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arXiv · 2011.02035

Global dynamics of small solutions to the modified fractional Korteweg-de Vries and nonlinear Schr\"{o}dinger equations

Jean-Claude Saut·Yuexun Wang
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Abstract

This paper concerns the modified fractional Korteweg-de Vries (modified fKdV) and nonlinear Schr\"{o}dinger (modified fNLS) equations, with the dispersions |D|^{\alpha}\partial_x and |D|^{\alpha+1}, respectively. We prove the global existence of small solutions for both the Cauchy problems to the modified fKdV and fNLS equations, with a modified scattering which has a logarithmic phase correction. Our results cover the full range -1<\alpha<1, \alpha\neq 0 for both the modified fKdV and fNLS equations.

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Jean-Claude Saut, Yuexun Wang. 2020-11-03. Global dynamics of small solutions to the modified fractional Korteweg-de Vries and nonlinear Schr\"{o}dinger equations. https://doi.org/10.1080/03605302.2021.1904416

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