...
Research Article

9. Parameterless discrete Painlevé equations and their Miura relations

B. Grammaticos, A. Ramani
Pages: 141 - 149
We present a study of discrete Painlevé equations which do not have any parameter, apart from those that can be removed by the appropriate scaling. We find four basic equations of this type as well as several more related to the basic ones by Miura transformations, which we derive explicitly. We obtain...