The theory of the Relativistic Schrödinger Equations is further developped and extended to non-linear field equations. The technical advantage of the Relativistic Schrödinger approach is demonstrated explicitly by solving the coupled Einstein-Klein-Gordon equations including a non-linear Higgs potential in case of a Robertson-Walker universe. The numerical results yield the effect of dynamical ...

We present new solutions in terms of elementary functions of the multi-component nonlinear Schrödinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton, breather, dromion and lump solutions. These solutions are given in a simple determinantal form and are obtained as limiting cases in suitable degenerations of previously derived algebro-geometric solutions. ...

A class of discrete nonlinear Schrödinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrödinger equation and the Ablowitz-Ladik equation. As a common property, these equations possess three kinds of exact analytical sta...

In this paper, we study analytically and numerically the singular limits of the nonlinear Klein–Gordon–Schrödinger (KGS) equations in Rd (d = 1, 2, 3) both with and without a damping term to the nonlinear Schrödinger–Yukawa (SY) equations. By using the two-scale matched asymptotic expansion, formal limits of the solution of the KGS equations to the solution of the SY equations are derived with ...

This paper obtains the exact 1-soliton solutions to generalized nonlinear Schrödinger equation. Nonlinear Schrödinger equation has been widely applied in many branches of nonlinear sciences such as nonlinear optics, nonlinear optical fibers and quantum mechanics. So, finding exact solutions of such equations are very helpful in the theories and numerical studies. In this paper, the He’s semi-in...

We suggest a generalized Lax pair on a Hermitian symmetric space to generate a new coupled higher-order nonlinear Schrödinger equation of a dual type which contains both bright and dark soliton equations depending on parameters in the Lax pair. Through the generalized ways of reduction and the scaling transformation for the coupled higher-order nonlinear Schrödinger equation, two integrable typ...

Multiscale Computation and Analysis for Schrödinger-Poisson System in Heterogeneous Materials Liqun Cao Chinese Academy of Sciences, China [email protected] In this talk, we discuss the multiscale computation for Schrödinger-Poisson system arising from the electronic properties of semiconductors such as quantum wells, wires and dots, and CMOS transistor. We first introduce the Schrödinger equat...

We prove that for the L-critical nonlinear Schrödinger equations, the wave operators and their inverse are related explicitly in terms of the Fourier transform. We discuss some consequences of this property. In the onedimensional case, we show a precise similarity between the L-critical nonlinear Schrödinger equation and a nonlinear Schrödinger equation of derivative type.