A NOTE ON THE NUMERICAL AND N-SOLITON SOLUTIONS OF THE BENJAMIN-ONO EVOLUTION EQUATION

An efficient pseudospectral method is applied for the numerical solution of the weakly non-linear Benjamin-Ono equation for arbitrary initial conditions. The general solution at large time is shown to evolve into an ordered pattern of Lorentzian solitons and a dispersive train moving in opposite directions. A practical new relationship for estimating the number of solitons is proposed in terms of the soliton-number (representing the ratio between nonlinearity and dispersion effects) and the shape of the initial disturbance.