Large time asymptotics for the higher-order nonlinear nonlocal Schrödinger equation

Juárez-Campos, Beatriz; Naumkin, Pavel I.

doi:10.1016/j.na.2020.112238

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2021

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“…Asymptotic behavior of the fourth-order NLS and its related equations have been studied by several researchers. See [1,2,[5][6][7][8][9][10][11][12]14,15,19] and references therein. In particular, Ben-Artzi, Koch, and Saut [2] showed the dispersive estimates for the fourth-order Schrödinger equations.…”

Section: Introductionmentioning

confidence: 99%

Long-time behavior of solutions to a fourth-order nonlinear Schrödinger equation with critical nonlinearity

Okamoto

Uriya

2021

J. Evol. Equ.

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We consider the long-time behavior of solutions to a fourth-order nonlinear Schrödinger (NLS) equation with a derivative nonlinearity. By using the method of testing by wave packets, we construct an approximate solution and show that the solution for the fourth-order NLS has the same decay estimate for linear solutions. We prove that the self-similar solution is the leading part of the asymptotic behavior.

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