非线性分数阶Schrodinger方程组的同步向量解  

Segregated Vector Solutions for Nonlinear Fractional Schrodinger Systems

作　　者：童航江 郭青[1] TONG Hangjiang;GUO Qing(College of Science,Minzu University of China,Bejing 100081,China)

机构地区：[1]中央民族大学理学院,北京100081

出　　处：《中央民族大学学报（自然科学版）》2023年第3期21-27,33,共8页Journal of Minzu University of China(Natural Sciences Edition)

摘　　要：本文主要研究下面非线性分数阶Schrodinger方程组{-iδ/δtΦ_(j)=(-△)^(s)Φ_(j)-V_(j)(x)Φ_(j)+μ_(j)|Φ_(j)|^(2)Φ_(j)+Φ_(j)∑^(N)_(l=1,k≠j)|Φ_(l)|^(2),x∈R^(R)Φ_(j)=Φ_(j)(x,t)∈C,t>0,j=1,…,N其中s∈(0,1),P(x)=P(|x|)和Q(x)=Q(|x|)是连续正的径向对称函数,μ>0,ν>0和β∈R是耦合常数。(-Δ)^(s)是非局部算子,在吸引情况下,我们构造了无穷多个正的同步向量解。In this paper,we study the following nonlinear fractional Schrodinger equations{-iδ/δtΦ_(j)=(-△)^(s)Φ_(j)-V_(j)(x)Φ_(j)+μ_(j)|Φ_(j)|^(2)Φ_(j)+Φ_(j)∑^(N)_(l=1,k≠j)|Φ_(l)|^(2),x∈R^(R)Φ_(j)=Φ_(j)(x,t)∈C,t>0,j=1,…,NWhere s∈(0,1),P(x)=P(|x|)and Q(x)=Q(|x|)are continuous positive radial function,μ>0,ν>0 andβ∈R is a coupling constant,(-Δ)^(s) is a non-local operator.In the case of attraction,we construct an unbounded sequence of non-radial positive vector solutions of synchronized type.

关 键 词：SCHRODINGER方程组 分数阶 同步解 

分 类 号：O175.29[理学—数学]