On the radius of spatial analyticity for the higher order nonlinear dispersive equation

Aissa Boukarou; Kaddour Guerbati; Khaled Zennir

Mathematica Bohemica (2022)

  • Volume: 147, Issue: 1, page 19-32
  • ISSN: 0862-7959

Abstract

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In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data u 0 . The analytic initial data can be extended as holomorphic functions in a strip around the x -axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).

How to cite

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Boukarou, Aissa, Guerbati, Kaddour, and Zennir, Khaled. "On the radius of spatial analyticity for the higher order nonlinear dispersive equation." Mathematica Bohemica 147.1 (2022): 19-32. <http://eudml.org/doc/297802>.

@article{Boukarou2022,
abstract = {In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data $u_\{0\}$. The analytic initial data can be extended as holomorphic functions in a strip around the $x$-axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).},
author = {Boukarou, Aissa, Guerbati, Kaddour, Zennir, Khaled},
journal = {Mathematica Bohemica},
keywords = {higher order nonlinear dispersive equation; radius of spatial analyticity; approximate conservation law},
language = {eng},
number = {1},
pages = {19-32},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the radius of spatial analyticity for the higher order nonlinear dispersive equation},
url = {http://eudml.org/doc/297802},
volume = {147},
year = {2022},
}

TY - JOUR
AU - Boukarou, Aissa
AU - Guerbati, Kaddour
AU - Zennir, Khaled
TI - On the radius of spatial analyticity for the higher order nonlinear dispersive equation
JO - Mathematica Bohemica
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 147
IS - 1
SP - 19
EP - 32
AB - In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data $u_{0}$. The analytic initial data can be extended as holomorphic functions in a strip around the $x$-axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).
LA - eng
KW - higher order nonlinear dispersive equation; radius of spatial analyticity; approximate conservation law
UR - http://eudml.org/doc/297802
ER -

References

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