From the study of the dynamics for the ring-like soliton clusters, we find that there exists a critical value of the ring radius, dcr, for the stationary rotation of the clusters with respect to the beam centre even i...From the study of the dynamics for the ring-like soliton clusters, we find that there exists a critical value of the ring radius, dcr, for the stationary rotation of the clusters with respect to the beam centre even in the presence of the relatively strong noise, and that the soliton clusters will not rotate but only undergo periodic collisions in the form of simple harmonic oscillator if the ring radius is large enough. We also show that the direction of the rotation can be opposite to the direction of phase gradient when the relative phase difference is within the domain 0 〈 ｜θ｜ 〈 π, while along the direction of phase gradient when the relative phase difference is within the domain π 〈｜θ｜ 〈 2π展开更多
A qualitative analysis method to efficiently solve the shallow wave equations is improved, so that a more complicated nonlinear Schr6dinger equation can be considered. By using the detailed study, some quite strange o...A qualitative analysis method to efficiently solve the shallow wave equations is improved, so that a more complicated nonlinear Schr6dinger equation can be considered. By using the detailed study, some quite strange optical solitary waves are obtained in which the bright and dark optical solitary waves are allowed to coexist.展开更多
This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the li...This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ = {u ∈ H^1; fRN ｜x｜^2｜u｜^2dx 〈 ＋∞）}. Moreover, an interesting concentration property of the blow-up solutions with critical mass is gotten, which reads that ｜u（t, x）｜^2→ ｜｜Q｜｜L^2 2 δx=x1 as t → T.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos 10474023 and 10674050)Specialized Research Fund for the Doctoral Program of Higher Education,China (Grant No 20060574006)the Program for Innovative Research Team of the Higher Education in Guangdong Province,China (Grant No 06CXTD005)
文摘From the study of the dynamics for the ring-like soliton clusters, we find that there exists a critical value of the ring radius, dcr, for the stationary rotation of the clusters with respect to the beam centre even in the presence of the relatively strong noise, and that the soliton clusters will not rotate but only undergo periodic collisions in the form of simple harmonic oscillator if the ring radius is large enough. We also show that the direction of the rotation can be opposite to the direction of phase gradient when the relative phase difference is within the domain 0 〈 ｜θ｜ 〈 π, while along the direction of phase gradient when the relative phase difference is within the domain π 〈｜θ｜ 〈 2π
基金supported by the National Natural Science Foundation of China (Grant No. 11101191)
文摘A qualitative analysis method to efficiently solve the shallow wave equations is improved, so that a more complicated nonlinear Schr6dinger equation can be considered. By using the detailed study, some quite strange optical solitary waves are obtained in which the bright and dark optical solitary waves are allowed to coexist.
基金Supported by National Science Foundation of China (11071177)Excellent Youth Foundation of Sichuan Province (2012JQ0011)
文摘This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ = {u ∈ H^1; fRN ｜x｜^2｜u｜^2dx 〈 ＋∞）}. Moreover, an interesting concentration property of the blow-up solutions with critical mass is gotten, which reads that ｜u（t, x）｜^2→ ｜｜Q｜｜L^2 2 δx=x1 as t → T.
