The cubic fourth-order Schrödinger equation
نویسندگان
چکیده
منابع مشابه
The Cubic Fourth-order Schrödinger Equation
Fourth-order Schrödinger equations have been introduced by Karpman and Shagalov to take into account the role of small fourth-order dispersion terms in the propagation of intense laser beams in a bulk medium with Kerr nonlinearity. In this paper we investigate the cubic defocusing fourth order Schrödinger equation i∂tu +∆ 2 u + |u|u = 0 in arbitrary space dimension R for arbitrary initial data....
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 کاملDynamics of solitons and quasisolitons of the cubic third-order nonlinear Schrödinger equation.
The dynamics of soliton and quasisoliton solutions of the cubic third-order nonlinear Schrödinger equation is studied. Regular solitons exist due to a balance between the nonlinear terms and (linear) third-order dispersion; they are not important at small alpha(3) (alpha(3) is the coefficient in the third derivative term) and vanish at alpha(3)-->0. The most essential, at small alpha(3), is a q...
متن کاملFourth order real space solver for the time-dependent Schrödinger equation with singular Coulomb potential
We present a novel numerical method and algorithm for the solution of the 3D axially symmetric timedependent Schrödinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent potential. We use fourth order finite difference real space discretization, with special formulae for the arising Neumann and Robin boundary conditions along the sy...
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 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: Journal of Functional Analysis
سال: 2009
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2008.11.009