Stability of Periodic Waves of 1D Cubic Nonlinear Schrödinger Equations
نویسندگان
چکیده
منابع مشابه
Stability of Periodic Traveling Waves for Nonlinear Dispersive Equations
We study the stability and instability of periodic traveling waves for Korteweg-de Vries type equations with fractional dispersion and related, nonlinear dispersive equations. We show that a local constrained minimizer for a suitable variational problem is nonlinearly stable to period preserving perturbations. We then discuss when the associated linearized equation admits solutions exponentiall...
متن کاملPeriodic waves of a discrete higher order nonlinear Schrödinger equation ∗
The Hirota equation is a higher order extension of the nonlinear Schrödinger equation by incorporating third order dispersion and one form of self steepening effect. New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete per...
متن کاملArtificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
This paper addresses the construction of nonlinear integro-differential artificial boundary conditions for one-dimensional nonlinear cubic Schrödinger equations. Several ways of designing such conditions are provided and a theoretical classification of their accuracy is given. Semi-discrete time schemes based on the method developed by Durán and Sanz-Serna [IMA J. Numer. Anal. 20 (2) (2000), pp...
متن کاملStability and Evolution of Solitary Waves in Perturbed Generalized Nonlinear Schrödinger Equations
In this paper, we study the stability and evolution of solitary waves in perturbed generalized nonlinear Schrödinger (NLS) equations. Our method is based on the completeness of the bounded eigenstates of the associated linear operator in L2 space and a standard multiple-scale perturbation technique. Unlike the adiabatic perturbation method, our method details all instability mechanisms caused b...
متن کاملNo stability switching at saddle-node bifurcations of solitary waves in generalized nonlinear Schrödinger equations.
Saddle-node bifurcations arise frequently in solitary waves of diverse physical systems. Previously it was believed that solitary waves always undergo stability switching at saddle-node bifurcations, just as in finite-dimensional dynamical systems. Here we show that this is not true. For a large class of generalized nonlinear Schrödinger equations with real or complex potentials, we prove that ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics Research eXpress
سال: 2017
ISSN: 1687-1200,1687-1197
DOI: 10.1093/amrx/abx004