@Article{JMS-49-293,
author = {Yuan , Juan-MingChen , Hongqiu and Sun , Shu-Ming},
title = {Existence and Orbital Stability of Solitary-Wave Solutions for Higher-Order BBM Equations},
journal = {Journal of Mathematical Study},
year = {2016},
volume = {49},
number = {3},
pages = {293--318},
abstract = {<p style="text-align: justify;">This paper discusses the existence and stability of solitary-wave solutions
of a general higher-order Benjamin-Bona-Mahony (BBM) equation, which involves
pseudo-differential operators for the linear part. One of such equations can be derived
from water-wave problems as second-order approximate equations from fully nonlinear
governing equations. Under some conditions on the symbols of pseudo-differential
operators and the nonlinear terms, it is shown that the general higher-order BBM equation
has solitary-wave solutions. Moreover, under slightly more restrictive conditions,
the set of solitary-wave solutions is orbitally stable. Here, the equation has a nonlinear
part involving the polynomials of solution and its derivatives with different degrees
(not homogeneous), which has not been studied before. Numerical stability and instability
of solitary-wave solutions for some special fifth-order BBM equations are also
given.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v49n3.16.05},
url = {http://global-sci.org/intro/article_detail/jms/10123.html}
}