Journal of Nonlinear Mathematical Physics

It is shown that A:= H1, η (G), the sympectic reflection algebra over ℂ, has TG independent traces, where TG is the number of conjugacy classes of elements without eigenvalue 1 belonging to the finite group G ⊂ Sp(2N) ⊂ End(ℂ2N) generated by the system of symplectic reflections. Simultaneously, we show...

We consider the Hamiltonian polynomial function H of degree fourth given by either H(x,y,px,py)=12(px2+py2)+12(x2+y2)+V3(x,y)+V4(x,y) , or H(x,y,px,py)=12(-px2+py2)+12(-x2+y2)+V3(x,y)+V4(x,y) , where V3 (x, y) and V4 (x, y) are homogeneous polynomials of degree three and four, respectively....

We have classified symmetric solutions around the origin to the four dimensional degenerate Painlevé type equation NYA4 with generic values of parameters. We obtained sixteen meromorphic solutions, which are transformed each other by the Bäcklund transformation. We calculated the linear monodromy for...

In this paper, we obtain µ -symmetry and µ -conservation law of the extended mKdV equation. The extended mKdV equation dose not admit a variational problem since it is of odd order. First we obtain µ -conservation law of the extended mKdV equation in potential form because it admits a variational problem,...

The paper is to reveal the direct links between the well known Sylvester equation in matrix theory and some integrable systems. Using the Sylvester equation KM + MK = r sT we introduce a scalar function S(i, j) = sT Kj (I + M)−1Kir which is defined as same as in discrete case. S(i, j) satisfy some recurrence...

A relatively new approach to analyzing integrability, based upon differential-algebraic and symplectic techniques, is applied to some “dark equations ”of the type introduced by Boris Kupershmidt. These dark equations have unusual properties and are not particularly well-understood. In particular, dark...

In this paper, we construct a new integrable equation which is a generalization of q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the generalized q-Toda equation and a whole integrable generalized q-Toda hierarchy are also constructed....

A new multi-symplectic formulation of the two-component Camassa-Holm equation (2CH) is presented, and the associated local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. A multi-symplectic discretisation based on this new formulation is exemplified by means of...

In this paper, nonlocal symmetry of the (2+1) dimensional modified generalized long dispersive wave system and its applications are investigated. The nonlocal symmetry related to the eigenfunctions in Lax pairs is derived, and infinitely many nonlocal symmetries are obtained. By introducing three potentials,...