Investigation of solitons in the Benjamin-Ono nonlinear system

Abstract

The Benjamin-Ono equation which describes deep internal water waves is reviewed and its soliton solutions are investigated both theoretically and numerically in periodic domain. To obtain the equation, instead of the formal scale-parameter expansions, the nonlinear effect which represents the inertia of the fluid is appended to the linear wave equation from the dispersion relation. An efficient way to generate N-solitons is to set the initial condition to be N-multiple of the single soliton solution. The case of N=2 is predicted and numerically confirmed. We studied the dynamics of the solitons by investigating the motions of the center of mass (COM) for several initial conditions. We observed irregular cycling motions of the COM and the relative recurrence times of initial conditions were order of ten times of the cycling time of COM.