Reduction of linearized Benjamin-Ono equation to the Schrodinger equation

M. Jahanshahi, N. Aliev
2007 International Mathematical Forum  
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