Global analytic solutions and traveling wave solutions of the Cauchy problem for the Novikov equation
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Abstract:
In this paper, we mainly study the existence and uniqueness of the analytic solutions for the Novikov equation. We first investigate whether the equation has analytic solutions which exist globally in time, provided the initial data satisfies certain sign conditions. We also get the analyticity of the Cauchy problem for a family of nonlinear wave equations. Finally, we prove that the Novikov equation has a family of traveling wave solutions.References
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Additional Information
- Xinglong Wu
- Affiliation: Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, People’s Republic of China – and – Department of Mathematics, Wuhan University of Technology, Wuhan 430070, People’s Republic of China
- Email: wxl8758669@aliyun.com
- Received by editor(s): May 10, 2015
- Received by editor(s) in revised form: September 26, 2015
- Published electronically: December 26, 2017
- Communicated by: Joachim Krieger
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1537-1550
- MSC (2010): Primary 35G25, 35L05
- DOI: https://doi.org/10.1090/proc/12981
- MathSciNet review: 3754340