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.
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