A special form of solution to complex valued Benjamin-Ono equations

초록

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. © 2024 Elsevier B.V.

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