TY - JOUR
T1 - Existence and Orbital Stability of Solitary-Wave Solutions for Higher-Order BBM Equations
AU - Yuan , Juan-Ming
AU - Chen , Hongqiu
AU - Sun , Shu-Ming
JO - Journal of Mathematical Study
VL - 3
SP - 293
EP - 318
PY - 2016
DA - 2016/09
SN - 49
DO - http://doi.org/10.4208/jms.v49n3.16.05
UR - https://global-sci.org/intro/article_detail/jms/10123.html
KW - Higher-order BBM equations, solitary-wave solutions, orbital stability.
AB - <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>