Abstract
We investigate a special form of solution to the complex valued Benjamin–Ono (cBO) equation. Under the special form of solution involving Hilbert transform, the complex valued (modified) Benjamin–Ono equations are equivalent to the quadratic (cubic) derivative Schrödinger equations. The soliton interaction dynamics is used to construct a finite time blowup solution of the cBO equation on R. We also find static solutions. Applying Cole–Hopf transformation to quadratic derivative Schrödinger equation, we derive a linear Schrödinger equation with a special form of initial data from which some solutions to cBO equation can be obtained by an inverse transform.
Sign-in/Register to access full text options 
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 callDisclaimer: 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.
