Journal of Nonlinear Mathematical Physics

Volume 21, Issue 1, February 2014
Research Article

1. Conditions and evidence for non-integrability in the Friedmann-Robertson-Walker Hamiltonian

Sergi Simon
Pages: 1 - 16
This is an example of application of Ziglin-Morales-Ramis algebraic studies in Hamiltonian integrability, more specifically the result by Morales, Ramis and Simó on higher-order variational equations, to the well-known Friedmann-Robertson-Walker cosmological model. A previous paper by the author formalises...
Research Article

2. Generalized Wronskian and Grammian Solutions to a Isospectral B-type Kadomtsev-Petviashvili equation

Jianjun Cheng, Zhen Wang, Hongqing Zhang
Pages: 17 - 33
Generally speaking, the BKP hierarchy which only has Pfaffian solutions. In this paper, based on the Grammian and Wronskian derivative formulae, generalized Wronskian and Grammian determinant solutions are obtained for the isospectral BKP equation (the second member on the BKP hierarchy) in the Hirota...
Research Article

3. On geometric quantization of the Dirac magnetic monopole

Graham M. Kemp, Alexander P. Veselov
Pages: 34 - 42
We give a simple derivation of the spectrum of the Dirac magnetic monopole on a unit sphere S2 based on geometric quantization and the Frobenius reciprocity formula. The starting point is the calculation by Novikov and Schmelzer of the canonical symplectic structure on the coadjoint orbits of the isometry...
Research Article

4. Revisiting Noether's Theorem on constants of motion

Gianluca Gorni, Gaetano Zampieri
Pages: 43 - 73
In this paper we revisit Noether's theorem on the constants of motion for Lagrangian mechanical systems in the ODE case, with some new perspectives on both the theoretical and the applied side. We make full use of invariance up to a divergence, or, as we call it here, Bessel-Hagen (BH) invariance....
Research Article

5. Integrable Substructure in a Korteweg Capillarity Model. A Karman-Tsien Type Constitutive Relation

Colin Rogers
Pages: 74 - 88
A classical Korteweg capillarity system with a Karman-Tsien type (κ, ρ) constitutive relation is shown, via a Madelung transformation and use of invariants of motion, to admit integrable Hamiltonian subsystems.
Research Article

6. On nonlinear coherent states properties for electron-phonon dynamics

Isiaka Aremua, Mahouton Norbert Hounkonnou, Ezinvi Baloïtcha
Pages: 89 - 119
This work addresses a construction of a dual pair of nonlinear coherent states (NCS) in the context of changes of bases in the underlying Hilbert space for a model pertaining to an electron-phonon model in the condensed matter physics, obeying a f-deformed Heisenberg algebra. The existence and properties...
Research Article

7. On characteristic integrals of Toda field theories

Zhaohu Nie
Pages: 120 - 131
Characteristic integrals of Toda field theories associated to general simple Lie algebras are constructed using systematic techniques, and complete mathematical proofs are provided. Plenty of examples illustrating the results are presented in explicit forms.
Research Article

8. A class of third-order nonlinear evolution equations admitting invariant subspaces and associated reductions

Yujian Ye, Wen-Xiu Ma, Shoufeng Shen, Danda Zhang
Pages: 132 - 148
With the aid of symbolic computation by Maple, a class of third-order nonlinear evolution equations admitting invariant subspaces generated by solutions of linear ordinary differential equations of order less than seven is analyzed. The presented equations are either solved exactly or reduced to finite-dimensional...