Zakharov-Ito equation and Generalized Heisenberg ferromagnet-type equation: equivalence and related geometric curve flows

Pseudo-Hermitian Reduction of a Generalized Heisenberg Ferromagnet Equation. II. Special Solutions

This paper is a continuation of our previous work in which we studied a sl(3) Zakharov-Shabat type auxiliary linear problem with reductions of Mikhailov type and the integrable hierarchy of nonlinear evolution equations associated with it. Now, we shall demonstrate how one can construct special solutions over constant background through Zakharov-Shabat's dressing technique. That approach will be illustrated on the example of a generalized Heisenberg ferromagnet equation related to the linear problem for sl(3). In doing this, we shall discuss the difference between the Hermitian and pseudo-Herm…

The Generalised Zakharov-Shabat System and the Gauge Group Action

The generalized Zakharov-Shabat systems with complex-valued non-regular Cartan elements and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their gauge equivalent are studied. This study includes: the properties of fundamental analytical solutions (FAS) for the gauge-equivalent to CBC systems and the minimal set of scattering data; the description of the class of nonlinear evolutionary equations, solvable by the inverse scattering method, and the recursion operator, related to such systems; the hierarchies of Hamiltonian structures. The results are illustrated on the exampl…

On Soliton Interactions for a Hierarchy of Generalized Heisenberg Ferromagnetic Models on SU(3)/S(U(1) $\times$ U(2)) Symmetric Space

We consider an integrable hierarchy of nonlinear evolution equations (NLEE) related to linear bundle Lax operator L. The Lax representation is Z2 \times Z2 reduced and is naturally associated with the symmetric space SU(3)/S(U(1) \times U(2)). The simplest nontrivial equation in the hierarchy is a generalization of Heisenberg ferromagnetic model. We construct the N-soliton solutions for an arbitrary member of the hierarchy by using the Zakharov-Shabat dressing method with an appropriately chosen dressing factor. Two types of soliton solutions: quadruplet and doublet solitons are found. The one…

模拟浅水波的两分量可积系统：常涡度情形

Two component integrable systems modelling shallow water waves: the constant vorticity case

本文从 Euler 方程等基本条件出发，通过渐近展开推导出包含常涡度的浅水波近似模型方程，并将其与三个两分量可积系统相关联，揭示了常涡度对浅水波方程的具体影响。