Symmetric exponential integrators for the cubic Schrödinger equation
نویسندگان
چکیده
preprint numerics no. 3/2006 norwegian university of science and technology trondheim, norway
منابع مشابه
Symmetric Exponential Integrators with an Application to the Cubic Schrödinger Equation
In this article, we derive and study symmetric exponential integrators. Numerical experiments are performed for the cubic Schrödinger equation and comparisons with classical exponential integrators and other geometric methods are also given. Some of the proposed methods preserve the L2-norm and/or the energy of the system.
متن کاملConservation of phase space properties using exponential integrators on the cubic Schrödinger equation
preprint numerics no. 1/2006 norwegian university of science and technology trondheim, norway The cubic nonlinear Schrödinger (nls) equation with periodic boundary conditions is solvable using Inverse Spectral Theory. The " nonlinear " spectrum of the associated Lax pair reveals topological properties of the nls phase space that are difficult to assess by other means. In this paper we use the i...
متن کاملOn Instability for the Quintic Nonlinear Schrödinger Equation of Some Approximate Periodic Solutions
Using the Fermi Golden Rule analysis developed in [CM], we prove asymptotic stability of asymmetric nonlinear bound states bifurcating from linear bound states for a quintic nonlinear Schrödinger operator with symmetric potential. This goes in the direction of proving that the approximate periodic solutions for the cubic Nonlinear Schrödinger Equation (NLSE) with symmetric potential in [MW] do ...
متن کاملErgodicity for the Weakly Damped Stochastic Non-linear Schrödinger Equations
We study a damped stochastic non-linear Schrödinger (NLS) equation driven by an additive noise. It is white in time and smooth in space. Using a coupling method, we establish convergence of the Markovian transition semi-group toward a unique invariant probability measure. This kind of method was originally developped to prove exponential mixing for strongly dissipative equations such as the Nav...
متن کاملThe Cubic Nonlinear Schrödinger Equation in Two Dimensions with Radial Data
We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iut +∆u = ±|u|u for large spherically symmetric Lx(R ) initial data; in the focusing case we require, of course, that the mass is strictly less than that of the ground state. As a consequence, we deduce that in the focusing case, any spherically symmetric blowup solution must conc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006