Journal of Nonlinear Mathematical Physics

Volume 21, Issue 4, October 2014
Research Article

1. Algebro-geometric solutions for the two-component Hunter-Saxton hierarchy

Yu Hou, Engui Fan
Pages: 473 - 508
This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the two-component Hunter-Saxton (HS2) hierarchy through an algebro-geometric initial value problem. Our main tools include the polynomial recursive formalism, the hyperelliptic...
Research Article

2. Bi-Hamiltonian structure of multi-component Novikov equation

Hongmin Li, Yuqi Li, Yong Chen
Pages: 509 - 520
In this paper, we present the multi-component Novikov equation and derive it's bi-Hamiltonian structure.
Research Article

3. Integration of some examples of geodesic flows via solvable structures

Diego Catalano Ferraioli, Paola Morando
Pages: 521 - 532
Solvable structures are particularly useful in the integration by quadratures of ordinary differential equations. Nevertheless, for a given equation, it is not always possible to compute a solvable structure. In practice, the simplest solvable structures are those adapted to an already known system of...
Research Article

4. The gauge transformation of the q-deformed modified KP hierarchy

Jipeng Cheng, Jinzheng Wang, Xingyong Zhang
Pages: 533 - 542
In this paper, we mainly study three types of gauge transformation operators for the q-mKP hierarchy. The successive applications of these gauge transformation operators are derived. And the corresponding communities between them are also investigated.
Research Article

5. On deformation and classification of ∨-systems

V. Schreiber, A.P. Veselov
Pages: 543 - 583
The ∨-systems are special finite sets of covectors which appeared in the theory of the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. Several families of ∨-systems are known, but their classification is an open problem. We derive the relations describing the infinitesimal deformations...
Research Article

6. On the study of unitary representations of the twisted Heisenberg-Virasoro algebra via highest weight modules over affine Lie algebras*

Namhee Kwon
Pages: 584 - 592
In this paper, we first construct an analogue of the Sugawara operators for the twisted Heisenberg-Virasoro algebra. By using these operators, we show that every integrable highest weight module over an affine Lie algebra can be viewed as a unitary representation of the twisted Heisenberg-Virasoro algebra....
Research Article

7. Simple and collective twisted symmetries

G. Gaeta
Pages: 593 - 627
After the introduction of λ -symmetries by Muriel and Romero, several other types of so called “twisted symmetries” have been considered in the literature (their name refers to the fact they are defined through a deformation of the familiar prolongation operation); they are as useful as standard symmetries...
Research Article

8. Hybrid Ermakov-Painlevé IV Systems

Colin Rogers
Pages: 628 - 642
Ermakov-Painlevé IV coupled systems are introduced and associated Ermakov-type invariants isolated. These invariants are used to obtain systematic reduction of the system in terms of the canonical Painlevé IV equation. The procedure is applied to a Ermakov-Painlevé IV symmetry reduction of a coupled...
Research Article

9. Symmetry reductions and exact solutions of Lax integrable 3-dimensional systems

H. Baran, I.S. Krasil'shchik, O.I. Morozov, P. Vojčák
Pages: 643 - 671
We present a complete description of 2-dimensional equations that arise as symmetry reductions of four 3- dimensional Lax-integrable equations: (1) the universal hierarchy equation uyy = uzuxy− uyuxz; (2) the 3D rdDym equation uty = uxuxy− uyuxx; (3) the equation uty = utuxy− uyutx, which we call modified...