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Reduction of linearized Benjamin-Ono equation to the Schrodinger equation

2007
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International Mathematical Forum
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Laplace equation and Cauchy-Riemann equations have important role in complex analysis theory and boundary value problems. We know that the real and imaginary parts of Cauchy-Riemann equation are the solutions of Laplace equation. In other words, these functions are harmonic functions. In this paper, we show that there is a similar relation between linearized Benjamin-Ono equation and Schrödinger equations. In other words, we can write the solution of linearized Benjamin-Ono equation by real and imaginary parts of Schrödinger equation.

doi:10.12988/imf.2007.07049
fatcat:wsvkkhptwngxdpkr6rkf57wdve