A Fourier Integrator for the Cubic Nonlinear Schrödinger Equation with Rough Initial Data
نویسندگان
چکیده
منابع مشابه
Instabilities in the two-dimensional cubic nonlinear Schrödinger equation.
The two-dimensional cubic nonlinear Schrödinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional traveling wave solution of NLS with linear phase is unstable with respect to some infinitesimal perturbation with two-dimensional structure. If the coefficients ...
متن کاملDrag force in bimodal cubic-quintic nonlinear Schrödinger equation.
We consider a system of two cubic-quintic nonlinear Schrödinger equations in two dimensions, coupled by repulsive cubic terms. We analyze situations in which a probe lump of one of the modes is surrounded by a fluid of the other one and analyze their interaction. We find a realization of D'Alembert's paradox for small velocities and nontrivial drag forces for larger ones. We present numerical a...
متن کاملLow Regularity Local Well-Posedness of the Derivative Nonlinear Schrödinger Equation with Periodic Initial Data
The Cauchy problem for the derivative nonlinear Schrödinger equation with periodic boundary condition is considered. Local well-posedness for data u0 in the space b H r (T), defined by the norms ‖u0‖ b Hs r (T) = ‖〈ξ〉 s b u0‖lr′ ξ , is shown in the parameter range s ≥ 1 2 , 2 > r > 4 3 . The proof is based on an adaptation of the gauge transform to the periodic setting and an appropriate varian...
متن کاملBreathers for the Discrete Nonlinear Schrödinger Equation with Nonlinear Hopping
We discuss the existence of breathers and lower bounds on their power, in nonlinear Schrödinger lattices with nonlinear hopping. Our methods extend from a simple variational approach to fixed-point arguments, deriving lower bounds for the power which can serve as a threshold for the existence of breather solutions. Qualitatively, the theoretical results justify non-existence of breathers below ...
متن کاملCauchy Problem of Nonlinear Schrödinger Equation with Initial Data in Sobolev Space W
In this paper, we consider in R the Cauchy problem for nonlinear Schrödinger equation with initial data in Sobolev space W s,p for p < 2. It is well known that this problem is ill posed. However, We show that after a linear transformation by the linear semigroup the problem becomes locally well posed in W s,p for 2n n+1 < p < 2 and s > n(1− 1 p ). Moreover, we show that in one space dimension, ...
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: SIAM Journal on Numerical Analysis
سال: 2019
ISSN: 0036-1429,1095-7170
DOI: 10.1137/18m1198375