Solitary waves of the equal width wave equation

A numerical solution of the equal width wave equation, based on Galerkin's method using cubic B-spline finite elements is used to simulate the migration and interaction of solitary waves. The interaction of two solitary waves is seen to cause the creation of a source for solitary waves. Usually these are of small magnitude, but when the amplitudes of the two interacting waves are equal and opposite the source produces trains of solitary waves whose amplitudes are of the same order as those of the initiating waves. The three invariants of the motion are evaluated to determine the conservation properties of the system. Finally, the temporal evolution of a Maxwellian initial pulse is studied. For small δ ( U t + UU x − δU xxt =0) only positive waves are formed and the behaviour mimics that of the KdV and FILW equations. For larger values of d both positive and negative solitary waves are generated.