Journal of Nonlinear Mathematical Physics

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Volume 23, Issue 3, June 2016, Pages 423 - 438

Orbital stability of the smooth solitary wave with nonzero asymptotic value for the mCH equation

Authors
Chaohong Pan
School of Mathematics and Physics, University of South China, Hengyang, 421001, China,pan.ch@mail.scut.edu.cn
Lijing Zheng
School of Mathematics and Physics, University of South China, Hengyang, 421001, China,zhenglijing817@163.com
Received 18 March 2016, Accepted 8 June 2016, Available Online 6 January 2021.
DOI
10.1080/14029251.2016.1204720How to use a DOI?
Keywords
Orbital stability; Solitary wave; The mCH equation
Abstract

This paper is concerned with orbital stability of the smooth solitary wave with nonzero asymptotic value for the mCH equation

ut−uxxt+2kux+au2ux=2uxuxx+uuxxx.
Under the parametric conditions a > 0 and k<18a , an interesting phenomenon is discovered, that is, for the stability there exist three bifurcation wave speeds
c1=1+1−8ak2a,  c2=92a  and  c3=9+39−8ak2a
such that the following conclusions hold.

  1. When wave speed belongs to the interval (c1, c2) for −638a<k<18a , the smooth solitary wave is orbitally stable.

  2. When wave speed belongs to the interval (c2, c3) for −638a<k<18a , the smooth solitary wave is orbitally unstable.

  3. When wave speed belongs to the interval (c1, c3) for k≤−638a , the smooth solitary wave is orbitally unstable.

Copyright
© 2016 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
23 - 3
Pages
423 - 438
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2016.1204720How to use a DOI?
Copyright
© 2016 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Chaohong Pan
AU  - Lijing Zheng
PY  - 2021
DA  - 2021/01/06
TI  - Orbital stability of the smooth solitary wave with nonzero asymptotic value for the mCH equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 423
EP  - 438
VL  - 23
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2016.1204720
DO  - 10.1080/14029251.2016.1204720
ID  - Pan2021
ER  -