Journal of Nonlinear Mathematical Physics

Volume 17, Issue 2, June 2010
Letter to Editor

1. On the Propagation of Binary Signals in a Two-Dimensional Nonlinear Lattice with Nearest-Neighbor Interactions

Javier Ruiz-Ramírez, Jorge Eduardo Macías-Díaz
Pages: 127 - 136
In this work, we use a computational technique with multiple properties of consistency in order to approximate solutions of a bounded β-Fermi–Pasta–Ulam lattice in two space dimensions subject to harmonic driving in two adjacent boundaries. The processes of nonlinear supratransmission and infratransmission...
Research Article

2. A Weil Representation of sp(4) Realized by Differential Operators in the Space of Smooth Functions on S2 × S1

H. Fakhri
Pages: 137 - 144
In the space of complex-valued smooth functions on S2 × S1, we explicitly realize a Weil representation of the real Lie algebra sp(4) by means of differential generators. This representation is a rare example of highest weight irreducible representation of sp(4) all whose weight spaces are 1-dimensional....
Research Article

3. Profiles of Inflated Surfaces

Igor Pak, Jean-Marc Schlenker
Pages: 145 - 157
We study the shape of inflated surfaces introduced in [3] and [12]. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry plane. We show that such profiles are in a one-parameter family of curves...
Research Article

4. Novikov Super-Algebras with Associative Non-Degenerate Super-Symmetric Bilinear Forms

Junna Ni, Zhiqi Chen
Pages: 159 - 166
Novikov super-algebras are related to quadratic conformal super-algebras which correspond to Hamiltonian pairs and play fundamental role in completely integrable systems. In this paper, we focus on quadratic Novikov super-algebras, which are Novikov super-algebras with associative non-degenerate super-symmetric...
Research Article

5. Lagrangians for Dissipative Nonlinear Oscillators: The Method of Jacobi Last Multiplier

M. C. Nucci, K. M. Tamizhmani
Pages: 167 - 178
We present a method devised by Jacobi to derive Lagrangians of any second-order differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness and the power of Jacobi's method by applying it to several equations, including a class of equations recently studied...
Research Article

6. A New Set of Admitted Transformations for Autonomous Stochastic Ordinary Differential Equations

Sergey V. Meleshko, Eckart Schulz
Pages: 179 - 196
This paper investigates symmetries of autonomous ordinary stochastic differential equations. Change of time includes the stochastic process itself, and is uniquely determined by the transformation of the spatial variable. As a particular feature, the time change by an admitted Lie symmetry group may...
Research Article

7. Vadermonde-Type Odd-Soliton Solutions for the Whitham–Broer–Kaup Model in the Shallow Water Small-Amplitude Regime

Lei Wang, Yi-Tian Gao, Xiao-Ling Gai, Xin Yu, Zhi-Yuan Sun
Pages: 197 - 211
Under investigation in this paper, with symbolic computation, is the Whitham–Broer–Kaup (WBK) system for the dispersive long waves in the shallow water small-amplitude regime. N-fold Darboux transformation (DT) for a spectral problem associated with the WBK system is constructed. Odd-soliton solutions...
Research Article

8. Complex Representation of Planar Motions and Conserved Quantities of the Kepler and Hooke Problems

Y. Grandati, A. Bérard, H. Mohrbach
Pages: 213 - 225
Using a complex representation of planar motions, we show that the dynamical conserved quantities associated to the isotropic harmonic oscillator (Fradkin–Jauch–Hill tensor) and to the Kepler's problem (Laplace–Runge–Lenz vector) find a very simple and natural interpretation. In this frame we also...
Research Article

9. A Yang–Mills Electrodynamics Theory on the Holomorphic Tangent Bundle

Gheorghe Munteanu
Pages: 227 - 242
Considering a complex Lagrange space ([24]), in this paper the complex electromagnetic tensor fields are defined as the sum between the differential of the complex Liouville 1-form and the symplectic 2-form of the space relative to the adapted frames of the Chern–Lagrange complex nonlinear connection....
Research Article

10. Classification of (n + 2)-Dimensional Metric n-Lie Algebras

Mingming Ren, Zhiqi Chen, Ke Liang
Pages: 243 - 249
In this paper, we give the classification of (n + 2)-dimensional metric n-Lie algebras in terms of some facts about n-Lie algebras.