Volume 15, Issue 3, November 2008
Pages: 270 - 282
Pseudo horizontally weakly conformal maps  extend both holomorphic and (semi)conformal maps into an almost Hermitian manifold. We find critical points for the (generalized) Faddeev-Hopf model  in this larger class.
Pages: 283 - 290
We present a clarification of a recent inverse scattering algorithm developed for the Camassa-Holm equation.
Pages: 291 - 298
A three-component nonlinear Schrodinger-type model which describes spinor Bose-Einstein condensate (BEC) is considered. This model is integrable by the inverse scattering method and using Zakharov-Shabat dressing method we obtain three types of soliton solutions. The multi-component nonlinear Schr¨odinger...
Pages: 299 - 315
A direct method to construct polynomial integrals for third order ordinary difference equation (OE) w(n + 3) = F(w(n),w(n + 1),w(n + 2)) and fourth order OE w(n+4) = F(w(n),w(n+1),w(n+2),w(n+3)) is presented. The effectiveness of the method to construct more than one polynomial integral for N-th order...
Pages: 316 - 332
We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including those of the non-Lie type. An explicit example is made of the...
Pages: 333 - 347
A method is proposed in this paper to construct a new extended q-deformed KP (q-KP) hiearchy and its Lax representation. This new extended q-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey hierarchy...
Pages: 348 - 352
The integrals of the Benney system are shown to possess a group structure. The KP hierarchy breaks the group law down.