Nonlinear Schrödinger equations (NLSs) with focusing power nonlinearities have solitary
wave solutions. The spectra of the linearized operators around these solitary waves are …

We consider the stability of periodic travelling-wave solutions to a generalized Korteweg–de
Vries (gKdV) equation and prove an index theorem relating the number of unstable and …

We consider a class of nonlinear Schrödinger/Gross–Pitaeveskii (NLS-GP) equations, ie,
NLS with a linear potential. NLS-GP plays an important role in the mathematical modeling of …

Nonlinear dispersive waves are wave phenomena resulting from the interacting effects of
nonlinearity and dispersion. Dispersion refers to the property that waves of different …

We prove the asymptotic stability of the moving kinks for the nonlinear relativistic wave
equations in one space dimension with a Ginzburg-Landau potential: starting in a small …

We prove the asymptotic stability of kink for the nonlinear relativistic wave equations of the
Ginzburg–Landau type in one space dimension: for any odd initial condition in a small …

The long-time asymptotics is analyzed for finite energy solutions of the 1D Schrödinger
equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to …

We study the point spectrum of the linearization at a solitary wave solution ϕ ω (x) e− i ω t to
the nonlinear Dirac equation in R n, for all n≥ 1, with the nonlinear term given by f (ψ⁎ β ψ) …

Consider the focusing cubic semilinear Schroedinger equation in R^ 3 i\partial_t\psi+\Delta\
psi+|\psi|^ 2\psi= 0. It admits an eight-dimensional manifold of special solutions called …

Abstract Let H=− Δ+ V, where V is a real valued potential on R^ 2 satisfying ‖ V (x)|\lesssim
⟨ x ⟩^-3-. We prove that if zero is a regular point of the spectrum of H=− Δ+ V, then ‖ w^-1 …