Journal of Nonlinear Mathematical Physics

Pseudo horizontally weakly conformal maps [16] extend both holomorphic and (semi)conformal maps into an almost Hermitian manifold. We find critical points for the (generalized) Faddeev-Hopf model [28] in this larger class.

We present a clarification of a recent inverse scattering algorithm developed for the Camassa-Holm equation.

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...

A direct method to construct polynomial integrals for third order ordinary difference equation (O
E) w(n + 3) = F(w(n),w(n + 1),w(n + 2)) and fourth order O
E 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...

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...

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...

The integrals of the Benney system are shown to possess a group structure. The KP hierarchy breaks the group law down.