Journal of Nonlinear Mathematical Physics

Volume 20, Issue 4, December 2013
Letter to Editor

1. Classical solutions of a massless Wess-Zumino model

Marco Frasca
Pages: 464 - 468
We provide a current expansion for the classical equations of motion of the massles Wess-Zumino model. In the low-energy limit, there appears a massive behavior for bosonic degrees of freedom and, at small coupling, the fermion field shows the same mass and supersymmetry is overall preserved. In the...
Letter to Editor

2. Properties of the zeros of the sum of three polynomials

Francesco Calogero
Pages: 469 - 474
A system of algebraic equations satisfied by the zeros of the sum of three polynomials are reported.
Letter to Editor

3. On the nonexistence of Liouvillian first integrals for generalized Liénard polynomial differential systems

Guillaume Chèze, Thomas Cluzeau
Pages: 475 - 479
We consider generalized Liénard polynomial differential systems of the form ẋ = y, ẏ = -g(x) - f (x) y, with f (x) and g(x) two polynomials satisfying deg(g) ≤ deg(f). In their work, Llibre and Valls have shown that, except in some particular cases, such systems have no Liouvillian first integral. In...
Research Article

4. q-Oscillator Algebra And d-Orthogonal Polynomials

Fethi Bouzeffour, Ali Zagouhani
Pages: 480 - 494
In this paper we express the matrix coefficients of the Fock representation of a q-oscillator algebra in terms of the d-orthogonal Al-Salam Carlitz polynomials. Also, we derive a generating functions, recurrence relations and q-difference equations for these d-orthogonal polynomials.
Research Article

5. Functional representation of the negative DNLS hierarchy

V.E. Vekslerchik
Pages: 495 - 513
This paper is devoted to the negative flows of the derivative nonlinear Schrödinger hierarchy (DNLSH). The main result of this work is the functional representation of the extended DNLSH, composed of both positive (classical) and negative flows. We derive a finite set of functional equations, constructed...
Research Article

6. Darboux transformation and novel solutions for the long wave-short wave model

Xin Huang, Boling Guo, Liming Ling
Pages: 514 - 528
Firstly, we establish the relation between the loop group method and gauge transformation method for 3×3 spectral problem. Some novel solutions of long wave-short wave model are obtained by Darboux transformation method. Besides, we give the analysis and classification of solution in detail.
Research Article

7. The Virasoro action on the tau function for the constrained discrete KP hierarchy

Jipeng Cheng, Maohua Li, Jingsong He
Pages: 529 - 538
With the help of the squared eigenfunction potential, the action of the Virasoro symmetry on the tau function of the constrained discrete KP hierarchy is derived.
Research Article

8. Equilibria of a solvable N-body problem and related properties of the N numbers xn at which the Jacobi polynomial of order N has the same value

Oksana Bihun, Francesco Calogero
Pages: 539 - 551
The class of solvable N-body problems of “goldfish” type has been recently extended by including (the additional presence of) three-body forces. In this paper we show that the equilibria of some of these systems are simply related to the N roots xn of the polynomial equation PN(α,β) (x)= w, where...
Research Article

9. Miura-reciprocal transformations for non-isospectral Camassa-Holm hierarchies in 2 + 1 dimensions

P. G. Estévez, C. Sardón
Pages: 552 - 564
We present two hierarchies of partial differential equations in 2 + 1 dimensions. Since there exist reciprocal transformations that connect these hierarchies to the Calogero-Bogoyavlenski-Schiff equation and its modified version, we can prove that one of the hierarchies can be considered as a modified...
Research Article

10. Contiguity relations for linearisable systems of Gambier type

A. Ramani, B. Grammaticos, P. Guha
Pages: 565 - 576
We introduce the Schlesinger transformations for the Gambier, linearisable, equation and by combining the former construct the contiguity relations of the solutions of the latter. We extend the approach to the discrete domain obtaining thus the Schlesinger transformations and the contiguity relations...
Research Article

11. On Bianchi permutability of Bäcklund transformations for asymmetric quad-equations

Raphael Boll
Pages: 577 - 605
We prove the Bianchi permutability (existence of superposition principle) of Bäcklund transformations for asymmetric quad-equations. Such equations and their Bäcklund transformations form 3D consistent systems of a priori different equations. We perform this proof by using 4D consistent systems of quad-equations,...
Research Article

12. Four-Wave Semidiscrete Nonlinear Integrable System with 𝒫𝒯-Symmetry

Oleksiy O. Vakhnenko
Pages: 606 - 622
The new type of third-order spectral operator suitable to generate new multifield semidiscrete nonlinear systems with two coupling parameters in the framework of zero-curvature equation is proposed. The evolution operator corresponding to the first integrable system in an infinite hierarchy is explicitly...