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arXiv · 2609.33381

Scattering of group-invariant solutions below the ground state for the fourth-order NLS

Koichi Komada
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Abstract

We consider the focusing, $L^2$-supercritical and $\dot{H}^2$-subcritical nonlinear fourth-order Schrödinger equation. The scattering of radially symmetric solutions below the ground state was proved by Guo [Comm. Partial Differential Equations (2016)] and Dinh [Nonlinearity (2021)]. In this paper, we extend the scattering results to group-invariant solutions. In Komada--Masaki [Nonlinearity (2024)], the scattering of group-invariant solutions below the ground state was proved under a certain hypothesis. To remove the hypothesis, we establish the non-optimal scattering result for general solutions, where the threshold of action is less than certain fraction of the action of the ground state. This result is analogous to that in Pausader--Shao [J. Hyperbolic Differ. Equ. (2010)] for the $L^2$-critical nonlinear fourth-order Schrödinger equation.

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Koichi Komada. 2026-09-27. Scattering of group-invariant solutions below the ground state for the fourth-order NLS. https://arxiv.org/abs/2609.33381

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