We present lower bounds for the uniform radius of spatial analyticity of solutions to the fourth-order nonlinear Schrödinger equations. The main ingredients in the presentation of our results are a method of approximate conservation law in modified Gevrey spaces, Strichartz-type estimates, and Sobolev embedding.
BaşakoğluE.GrürelT. B.YılmazO. (2023). Global well-posedness for the fourth-order nonlinear Schrödinger equations on , arXiv preprint. https://doi.org/10.48550/arXiv.2308.06210
2.
CuiS.GuoC. (2007). Well-posedness of higher-order nonlinear Schrödinger equations in Sobolev spaces and applications. Nonlinear Analysis, 67(3), 687–707. https://doi.org/10.1016/j.na.2006.06.020
3.
DuferaT. T.MebrateS.TesfahunA. (2022). On the persistence of spatial analyticity for the beam equation. Journal of Mathematical Analysis and Applications, 509, 126001. https://doi.org/10.1016/j.jmaa.2022.126001
4.
EsfahaniA.TesfahunA. (2024). Well-posedness and analyticity of solutions for the sixth-order Boussinesq equation. Communications in Contemporary Mathematics, 27, 2450005. https://doi.org/10.1142/S0219199724500056
5.
FigueiraR. O.PantheeM. (2024). New lower bounds for the radius of analyticity for the mKdV equation and a system of mKdV-type equations. Journal of Evolution Equations, 24, 42. https://doi.org/10.1007/s00028-024-00977-4
6.
FoiasC.TemamR. (1989). Gevrey class regularity for the solutions of the Navier–Stokes equations. Journal of Functional Analysis, 87, 359–369. http://doi.org/10.1016/0022-1236(89)90015-3
7.
GetachewT.BelaynehB. (2024). New asymptotic lower bound for the radius of analyticity of solutions to nonlinear Schrödinger equation. Analysis and Applications, 22(5), 815–832. https://doi.org/10.1142/S0219530524500039
8.
GetachewT.BelaynehB.TesfahunA. (2024). Propagation of radius of analyticity for solutions to a fourth order nonlinear Schrödinger equation. The Mathematical Methods in the Applied Sciences, 47, 14867–14877. https://doi.org/10.1002/mma.10309
9.
GuoC. (2010). Global existence of solutions for a fourth-order nonlinear Schrödinger equation in dimensions. Nonlinear Analysis: Theory, Methods & Applications, 73(2), 555–563. https://doi.org/10.1016/j.na.2010.03.052
10.
KarpmanV. (1996). Lyapunov approach to the soliton stability in highly dispersive systems. I. Fourth order nonlinear Schrödinger equations. Physics Letters A, 215(5-6), 254–256. https://doi.org/10.1016/0375-9601(96)00231-9
11.
KarpmanV.ShagalovA. (2000). Stability of solitons described by nonlinear Schrödinger–type equations with higher-order dispersion. Journal of Physics D, 144(1-2), 194–210. https://doi.org/10.1016/S0167-2789(00)00078-6
12.
KatznelsonY. (1976). An introduction to harmonic analysis. Dover Publications, Inc.
13.
MebrateS.DuferaT. T.TesfahunA. (2024). Improved lower bound for the radius of analyticity of solutions to the fifth order, KdV-BBM type equation. Bulletin of the Iranian Mathematical Society, 50(4), 62. https://doi.org/10.1007/s41980-024-00882-z
14.
SelbergS.da SilvaD. O. (2015). Lower bounds on the radius of spatial analyticity for the KdV equation. Annales Henri Poincaré, 18(3), 1009–1023.
15.
SelbergS.TesfahunA. (2015). On the radius of spatial analyticity for the 1d Dirac–Klien–Gordon equations. Journal of Difference Equations, 259, 4732–4744. https://doi.org/10.1016/j.jde.2015.06.007
16.
TaoT. (2006). Nonlinear dispersive equations: Local and global analysis. Proceedings of the American Mathematical Society, 2006, 106. https://doi.org/10.1090/cbms/106
17.
TesfahunA. (2017). On the radius of spatial analyticity for cubic nonlinear Schrödinger equations. Journal of Differential Equations, 263(11), 7496–7512. https://doi.org/10.1016/j.jde.2017.08.009
18.
TesfahunA. (2019). Asymptotic lower bound for the radius of spatial analyticity to solutions of KdV equation. Communications in Contemporary Mathematics, 21(8), 1850061. https://doi.org/10.1142/S021919971850061X
19.
TesfahunA. (2019). Remark on the persistence of spatial analyticity for cubic nonlinear Schrödinger equation on the circle. Nonlinear Differential Equations and Applications NoDEA, 26(2), 1–13. https://doi.org/10.1007/s00030-019-0558-6
20.
ZhangZ.DengY.LiX. (2024). New lower bounds on the radius of spatial analyticity for the higher order nonlinear dispersive equation on the real line. Journal of Mathematical Physics, 65, 081501. https://doi.org/10.1063/5.0211479