Year: 2016
Author: Juan-Ming Yuan, Hongqiu Chen, Shu-Ming Sun
Journal of Mathematical Study, Vol. 49 (2016), Iss. 3 : pp. 293–318
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v49n3.16.05
Journal of Mathematical Study, Vol. 49 (2016), Iss. 3 : pp. 293–318
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Higher-order BBM equations solitary-wave solutions orbital stability.