of the periodic nonlinear Schrödinger equation, where u(x, t) is a complex valued function in the class of smooth period one functions. In this work, we explain in what sense the generic level set of the constants of motion for the periodic nonlinear Schrödinger equation is an infinite dimensional torus, why the solution of the Hamiltonian equation is almost periodic in time, and describe how n...

We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schrödinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our result covers cases where the bifurcation equation is infinitedimensional, such as the nonlinear Schrödinger equation with zero mass, for which solutions which at ...

(Received 25 June 1998, revised version received 05 January 1999) The Lax pair for a derivative nonlinear Schrödinger equation proposed by Chen-Lee-Liu is generalized into matrix form. This gives new types of integrable coupled derivative nonlinear Schrödinger equations. By virtue of a gauge transformation, a new multi-component extension of a derivative nonlinear Schrödinger equation proposed ...

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.

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...

The spectrum of a Schrödinger operator with a perfect honeycomb lattice potential has special points, called Dirac points where the lowest two branches of the spectrum touch. Deformations can result in the merging and disappearance of the Dirac points and the originally intersecting dispersion relation branches separate. Corresponding to these deformations, nonlinear envelope equations are deri...

Abstract. We exhibit a change of variables that turns the critical nonlinear Schrödinger equation into the critical nonlinear Schrödinger equation with isotropic harmonic potential, in any space dimension. This change of variables is isometric on L, and bijective on some time intervals. Using the known results for the critical nonlinear Schrödinger equation, this provides information for the pr...

With the help of a multi-scale expansion method, Lou derived a type of the higher-order nonlinear Schrödinger equation from the nondimensional barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a betaplane channel to describe nonlinear modulated Rossby waves [1]. This higher-order nonlinear Schrödinger equation includes fourth-order dispersion with ...