Interacting Benjamin-Ono Equations

抄録

Interacting (Int) Benjamin-Ono (BO) equations, certain coupled nonlinear integro-differential equations, are results of an extension or a decoupling of the BO equation. By using new operators, the solutions u_i of Int BO equations are obtained starting from the exact N-soliton solution of the original BO equation. Then by examining weighted mean of pole positions of u_i, very simple and clear-cut results are obtained: the center of gravity of u_i moves with constant speed etc. Two-soliton interaction profiles are shown. Also shown the direct relationship of the solution u of the BO equation and the solution ψ_i′ of its inverse scattering transform.