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math.AP2026
Scattering of non-radial solutions for the fourth-order Schrödinger equation with -critical and supercritical nonlinearity
Takahisa Inui, Koichi Komada, Kuranosuke Nishimura
We consider the focusing nonlinear fourth-order Schrödinger equation \begin{equation*} i \partial_t u + μΔu - Δ^2 u = - |u|^{p-1} u, \ \ \ (t,x) \in \mathbb{R} \times \mathbb{R}^d,…
math.AP2026
Scattering for the quadratic NLS system in without mass resonance or radial symmetry
Takahisa Inui, Kuranosuke Nishimura
We consider the quadratic NLS system \begin{equation*} \begin{cases} i\partial_tu+Δu=v\bar{u},\newline i\partial_tv+κΔv=u^2, \end{cases} \qquad (t,x)\in\mathbb{R}\times\mathbb{R}^5…