Nonlinear stability and convergence of finite-difference methods for the good Boussinesq equation

Note that 40 determines the initial position of the wave, and that, due to the square root in (1.2), the parameter P can only take values in 0<P=< 1. Thus, the solitary waves (1.1) only exist for a finite range of velocities l < c < l . Of course, a positive (respectively negative) velocity corresponds to a wave moving to the right (respectively to the left). When two solitary waves with parameters P1 and P2 are initially well separated and approach each other, a nonlinear interaction takes place. If PI and P2 are of moderate size, the incoming waves emerge of the interaction without