Stability of Spectral Eigenspaces in Nonlinear Schrödinger Equations

Inertia law for spectral stability of solitary waves in coupled nonlinear Schrödinger equations

Spectral stability analysis for solitary waves is developed in the context of the Hamiltonian system of coupled nonlinear Schrödinger equations. The linear eigenvalue problem for a non-self-adjoint operator is studied with two self-adjoint matrix Schrödinger operators. Sharp bounds on the number and type of unstable eigenvalues in the spectral problem are found from the inertia law for quadrati...

Stability and instability of standing waves for nonlinear Schrödinger equations

Instabilities of Multihump Vector Solitons in Coupled Nonlinear Schrödinger Equations

Spectral stability of multihump vector solitons in the Hamiltonian system of coupled nonlinear Schrödinger (NLS) equations is investigated both analytically and numerically. Using the closure theorem for the negative index of the linearized Hamiltonian, we classify all possible bifurcations of unstable eigenvalues in the systems of coupled NLS equations with cubic and saturable nonlinearities. ...

A Legendre-spectral scheme for solution of nonlinear system of Volterra-Fredholm integral equations

This paper gives an ecient numerical method for solving the nonlinear systemof Volterra-Fredholm integral equations. A Legendre-spectral method based onthe Legendre integration Gauss points and Lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.

On the Spectral Stability of Solitary Wave Solutions of the Vector Nonlinear Schrödinger Equation

We consider a system of coupled cubic nonlinear Schrödinger (NLS) equations i ∂ψj ∂t = − ∂ψj ∂x2 + ψj n ∑ k=1 αjk|ψk| j = 1, 2, . . . , n, where the interaction coefficients αjk are real. The spectral stability of solitary wave solutions (both bright and dark) is examined both analytically and numerically. Our results build on preceding work by Nguyen et al. and others. Specifically, we present...