Nonlinear dynamics of the solitary wave, boundary-forcing and wave undulation solutions of the nonlinear Equal Width Wave equation

A highly accurate numerical algorithm has been preferred and used toget numerical solutions of solitary wave, boundary-forcing and waveundulation solutions of the nonlinear Equal Width Wave (EW) equation. Sincethe boundary-forcing solutions of the EW equation do not exist in theliterature it's firstly obtained successfully and introduced in this study.Wave generation with different values of the impulse, which is related to the forced-boundary in the EW equation, is investigated.Using low-order modified B-spline and less number of nodal points are twoadvantages of the present algorithm. Choosing modified cubic B-splinesprevents the appearance of the dummy points. To see the difference betweenthe present technique with other methods four applications existing in theliterature with many different values of parameters are investigated andcomparisons with nearly forty different techniques are reported. For all ofthe comparisons, undoubtedly present algorithm produces better resultsexcept only one method using more than three times nodal points. Theproduced invariants are also in good agreement with the exact values. Ratesof the convergence are computed.