Journal of Nonlinear Mathematical Physics

A systematic investigation to derive nonlinear lattice equations governed by partial difference equations (PΔΔE) admitting specific Lax representation is presented. Further it is shown that for a specific value of the parameter the derived nonlinear PΔΔE's can be transformed into a linear PΔΔE's...

Certain techniques to obtain properties of the zeros of polynomials satisfying second-order ODEs are reviewed. The application of these techniques to the classical polynomials yields formulas which were already known; new are instead the formulas for the zeros of the (recently identified, and rather...

We consider the Hamiltonian function defined by the cubic polynomial H=12(px2+py2)+12(x2+y2)+A3x3+Bxy2+Dx2y , where A, B, D ∈ ℝ are parameters and so H is an extension of the well known Hénon-Heiles problem. Our main contribution for D ≠ 0, A + B ≠ 0 and other technical restrictions are in three...

In this paper, we construct the bilinear identities for the wave functions of an extended Kadomtsev-Petviashvili (KP) hierarchy, which is the KP hierarchy with particular extended flows. By introducing an auxiliary parameter, whose flow corresponds to the so-called squared eigenfunction symmetry of KP...

The aim of this paper is to study the formation of delta standing wave for a scalar conservation law with a linear flux function involving discontinuous coefficients. In order to deal with it, we approximate the discontinuous coefficients by piecewise affine ones and then apply the method of characteristics...

In this paper, using the properties of hyperelliptic σ- and ℘- functions, ℘μν : = ∂μ∂ν log σ, we propose an algorithm to obtain particular solutions of the coupled nonlinear differential equations, such as a general (2+1)- dimensional breaking soliton equation and static Veselov-Novikov(SVN) equation,...

Starting from known solutions of the functional Yang-Baxter equations, we construct a series of nonautonomous integrable recurrences, “median graphs”, and give their explicit solution.

It is shown that HW (ℛ) (η), the algebra of observables of the rational Calogero model based on the root system ℛ ⊂ ℝN, has Tℛ independent traces, where Tℛ is the number of conjugacy classes of elements without eigenvalue 1 belonging to the Coxeter group W (ℛ) ⊂ End ℝN generated by the root system ℛ. Simultaneously,...

In the Coxeter group W (ℛ) generated by the root system ℛ, let T (ℛ) be the number of conjugacy classes having no eigenvalue +1 and let S (ℛ) be the number of conjugacy classes having no eigenvalue −1. The algebra HW (ℛ) of observables of the rational Calogero model based on the root system ℛ possesses...