In this article we obtain asymptotic formulas for the Bloch eigenvalues of operator generated by a system Schrodinger equations with periodic PT-symmetric complex-valued coefficients. Then using these classify spectrum and find condition on coefficients which contains half line.

ductor devices. A self consistent Schrodinger – Poisson solver allows calculation of bound state energies and associated carrier wave functions self consistently with electrostatic potential. Schrodinger solvers can be combined with Non-equilibrium Green’s Function (NEGF) Approach in order to model ballistic quantum transport in 2D or cylindrical devices with strong transverse confinement. An a...

Enlargement of Lie super algebra B(0, 1) was given firstly. Then nonlinear super integrable couplings of the super classical Boussinesq hierarchy based upon this enlarged matrix Lie super algebra were constructed secondly. And its super Hamiltonian structures were established by using super trace identity thirdly. As its reduction, special integrable couplings of classical Boussinesq hierarchy ...

ABSTRACT In this paper, we have been acquired the soliton solutions of the Variant Boussinesq equations. Primarily, we have used the enhanced (G'/G)-expansion method to find exact solutions of Variant Boussinesq equations. Then, we attain some exact solutions including soliton solutions, hyperbolic and trigonometric function solutions of this equation. MATHEMATICS SUBJECT CLASSIFICATION 35 K9...

The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated nu...

We study two coupled systems of nonlinear partial differential equations, namely, generalized Boussinesq-Burgers equations and 2 1 -dimensional Davey-Stewartson equations. The Lie symmetry method is utilized to obtain exact solutions of the generalized Boussinesq-Burgers equations. The travelling wave hypothesis approach is used to find exact solutions of the 2 1 dimensional Davey-Stewartson eq...

Wave group dynamics is studied in the framework of the extended Korteweg-de Vries equation. The nonlinear Schrodinger equation is derived for weakly nonlinear wave packets, and the condition for modulational instability is obtained. It is shown that wave packets are unstable only for a positive sign of the coe cient of the cubic nonlinear term in the extended Korteweg-de Vries equation, and for...

Boussinesq type equations have been widely studied to model the surface water wave. In this paper, we consider abcd system which is a family of including many well-known models such as classical system, BBM-BBM Bona-Smith etc. We propose local discontinuous Galerkin (LDG) methods, with carefully chosen numerical fluxes, numerically solve system. The main focus paper rigorously establish priori ...