TY - JOUR

T1 - Modified scattering for the higher-order anisotropic nonlinear Schrödinger equation in two space dimensions

AU - Hayashi, Nakao

AU - Naumkin, Pavel I.

N1 - Funding Information:
The work of N.H. was partially supported by JSPS KAKENHI under Grant Nos. JP20K03680 and JP19H05597. The work of P.I.N. was partially supported by CONACYT Project No. 283698 and PAPIIT Project No. IN103221.
Publisher Copyright:
© 2021 Author(s).

PY - 2021/7/1

Y1 - 2021/7/1

N2 - We study the asymptotic behavior of solutions to the Cauchy problem for the higher-order anisotropic nonlinear Schrödinger equation in two space dimensions. 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.

AB - We study the asymptotic behavior of solutions to the Cauchy problem for the higher-order anisotropic nonlinear Schrödinger equation in two space dimensions. 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.

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U2 - 10.1063/5.0052299

DO - 10.1063/5.0052299

M3 - Article

AN - SCOPUS:85109036388

SN - 0022-2488

VL - 62

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 7

M1 - 071502

ER -