We study the propagation of （l＋l）-dimensional spatial soliton in a nonlocal Kerr-type medium with weak non- locality. First, we show that an equation for describing the soliton propagation in weak nonlocality is a ...We study the propagation of （l＋l）-dimensional spatial soliton in a nonlocal Kerr-type medium with weak non- locality. First, we show that an equation for describing the soliton propagation in weak nonlocality is a nonlinear Schr6dinger equation with perturbation terms. Then, an approximate analytical solution of the equation is found by the perturbation method. We also find some interesting properties of the intensity profiles of the soliton.展开更多
In this article,we consider the long-time behavior of extensible beams with nonlocal weak damping:ε(t)u_(tt)+Δ^(2)u-m(‖▽u‖^(2))Δu+‖u_(t)‖^(p_(u_(t)))+f(u)=h,whereε(t)is a decreasing function vanishing at infi...In this article,we consider the long-time behavior of extensible beams with nonlocal weak damping:ε(t)u_(tt)+Δ^(2)u-m(‖▽u‖^(2))Δu+‖u_(t)‖^(p_(u_(t)))+f(u)=h,whereε(t)is a decreasing function vanishing at infinity.Within the theory of process on time-dependent spaces,we investigate the existence of the time-dependent attractor by using the Condition(C_(t))method and more detailed estimates.The results obtained essentially improve and complete some previous works.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10474023 and 10674050)the 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 of China (Grant No 06CXTD005)
文摘We study the propagation of （l＋l）-dimensional spatial soliton in a nonlocal Kerr-type medium with weak non- locality. First, we show that an equation for describing the soliton propagation in weak nonlocality is a nonlinear Schr6dinger equation with perturbation terms. Then, an approximate analytical solution of the equation is found by the perturbation method. We also find some interesting properties of the intensity profiles of the soliton.
基金National Natural Science Foundation of China(Grant Nos.12101265,12026431,11701230,11731005)Qing Lan Project of Jiangsu Province+1 种基金the dual creative(innovative and entrepreneurial)talents project in Jiangsu Province(Grant No.JSSCBS20210973)China Postdoctoral Science Foundation(Grant No.2022M721392)。
文摘In this article,we consider the long-time behavior of extensible beams with nonlocal weak damping:ε(t)u_(tt)+Δ^(2)u-m(‖▽u‖^(2))Δu+‖u_(t)‖^(p_(u_(t)))+f(u)=h,whereε(t)is a decreasing function vanishing at infinity.Within the theory of process on time-dependent spaces,we investigate the existence of the time-dependent attractor by using the Condition(C_(t))method and more detailed estimates.The results obtained essentially improve and complete some previous works.
