Existence and Orbital Stability of Solitary-Wave Solutions for Higher-Order BBM Equations

Existence and Orbital Stability of Solitary-Wave Solutions for Higher-Order BBM Equations

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.

Author Details

Juan-Ming Yuan

Hongqiu Chen

Shu-Ming Sun

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