Computer Simulation of Solitary Waves of the Nonlinear Wave Equation u_t+uu_x−γ²u_5x=0

Abstract

Computer simulation of the nonlinear wave equation u_t+uu_x−γ²u_5x=0 was carried out. The results show that one solitary wave with oscillatory tails propagates stably and it is described as u=λf{λ^1⁄4(x−λt)}.
It is found that the two-solitary wave interaction is classified into two types, T and B, according to the relative amplitudes of waves, and after type the T interaction, both identities of solitary waves before the interaction are conserved, while after type the B interaction their identities are approximately conserved.
Formation of a two-solitary wave’s bound state is observed after three-solitary wave interaction, and the condition of the bound state formation is discussed.