Modified scattering for subcritical fractional dNLS equations with order $$\alpha \in \left( 0,1\right) \cup \left( 1,\frac{3}{2}\right] $$
Year: 2026
Type: article
Abstract: We investigate the global in time existence of small solutions to the Cauchy problem for the subcritical fractional derivative nonlinear Schrödinger equation $$ \left\{ \begin{array}{c} i\partial _{t}u-\frac{1}{\alpha }\left| \partial _{x}\right| ^{\alpha } u=it^{\nu }\partial _{x}\left( \left| u\right| ^{2}u\right) ,\text t>0\textbf{,}x\in \mathbb {R},\\ u\left( 0,x\right) =u_{0}\left( x\right) ,\,x\in \mathbb {R}\textbf{,} \end{array} \right. $$ i ∂ t u - 1 α ∂ x α u = i t ν ∂ x u 2 u , t > 0 , x ∈ R , u 0 , x = u 0 x , x ∈ R , where $$\alpha \in \left( 0,1\right) \cup \left( 1,\frac{3}{2}\right] $$ α ∈ 0 , 1 ∪ 1 , 3 2 and $$0<\nu <\frac{1}{24}$$ 0 < ν < 1 24 . The parameter $$\nu >0$$ ν > 0 reflects the subcritical nature of the nonlinearity with respect to the large time asymptotic behavior of solutions. We assume that the initial data $$u_{0}$$ u 0 admits a small analytic extension in a suitable sector of the complex plane. Under these assumptions, we derive the precise large time asymptotics of the global solution.
Authors: Nakao Hayashi, Pavel I. Naumkin
Institutions: The University of Osaka, Centro de Ciencias Matemáticas
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,590
OpenAlex ID: W7118315607