Global Attractor for the 3rd Order Lugiato-Lefever Equation on 1D Torus

来源 :非线性偏微分方程和数学物理研讨会(NPDEMP 2016) | 被引量 : 0次 | 上传用户:songfeng816
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  We consider the third order Lugiato-Lefever equation:(0.2)(e)tu-(e)3u+iα(e)2xu+u+i|u|2u=f,t>0, x∈T,(0.3)u(0,x)= u0(x),x∈T.We assume that 2α/3(∈)Z.Equation(0.2)appears as a mathematical model,for example,for Kerr frequency comb generation in a whispering gallery mode resonator,octave-spanning Kerr frequency comb in a micro-ring resonator,and cavity solitons in micro-ring resonator near zero group-dispersion.
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