Bifurcation diagrams of coupled Schrödinger equations

Existence of infinitely many solutions for coupled system of Schrödinger-Maxwell's equations

Classification of Solitary Wave Bifurcations in Generalized Nonlinear Schrdinger Equations

Bifurcations of solitary waves are classified for the generalized nonlinear Schrödinger equations with arbitrary nonlinearities and external potentials in arbitrary spatial dimensions. Analytical conditions are derived for three major types of solitary wave bifurcations, namely, saddle-node, pitchfork, and transcritical bifurcations. Shapes of power diagrams near these bifurcations are also obt...

Symmetry breaking, coupling management, and localized modes in dual-core discrete nonlinear-Schrödinger lattices

We introduce a system of two linearly coupled discrete nonlinear Schrödinger equations (DNLSEs), with the coupling constant subject to a rapid temporal modulation. The model can be realized in bimodal Bose–Einstein condensates (BEC). Using an averaging procedure based on the multiscale method, we derive a system of averaged (autonomous) equations, which take the form of coupled DNLSEs with addi...

Coupled-Mode Equations and Gap Solitons in a Two-Dimensional Nonlinear Elliptic Problem with a Separable Periodic Potential

We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schrödinger operator and the relevant coupled-mode equations to describe this bifurcation. The coupled-mode equations are derived by the rigorous analysis based on the Fouri...

A minimal energy tracking method for non-radially symmetric solutions of coupled nonlinear Schrödinger equations

We aim at developing methods to track minimal energy solutions of time-independent mcomponent coupled discrete nonlinear Schrödinger (DNLS) equations. We first propose a method to find energy minimizers of the 1-component DNLS equation and use it as the initial point of the m-component DNLS equations in a continuation scheme. We then show that the change of local optimality occurs only at the b...