Modified scattering for the higher-order anisotropic nonlinear Schrödinger equation in two space dimensions
- 1 July 2021
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 62 (7), 071502
- https://doi.org/10.1063/5.0052299
Abstract
We study the asymptotic behavior of solutions to the Cauchy problem for the higher-order anisotropic nonlinear Schrödinger equation in two space dimensions , t > 0, with initial data , where . We will show the modified scattering for solutions. We continue to develop the factorization techniques, which were started in the papers of N. Hayashi and P. I. Naumkin [Z. Angew. Math. Phys. 59(6), 1002–1028 (2008); J. Math. Phys. 56(9), 093502 (2015)], N. Hayashi and T. Ozawa [Ann. I.H.P.: Phys. Theor. 48, 17–37 (1988)], and T. Ozawa [Commun. Math. Phys. 139(3), 479–493 (1991)]. The crucial point of our approach presented here is the L2-boundedness of the pseudodifferential operators.
Keywords
Funding Information
- Consejo Nacional de Ciencia y Tecnología (283698)
- Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica (IN103221)
- Japan Society for the Promotion of Science (JP20K03680, JP19H05597)
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