Randomized trial establishes global well-posedness in modulation space for fourth-order nonlinear Schrödinger equation, suggesting a robust theoretical framework.
The local and global well-posedness for the one dimensional fourth-order nonlinear Schrödinger equation are established in the modulation space [Formula: see text] for [Formula: see text] and [Formula: see text]. The local result is based on the [Formula: see text] spaces and crucial bilinear estimates. The key ingredient to obtain the global well-posedness is that we achieve a priori estimates of the solution in modulation spaces by utilizing the power series expansion of the perturbation determinant introduced by Killip–Vişan–Zhang for completely integrable PDEs.
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Chen et al. (2026) studied this question.
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