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Global analytic solutions and traveling wave solutions of the Cauchy problem for the Novikov equation


Author: Xinglong Wu
Journal: Proc. Amer. Math. Soc. 146 (2018), 1537-1550
MSC (2010): Primary 35G25, 35L05
DOI: https://doi.org/10.1090/proc/12981
Published electronically: December 26, 2017
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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.


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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

DOI: https://doi.org/10.1090/proc/12981
Keywords: Novikov equation, analytic solutions, global existence, traveling wave solutions
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
Article copyright: © Copyright 2017 American Mathematical Society

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