共查询到20条相似文献,搜索用时 15 毫秒
1.
We consider the Cauchy problem for a cubic nonlinear Schrödinger equation in the case of an odd initial data from H2∩H0,2. We prove the global existence in time of solutions to the Cauchy problem and construct the modified asymptotics for large values of time. 相似文献
2.
We study the global Cauchy problem for nonlinear Schrödinger equations with cubic interactions of derivative type in space dimension n?3. The global existence of small classical solutions is proved in the case where every real part of the first derivatives of the interaction with respect to first derivatives of wavefunction is derived by a potential function of quadratic interaction. The proof depends on the energy estimate involving the quadratic potential and on the endpoint Strichartz estimates. 相似文献
3.
We prove the global existence of analytic solutions to the Cauchy problem for the cubic Schrödinger equation in space dimension n?3 for sufficiently small data with exponential decay at infinity. Minimal regularity assumption regarding scaling invariance is imposed on the Cauchy data. 相似文献
4.
Gongbao Li 《Journal of Differential Equations》2011,251(12):3500-3521
In this paper, we study the nonlinear Schrödinger equation with electromagnetic fields
5.
Xiaoping Yuan 《Journal of Differential Equations》2003,195(1):230-242
It is shown that there are plenty of quasi-periodic solutions of nonlinear Schrödinger equations of higher spatial dimension, where the dimension of the frequency vectors of the quasi-periodic solutions are equal to that of the space. 相似文献
6.
In the present paper, we study the Modified Nonlinear Schrödinger Equations (MNSE). Without any growth condition on the nonlinear term, we obtain the existence of infinitely many small solutions for MNSE by a dual approach. 相似文献
7.
8.
Masahito Ohta 《Journal of Functional Analysis》2011,261(1):90-110
We study the instability of bound states for abstract nonlinear Schrödinger equations. We prove a new instability result for a borderline case between stability and instability. We also reprove some known results in a unified way. 相似文献
9.
We study semiclassical states of nonlinear Schrödinger equations with anisotropic type potentials which may exhibit a combination of vanishing and singularity while allowing decays and unboundedness at infinity. We give existence of spike type standing waves concentrating at the singularities of the potentials. 相似文献
10.
A. Azzollini 《Journal of Mathematical Analysis and Applications》2008,345(1):90-108
In this paper we study the nonlinear Schrödinger-Maxwell equations
11.
This paper is concerned with the standing wave for a class of nonlinear Schrödinger equations
iφt+Δφ−2|x|φ+μ|φ|p−1φ+γ|φ|q−1φ=0, 相似文献
12.
Zhou Gang 《Advances in Mathematics》2007,216(2):443-490
In this paper we study dynamics of solitons in the generalized nonlinear Schrödinger equation (NLS) with an external potential in all dimensions except for 2. For a certain class of nonlinearities such an equation has solutions which are periodic in time and exponentially decaying in space, centered near different critical points of the potential. We call those solutions which are centered near the minima of the potential and which minimize energy restricted to L2-unit sphere, trapped solitons or just solitons. In this paper we prove, under certain conditions on the potentials and initial conditions, that trapped solitons are asymptotically stable. Moreover, if an initial condition is close to a trapped soliton then the solution looks like a moving soliton relaxing to its equilibrium position. The dynamical law of motion of the soliton (i.e. effective equations of motion for the soliton's center and momentum) is close to Newton's equation but with a dissipative term due to radiation of the energy to infinity. 相似文献
13.
The existence and concentration behavior of a nodal solution are established for the equation
14.
Nils Ackermann 《Journal of Functional Analysis》2006,234(2):277-320
In an abstract setting we prove a nonlinear superposition principle for zeros of equivariant vector fields that are asymptotically additive in a well-defined sense. This result is used to obtain multibump solutions for two basic types of periodic stationary Schrödinger equations with superlinear nonlinearity. The nonlinear term may be of convolution type. If the superquadratic term in the energy functional is convex, our results also apply in certain cases if 0 is in a gap of the spectrum of the Schrödinger operator. 相似文献
15.
Ibtissem Damergi 《Journal of Mathematical Analysis and Applications》2009,352(1):336-344
In this article we investigate the possibility of finite time blow-up in H1(R2) for solutions to critical and supercritical nonlinear Schrödinger equations with an oscillating nonlinearity. We prove that despite the oscillations some solutions blow up in finite time. Conversely, we observe that for a given initial data oscillations can extend the local existence time of the corresponding solution. 相似文献
16.
17.
By using Lions’ second concentration-compactness principle and concentration-compactness principle at infinity to prove that the (PS) condition holds locally and by minimax methods and the Krasnoselski genus theory, we establish the multiplicity of solutions for a class of quasilinear Schrödinger equations arising from physics. 相似文献
18.
Raffaella Servadei 《Journal of Mathematical Analysis and Applications》2010,365(2):776-796
The soliton dynamics for a general class of nonlinear focusing Schrödinger problems in presence of non-constant external (local and nonlocal) potentials is studied by taking as initial datum the ground state solution of an associated autonomous elliptic equation. 相似文献
19.
The traveling wave solutions of the generalized nonlinear derivative Schrödinger equation and the high-order dispersive nonlinear Schrödinger equation are studied by using the approach of dynamical systems and the theory of bifurcations. With the aid of Maple, all bifurcations and phase portraits in the parametric space are obtained. All possible explicit parametric representations of the bounded traveling wave solutions (solitary wave solutions, kink and anti-kink wave solutions and periodic wave solutions) are given. 相似文献
20.
Benjamin Dodson 《Journal of Functional Analysis》2010,258(7):2373-2421
We prove the nonlinear Schrödinger equation has a local solution for any energy - subcritical nonlinearity when u0 is the characteristic function of a ball in Rn. Additionally, we establish the existence of a global solution for n?3 when and α?2. Finally, we establish the existence of a global solution when the initial function is radial, the nonlinear Schrödinger equation has an energy subcritical nonlinearity, and the initial function lies in Hρ+?(Rn)∩H1/2+?(Rn)∩H1/2+?,1(Rn). 相似文献