KdV type asymptotics for solutions to higher-order nonlinear Schrödinger equations
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We consider the Cauchy problem for the higher-order nonlinear Schrödinger equation
i∂tu - α/3 |∂x|3u - b/4 ∂4xu = λi∂x(|u|2u), (t, x) ∈ ℝ+ x ℝ,
u(0, x) = u0(x), x ∈ ℝ,
where α, b > 0, |∂x|α = F-1|ξ|α F and F is the Fourier transformation. Our purpose is to study the large time behavior of the solutions under the non-zero mass condition ∫ u0(x)dx ≠ 0.
CitationNaumkin, P. I., & Sánchez-Suárez, I. (2020). KdV type asymptotics for solutions to higher-order nonlinear Schrödinger equations. Electronic Journal of Differential Equations, 2020(77), pp. 1-34.
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