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• W4328107756 abstract "We study the large time asymptotic behavior of solutions to the Cauchy problem for the fractional derivative nonlinear Schrödinger equation in one space dimension{i∂tu−1α|∂x|αu=iλ∂x(|u|2u),t>0,x∈R,u(0,x)=u0(x),x∈R,where α∈(0,1)∪(1,2)∪(2,3), and λ∈R. The fractional derivative |∂x|α=F−1|ξ|αF, where F stands for the Fourier transformation ϕˆ(ξ)=12π∫Re−ixξϕ(x)dx, and F−1 is the inverse Fourier transformation. Equation (1.1) with α=2 is the derivative NLS equation and studied extensively. The case of α=1 corresponds to the so-called derivative half-wave equation. We prove that the modified scattering of solutions occurs when 0<α<3 without the exceptional point α=1." @default.
• W4328107756 created "2023-03-22" @default.
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• W4328107756 date "2023-09-01" @default.
• W4328107756 modified "2023-10-16" @default.
• W4328107756 title "Modified scattering for the derivative fractional nonlinear Schrödinger equation" @default.
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• W4328107756 doi "https://doi.org/10.1016/j.jmaa.2023.127222" @default.
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