Abstract

In this note we give a Bäcklund transformation, a recursion scheme for the infinite number of conservation laws and an inverse scattering problem for an integro-differential equation governing long internal gravity waves in a stratified fluid of finite total depth. They are shown to reduce to those of the Korteweg—de Vries equation in the shallow water limit and those of the Benjamin—Ono equation in the deep water limit.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.