Gauge equivalence between the two-dimensional continuous classical Heisenberg ferromagnets(CCHF) of spin 1 2 -the M-I equation with singleside anisotropy and the Zakharov equation(ZE) is established for the easy axis case. The anisotropic CCHF is shown to be gauge equivalent to the isotropic CCHF. Preprint CNLP-1994-05. Alma-Ata.1994 In the study of 1+1 dimensional ferromagnets, a well known La...

The generalized Zakharov–Shabat systems with complex-valued Cartan elements and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their gauge equivalent are studies. This 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 equati...

In this paper, the tanh and sine–cosine methods are used to construct exact periodic and soliton solutions of nonlinear evolution equations arising in mathematical physics. Many new families of exact travelling wave solutions of the generalized Hirota–Satsuma coupled KdV system, generalized-Zakharov equations and (2 + 1)-dimensional Broer–Kaup– Kupershmidt system are successfully obtained. The ...

Consider the Zakharov-Shabat (or Dirac) operator Tzs on L 2(R) L2(R) with real periodic vector potential q = (q1; q2) 2 H = L 2(T) L2(T). The spectrum of Tzs is absolutely continuous and consists of intervals separated by gaps (z n ; z + n ); n 2 Z. >From the Dirichlet eigenvalues mn; n 2 Z of the Zakharov-Shabat equation with Dirichlet boundary conditions at 0; 1, the center of the gap and the...

The vector optical solitons composed of bright and dark pulses are analyzed. It is shown that in the smallamplitude limit a bound state of these solitons is described by the generalized Zakharov system, which supports coupled soliton solutions, and under special conditions it reduces to an integrable model. In the limit in which the integrable model approximation is valid, numerical simulations...

We develop a general theory to treat the linear stability of certain special solutions of second order in time evolutionary PDEs. We apply these results to standing waves of the following problems: the Klein-Gordon equation, for which we consider both ground states and certain excited states, the Klein-Gordon-Zakharov system and the beam equation. We also discuss possible applications to some n...

where Ω is a bounded domain of R, n ≤ 2 with κ, α, λ > 0. The variable ψ stands for the dimensionless low frequency electron field, whereas φ denotes the dimensionless low frequency density. This system in one dimension describes the nonlinear interaction between high frequency electron waves and low frequency ion plasma waves in a homogeneous magnetic field, adapted to model the UHH plasma hea...