A note on fourth-order nonlinear Schrödinger equation
نویسندگان
چکیده
منابع مشابه
Model order reduction for nonlinear Schrödinger equation
We apply the proper orthogonal decomposition (POD) to the nonlinear Schrödinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving symplectic midpoint rule. A priori error estimates are derived for the POD reduced dynamical system. Numerical results for one and two dimensional NLS equations...
متن کاملThe Fourth-Order Dispersive Nonlinear Schrödinger Equation: Orbital Stability of a Standing Wave
Considered in this report is the one-dimensional fourth-order dispersive cubic nonlinear Schrödinger equation with mixed dispersion. Orbital stability, in the energy space, of a particular standing-wave solution is proved in the context of Hamiltonian systems. The main result is established by constructing a suitable Lyapunov function.
متن کاملQuasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation
We consider the cubic fourth order nonlinear Schrödinger equation on the circle. In particular, we prove that the mean-zero Gaussian measures on Sobolev spaces [Formula: see text], [Formula: see text], are quasi-invariant under the flow.
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 کاملLong-time Behavior for a Nonlinear Fourth-order Parabolic Equation
We study the asymptotic behavior of solutions of the initialboundary value problem, with periodic boundary conditions, for a fourth-order nonlinear degenerate diffusion equation with a logarithmic nonlinearity. For strictly positive and suitably small initial data we show that a positive solution exponentially approaches its mean as time tends to infinity. These results are derived by analyzing...
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: Annals of Functional Analysis
سال: 2015
ISSN: 2008-8752
DOI: 10.15352/afa/06-1-19