Volume 49, Issue 3
Existence and Orbital Stability of Solitary-Wave Solutions for Higher-Order BBM Equations

Juan-Ming Yuan, Hongqiu Chen & Shu-Ming Sun

J. Math. Study, 49 (2016), pp. 293-318.

Published online: 2016-09

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  • 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 BBMequation 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.
  • Keywords

Higher-order BBM equations solitary-wave solutions orbital stability

  • AMS Subject Headings

35Q35, 76B15, 76B25, 35Q35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jmyuan@pu.edu.tw (Juan-Ming Yuan)

hchen1@memphis.edu (Hongqiu Chen)

sun@math.vt.edu (Shu-Ming Sun)

  • BibTex
  • RIS
  • TXT
@Article{JMS-49-293, author = {Yuan , Juan-Ming and Chen , 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 = {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 BBMequation 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.}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v49n3.16.05}, url = {http://global-sci.org/intro/article_detail/jms/10123.html} }
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 KW - solitary-wave solutions KW - orbital stability AB - 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 BBMequation 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.
Juan-Ming Yuan, Hongqiu Chen & Shu-Ming Sun. (2019). Existence and Orbital Stability of Solitary-Wave Solutions for Higher-Order BBM Equations. Journal of Mathematical Study. 49 (3). 293-318. doi:10.4208/jms.v49n3.16.05
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