We make a quantitative study on the soliton interactions in the nonlinear Schro¨dinger equation(NLSE) and its variable–coefficient(vc) counterpart. For the regular two-soliton and double-pole solutions of the NL...We make a quantitative study on the soliton interactions in the nonlinear Schro¨dinger equation(NLSE) and its variable–coefficient(vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities(especially the soliton accelerations and interaction forces);whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles,particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics.展开更多
In this paper,we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p-Laplacian systems.By virtue of this method,we investigate t...In this paper,we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p-Laplacian systems.By virtue of this method,we investigate the qualitative properties of positive solutions for the following Schrodinger system with fractional p-Laplacian{(-△)^(s)_(p)u+au^(p-1)=f(u,v),(-△)^(t)_(p)v+bv(p-1)=g(u,v),where 0<s,t<1 and 2<p<∞.We obtain the radial symmetry in the unit ball or the whole space R^(N)(N≥2),the monotonicity in the parabolic domain and the nonexistence on the half space for positive solutions to the above system under some suitable conditions on f and g,respectively.展开更多
The conditions of blow_up of the solutions for one class of nonlinear Schrdinger equations by using the eigenvalue and eigenfunction of the Laplace operator are got, which complements and perfects the results of ZHA...The conditions of blow_up of the solutions for one class of nonlinear Schrdinger equations by using the eigenvalue and eigenfunction of the Laplace operator are got, which complements and perfects the results of ZHANG Jian.展开更多
In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence ...In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence of a ground state solution forλ>0 large enough.Furthermore,we verify the asymptotic behavior of ground state solutions asλ→+∞.展开更多
Based on the methods introduced by Klainerman and Ponce, and Cohn, a lower bounded estimate of the existence time for a kind of semilinear Schrdinger equation is obtained in this paper. The implementation of this me...Based on the methods introduced by Klainerman and Ponce, and Cohn, a lower bounded estimate of the existence time for a kind of semilinear Schrdinger equation is obtained in this paper. The implementation of this method depends on the L p-L q estimate and the energy estimate.展开更多
In this article, we consider the well-posedness of a coherently coupled Schrdinger system with four waves mixing in space dimension n ≤ 4. The Cauchy problem for the cubic system is studied in L^2 for n ≤ 2 and in...In this article, we consider the well-posedness of a coherently coupled Schrdinger system with four waves mixing in space dimension n ≤ 4. The Cauchy problem for the cubic system is studied in L^2 for n ≤ 2 and in H^1 for n ≤ 4. We obtain two sharp conditions between global existence and blow up.展开更多
基金Project supported by the Natural Science Foundation of Beijing Municipality (Grant No.1212007)the National Natural Science Foundation of China (Grant No.11705284)the Open Project Program of State Key Laboratory of Petroleum Resources and Prospecting,China University of Petroleum (Grant No.PRP/DX-2211)。
文摘We make a quantitative study on the soliton interactions in the nonlinear Schro¨dinger equation(NLSE) and its variable–coefficient(vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities(especially the soliton accelerations and interaction forces);whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles,particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics.
基金Supported by the National Natural Science Foundation of China(12101452,12071229,11771218)。
文摘In this paper,we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p-Laplacian systems.By virtue of this method,we investigate the qualitative properties of positive solutions for the following Schrodinger system with fractional p-Laplacian{(-△)^(s)_(p)u+au^(p-1)=f(u,v),(-△)^(t)_(p)v+bv(p-1)=g(u,v),where 0<s,t<1 and 2<p<∞.We obtain the radial symmetry in the unit ball or the whole space R^(N)(N≥2),the monotonicity in the parabolic domain and the nonexistence on the half space for positive solutions to the above system under some suitable conditions on f and g,respectively.
文摘The conditions of blow_up of the solutions for one class of nonlinear Schrdinger equations by using the eigenvalue and eigenfunction of the Laplace operator are got, which complements and perfects the results of ZHANG Jian.
基金supported by National Natural Science Foundation of China(11971393)。
文摘In this paper,we investigate a class of nonlinear Chern-Simons-Schr?dinger systems with a steep well potential.By using variational methods,the mountain pass theorem and Nehari manifold methods,we prove the existence of a ground state solution forλ>0 large enough.Furthermore,we verify the asymptotic behavior of ground state solutions asλ→+∞.
文摘Based on the methods introduced by Klainerman and Ponce, and Cohn, a lower bounded estimate of the existence time for a kind of semilinear Schrdinger equation is obtained in this paper. The implementation of this method depends on the L p-L q estimate and the energy estimate.
基金supported by the China National Natural Science Foundation under grant number 11171357
文摘In this article, we consider the well-posedness of a coherently coupled Schrdinger system with four waves mixing in space dimension n ≤ 4. The Cauchy problem for the cubic system is studied in L^2 for n ≤ 2 and in H^1 for n ≤ 4. We obtain two sharp conditions between global existence and blow up.
