Asymptotic stability of N-solitons in the cubic NLS equation
نویسندگان
چکیده
منابع مشابه
Asymptotic Stability of Small Solitons to 1d Nls with Potential
We consider asymptotic stability of a small solitary wave to supercritical 1-dimensional nonlinear Schrödinger equations iut + uxx = V u ± |u| u for (x, t) ∈ R × R, in the energy class. This problem was studied by Gustafson-Nakanishi-Tsai [16] in the 3-dimensional case using the endpoint Strichartz estimate. To prove asymptotic stability of solitary waves, we need to show that a dispersive part...
متن کاملAsymptotic stability of solitons for the Benjamin-Ono equation
In this paper, we prove the asymptotic stability of the family of solitons of the Benjamin-Ono equation in the energy space. The proof is based on a Liouville property for solutions close to the solitons for this equation, in the spirit of [16], [18]. As a corollary of the proofs, we obtain the asymptotic stability of exact multi-solitons.
متن کاملAsymptotic Stability of N-solitons of the Fpu Lattices
We study stability of N-soliton solutions of the FPU lattice equation. Solitary wave solutions of FPU cannot be characterized as a critical point of conservation laws due to the lack of infinitesimal invariance in the spatial variable. In place of standard variational arguments for Hamiltonian systems, we use an exponential stability property of the linearized FPU equation in a weighted space w...
متن کاملApproximation of Solitons in the Discrete NLS Equation
We study four different approximations for finding the profile of discrete solitons in the one-dimensional Discrete Nonlinear Schrödinger (DNLS) Equation. Three of them are discrete approximations (namely, a variational approach, an approximation to homoclinic orbits and a Green-function approach), and the other one is a quasi-continuum approximation. All the results are compared with numerical...
متن کاملOrbital stability in the cubic defocusing NLS equation: I. Cnoidal periodic waves
Periodic waves of the one-dimensional cubic defocusing NLS equation are considered. Using tools from integrability theory, these waves have been shown in [4] to be linearly stable and the Floquet–Bloch spectrum of the linearized operator has been explicitly computed. We combine here the first four conserved quantities of the NLS equation to give a direct proof that cnoidal periodic waves are or...
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 Hyperbolic Differential Equations
سال: 2017
ISSN: 0219-8916,1793-6993
DOI: 10.1142/s0219891617500151