384 research outputs found
Existence and Stability of standing waves for supercritical NLS with a Partial Confinement
We prove the existence of orbitally stable ground states to NLS with a
partial confinement together with qualitative and symmetry properties. This
result is obtained for nonlinearities which are -supercritical, in
particular we cover the physically relevant cubic case. The equation that we
consider is the limit case of the cigar-shaped model in BEC.Comment: Revised version, accepted on Comm. Math. Physic
Existence and multiplicity for elliptic problems with quadratic growth in the gradient
We show that a class of divergence-form elliptic problems with quadratic
growth in the gradient and non-coercive zero order terms are solvable, under
essentially optimal hypotheses on the coefficients in the equation. In
addition, we prove that the solutions are in general not unique. The case where
the zero order term has the opposite sign was already intensively studied and
the uniqueness is the rule.Comment: To appear in Comm. PD
Global bifurcation for asymptotically linear Schr\"odinger equations
We prove global asymptotic bifurcation for a very general class of
asymptotically linear Schr\"odinger equations \begin{equation}\label{1}
\{{array}{lr} \D u + f(x,u)u = \lam u \quad \text{in} \ {\mathbb R}^N, u \in
H^1({\mathbb R}^N)\setmimus\{0\}, \quad N \ge 1. {array}. \end{equation} The
method is topological, based on recent developments of degree theory. We use
the inversion in an appropriate Sobolev space
, and we first obtain bifurcation from the line of
trivial solutions for an auxiliary problem in the variables (\lambda,v) \in
{\mathbb R} \x X. This problem has a lack of compactness and of regularity,
requiring a truncation procedure. Going back to the original problem, we obtain
global branches of positive/negative solutions 'bifurcating from infinity'. We
believe that, for the values of covered by our bifurcation approach,
the existence result we obtain for positive solutions of \eqref{1} is the most
general so fa
On a functional satisfying a weak Palais-Smale condition
In this paper we study a quasilinear elliptic problem whose functional
satisfies a weak version of the well known Palais-Smale condition. An existence
result is proved under general assumptions on the nonlinearities.Comment: 18 page
Symbiotic Bright Solitary Wave Solutions of Coupled Nonlinear Schrodinger Equations
Conventionally, bright solitary wave solutions can be obtained in
self-focusing nonlinear Schrodinger equations with attractive self-interaction.
However, when self-interaction becomes repulsive, it seems impossible to have
bright solitary wave solution. Here we show that there exists symbiotic bright
solitary wave solution of coupled nonlinear Schrodinger equations with
repulsive self-interaction but strongly attractive interspecies interaction.
For such coupled nonlinear Schrodinger equations in two and three dimensional
domains, we prove the existence of least energy solutions and study the
location and configuration of symbiotic bright solitons. We use Nehari's
manifold to construct least energy solutions and derive their asymptotic
behaviors by some techniques of singular perturbation problems.Comment: to appear in Nonlinearit
Multi-solitary waves for the nonlinear Klein-Gordon equation
International audienceWe consider the nonlinear Klein-Gordon equation in . We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the composing boosted standing waves are stable. It is obtained by solving the equation backward in time around a sequence of approximate multi-solitary waves and showing convergence to a solution with the desired property. The main ingredients of the proof are finite speed of propagation, variational characterizations of the profiles, modulation theory and energy estimates
Long time dynamics and coherent states in nonlinear wave equations
We discuss recent progress in finding all coherent states supported by
nonlinear wave equations, their stability and the long time behavior of nearby
solutions.Comment: bases on the authors presentation at 2015 AMMCS-CAIMS Congress, to
appear in Fields Institute Communications: Advances in Applied Mathematics,
Modeling, and Computational Science 201
On the stability of standing waves of Klein-Gordon equations in a semiclassical regime
We investigate the orbital stability and instability of standing waves for
two classes of Klein-Gordon equations in the semi-classical regime.Comment: 9 page
Parallel declines in species and genetic diversity driven by anthropogenic disturbance: a multispecies approach in a French Atlantic dune system.
Numerous studies assess the correlation between genetic and species diversities, but the processes underlying the observed patterns have only received limited attention. For instance, varying levels of habitat disturbance across a region may locally reduce both diversities due to extinctions, and increased genetic drift during population bottlenecks and founder events. We investigated the regional distribution of genetic and species diversities of a coastal sand dune plant community along 240 kilometers of coastline with the aim to test for a correlation between the two diversity levels. We further quantify and tease apart the respective contributions of natural and anthropogenic disturbance factors to the observed patterns. We detected significant positive correlation between both variables. We further revealed a negative impact of urbanization: Sites with a high amount of recreational infrastructure within 10 km coastline had significantly lowered genetic and species diversities. On the other hand, a measure of natural habitat disturbance had no effect. This study shows that parallel variation of genetic and species diversities across a region can be traced back to human landscape alteration, provides arguments for a more resolute dune protection, and may help to design priority conservation areas
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