In this paper,we provide the boundedness property of the Riesz transforms associated to the Schrodinger operator■=-Δ+V in a new weighted Morrey space which is the generalized version of many previous Morrey type spa...In this paper,we provide the boundedness property of the Riesz transforms associated to the Schrodinger operator■=-Δ+V in a new weighted Morrey space which is the generalized version of many previous Morrey type spaces.The additional potential V considered in this paper is a non-negative function satisfying the suitable reverse Holder's inequality.Our results are new and general in many cases of problems.As an application of the boundedness property of these singular integral operators,we obtain some regularity results of solutions to Schrodinger equations in the new Morrey space.展开更多
We present three families of soliton solutions to the generalized （3＋l）-dimensional nonlinear Schrodinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics wi...We present three families of soliton solutions to the generalized （3＋l）-dimensional nonlinear Schrodinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters. Different shapes of bright solitons, a train of bright solitons and dark solitons are observed. The obtained results may raise the possibilities of relevant experiments and potential applications.展开更多
This paper discusses nonlinear SchrSdinger equation with a harmonic potential. By constructing a different cross-constrained variational problem and the so-called invariant sets, we derive a new threshold for blow-up ...This paper discusses nonlinear SchrSdinger equation with a harmonic potential. By constructing a different cross-constrained variational problem and the so-called invariant sets, we derive a new threshold for blow-up and global existence of solutions.展开更多
文摘In this paper,we provide the boundedness property of the Riesz transforms associated to the Schrodinger operator■=-Δ+V in a new weighted Morrey space which is the generalized version of many previous Morrey type spaces.The additional potential V considered in this paper is a non-negative function satisfying the suitable reverse Holder's inequality.Our results are new and general in many cases of problems.As an application of the boundedness property of these singular integral operators,we obtain some regularity results of solutions to Schrodinger equations in the new Morrey space.
基金supported by the Zhejiang Provincial Natural Science Foundations,China(Grant No.Y6090592)the National Natural Science Foundation of China(Grant Nos.11041003 and 10735030)+1 种基金the Ningbo Natural Science Foundation,China(Grant Nos.2010A610095,2010A610103,and 2009B21003)K.C.Wong Magna Fund in Ningbo University,China
文摘We present three families of soliton solutions to the generalized （3＋l）-dimensional nonlinear Schrodinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters. Different shapes of bright solitons, a train of bright solitons and dark solitons are observed. The obtained results may raise the possibilities of relevant experiments and potential applications.
基金Supported by the National Natural Science Foundation of China （No. 10747148, No. 10771151） and the Scientific Research Fund of Sichuan Provinciul Education Department （08ZA041）
文摘This paper discusses nonlinear SchrSdinger equation with a harmonic potential. By constructing a different cross-constrained variational problem and the so-called invariant sets, we derive a new threshold for blow-up and global existence of solutions.
