Asymptotic Properties of the Benjamin-Ono Equation

Abstract

The asymptotic properties of the Benjamin-Ono (BO) equation are investigated in the limit of the large similarity parameter. The number density funcction F(a) of the BO solitons, which is defined such that the number of solitons with amplitudes in the interval (a, a+da) is given by F(a)da, is derived by employing the infinite number of the conservation laws of the BO equation.
It is also shown that the amplitudes of solitons are closely related to the solution of the single algebraic equation which is derived from the conservation laws.