111 research outputs found
Sharp thresholds of blow-up and global existence for the coupled nonlinear Schrodinger system
In this paper, we establish two new types of invariant sets for the coupled
nonlinear Schrodinger system on , and derive two sharp thresholds
of blow-up and global existence for its solution. Some analogous results for
the nonlinear Schrodinger system posed on the hyperbolic space
and on the standard 2-sphere are also presented. Our arguments
and constructions are improvements of some previous works on this direction. At
the end, we give some heuristic analysis about the strong instability of the
solitary waves.Comment: 21 page
Coupled nonlinear Schrodinger systems with potentials
Coupled nonlinear Schrodinger systems describe some physical phenomena such
as the propagation in birefringent optical fibers, Kerr-like photorefractive
media in optics and Bose-Einstein condensates. In this paper, we study the
existence of concentrating solutions of a singularly perturbed coupled
nonlinear Schrodinger system, in presence of potentials. We show how the
location of the concentration points depends strictly on the potentials.Comment: 21 page
A Bi-Hamiltonian Structure for the Integrable, Discrete Non-Linear Schrodinger System
This paper shows that the Ablowitz-Ladik hierarchy of equations (a well-known
integrable discretization of the Non-linear Schrodinger system) can be
explicitly viewed as a hierarchy of commuting flows which: (a) are Hamiltonian
with respect to both a standard, local Poisson operator J and a new non-local,
skew, almost Poisson operator K, on the appropriate space; (b) can be
recursively generated from a recursion operator R (obtained by composing K and
the inverse of J.) In addition, the proof of these facts relies upon two new
pivotal resolvent identities which suggest a general method for uncovering
bi-Hamiltonian structures for other families of discrete, integrable equations.Comment: 33 page
On the low-regularity global well-posedness of a system of nonlinear Schrodinger Equation
In this article, we study the low-regularity Cauchy problem of a one
dimensional quadratic Schrodinger system with coupled parameter . When ,we prove the global well-posedness in
with , while for , we
obtain global well-posedness in with . We
have adapted the linear-nonlinear decomposition and resonance decomposition
technique in different range of
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