Doubly nonlocal system with Hardy–Littlewood–Sobolev critical nonlinearity
نویسندگان
چکیده
منابع مشابه
Dispersive shock waves with nonlocal nonlinearity.
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
متن کاملNonlocal ponderomotive nonlinearity in plasmonics.
We analyze an inherent nonlinearity of surface plasmon polaritons at the interface of Fermi-Dirac metal plasma, stemming from the depletion of electron density in high-intensity regions. The derived optical nonlinear coefficients are comparable with the experimental values for metals. We calculate the dispersion relations for the nonlinear propagation of high-intensity surface plasmon polariton...
متن کاملDoubly periodic waves of a discrete nonlinear Schrödinger system with saturable nonlinearity
A system of two discrete nonlinear Schrödinger equations of the Ablowitz-Ladik type with a saturable nonlinearity is shown to admit a doubly periodic wave, whose long wave limit is also derived. As a by-product, several new solutions of the elliptic type are provided for NLS-type discrete and continuous systems.
متن کاملPlanar Traveling Waves for Nonlocal Dispersion Equation with Monostable Nonlinearity
In this paper, we study a class of nonlocal dispersion equation with monostable nonlinearity in n-dimensional space ut − J ∗ u+ u+ d(u(t, x)) = ∫ Rn fβ(y)b(u(t− τ, x− y))dy, u(s, x) = u0(s, x), s ∈ [−τ, 0], x ∈ Rn, where the nonlinear functions d(u) and b(u) possess the monostable characters like Fisher-KPP type, fβ(x) is the heat kernel, and the kernel J(x) satisfies Ĵ(ξ) = 1 − K|ξ|α + o(|ξ|...
متن کاملDamped Wave Equation with a Critical Nonlinearity
We study large time asymptotics of small solutions to the Cauchy problem for nonlinear damped wave equations with a critical nonlinearity { ∂2 t u+ ∂tu−∆u+ λu 2 n = 0, x ∈ Rn, t > 0, u(0, x) = εu0 (x) , ∂tu(0, x) = εu1 (x) , x ∈ Rn, where ε > 0, and space dimensions n = 1, 2, 3. Assume that the initial data u0 ∈ H ∩H, u1 ∈ Hδ−1,0 ∩H−1,δ, where δ > n 2 , weighted Sobolev spaces are H = { φ ∈ L; ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2018
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2018.07.035