Abstract:A complete study of the modulation equations for the Benjamin-Bona-Mahony equation is performed. In particular, the boundary between the hyperbolic and elliptic regions of the modulation equations is found. When the wave amplitude is small, this boundary is approximately defined by 𝑘 = √ 3, where 𝑘 is the wave number.This particular value corresponds to the inflection point of the linear dispersion relation for the BBM equation. Numerical results are presented showing the appearance of the Benjamin-Feir inst… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.