Journal of Nonlinear Mathematical Physics

Volume 25, Issue 2, March 2018
Research Article

1. The Mixed Kuper-Camassa-Holm-Hunter-Saxton Equations

Ling Zhang, Beibei Hu
Pages: 179 - 187
In this paper, a mixed Kuper-CH-HS equation by a Kupershmidt deformation is introduced and its integrable properties are studied. Moreover, that the equation can be viewed as a constraint Hamiltonian flow on the coadjoint orbit of Neveu-Schwarz superalgebra is shown.
Research Article

2. Nonlocal symmetries of Plebański’s second heavenly equation

Aleksandra Lelito, Oleg I. Morozov
Pages: 188 - 197
We study nonlocal symmetries of Plebański’s second heavenly equation in an infinite-dimensional covering associated to a Lax pair with a non-removable spectral parameter. We show that all local symmetries of the equation admit lifts to full-fledged nonlocal symmetries in the infinite-dimensional covering....
Research Article

3. Magnetic curves in Sol3

Zlatko Erjavec, Jun-ichi Inoguchi
Pages: 198 - 210
Magnetic curves with respect to the canonical contact structure of the space Sol3 are investigated.
Research Article

4. Symmetry Reduction of Ordinary Differential Equations Using Moving Frames

Francis Valiquette
Pages: 211 - 246
The symmetry reduction algorithm for ordinary differential equations due to Sophus Lie is revisited using the method of equivariant moving frames. Using the recurrence formulas provided by the theory of equivariant moving frames, computations are performed symbolically without relying on the coordinate...
Research Article

5. Ermakov-Painlevé II Reduction in Cold Plasma Physics. Application of a Bäcklund Transformation

Colin Rogers, Peter A. Clarkson
Pages: 247 - 261
A class of symmetry transformations of a type originally introduced in a nonlinear optics context is used here to isolate an integrable Ermakov-Painlevé II reduction of a resonant NLS equation which encapsulates a nonlinear system in cold plasma physics descriptive of the uni-axial propagation of magneto-acoustic...
Research Article

6. Symmetry and integrability for stochastic differential equations

G. Gaeta, C. Lunini
Pages: 262 - 289
We discuss the interrelations between symmetry of an Ito stochastic differential equations (or systems thereof) and its integrability, extending in party results by R. Kozlov [J. Phys. A 43 (2010) & 44 (2011)]. Together with integrability, we also consider the relations between symmetries and reducibility...
Research Article

7. Inverse Spectral Problem and Peakons of an Integrable Two-component Camassa-Holm System

Fengfeng Dong, Lingjun Zhou
Pages: 290 - 308
In this paper, we are concerned with the explicit construction of peakon solutions of the integrable twocomponent system with cubic non-linearity. We establish the spectral and inverse spectral problem associated to the Lax pairs of the system. The inverse problem is solved by the classical results of...
Research Article

8. Bilinear Identities and Hirota’s Bilinear Forms for the (γn, σk)-KP Hierarchy

Yuqin Yao, Juhui Zhang, Runliang Lin, Xiaojun Liu, Yehui Huang
Pages: 309 - 323
In this paper, we discuss how to construct the bilinear identities for the wave functions of the (γn, σk)-KP hierarchy and its Hirota’s bilinear forms. First, based on the corresponding squared eigenfunction symmetry of the KP hierarchy, we prove that the wave functions of the (γn, σk)-KP hierarchy are...
Research Article

9. Pseudo-Hermitian Reduction of a Generalized Heisenberg Ferromagnet Equation. I. Auxiliary System and Fundamental Properties

A. B. Yanovski, T. I. Valchev
Pages: 324 - 350
We consider an auxiliary spectral problem originally introduced by Gerdjikov, Mikhailov and Valchev (GMV system) and its modification called pseudo-Hermitian reduction which is extensively studied here for the first time. We describe the integrable hierarchies of both systems in a parallel way and construct...