Large time asymptotics for the fractional Schrödinger equation with subcritical derivative nonlinearities

Nakao Hayashi () and Pavel I. Naumkin ()
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Nakao Hayashi: Osaka University
Pavel I. Naumkin: UNAM Campus Morelia

Partial Differential Equations and Applications, 2025, vol. 6, issue 5, 1-22

Abstract: Abstract We study the global in time existence of small solutions to the Cauchy problem for the fractional nonlinear Schrödinger equation of order $$ \alpha \in \left( \frac{3}{2},3\right) $$ α ∈ 3 2 , 3 . We consider the cubic derivative nonlinearity with a time growth of order $$\nu \in \left( 0,\frac{1}{24} \right) .$$ ν ∈ 0 , 1 24 . We remark that $$\nu >0$$ ν > 0 means that the problem is considered as subcritical case in the sense of the large time asymptotic behavior of solutions. We assume that the initial data have an analytic extension on the sector and are small, then we find the large time asymptotics of the solutions with a phase correction.

Keywords: Subcritical NLS equation; Modified scattering; Asymptotics for large time; 35B40; 35Q92 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00344-z

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