We establish uniform error bounds of a finite difference method for the Klein-Gordon-Zakharov (KGZ) system with a dimensionless parameter ε ∈ (0, 1], which is inversely proportional to the acoustic speed. In the subsonic limit regime, i.e. 0 < ε ≪ 1, the solution propagates highly oscillatory waves in time and/or rapid outgoing initial layers in space due to the singular perturbation in the Zak...

In this thesis, the Zakharov-Shabat scattering problem and several types of Landau-Lifschitz scattering problems are considered. The inverse scattering problem is that of seeking one or more coefficients in a system of differential equation from the scattering data which, generally, consists of a reflection coefficient and bound state data. We assume mainly that the coefficients to be determine...

In this paper, the (2+1)-dimensional extended quantum Zakharov-Kuznetsov equation is further explored. The shown to be self-adjoint and conserved vector constructed according related theorem. Then corresponding optimal system of one-dimensional subgroups determined. Similarity reductions under are performed. As a result, reduced into linear PDE with two independent variables.