Abstract
This paper discusses a soliton solution that is of a different structure than that is usually known. The equation with spatio-temporal dispersion is studied in this paper both analytically and numerically. The governing equations that are addressed in this paper are the Korteweg-de Vries (KdV) equation, modified KdV equation and finally KdV equation with power law nonlinearity. Numerically these three equations are all addressed with quintic B-spline collocation method and the stability analysis is carried out.
•This paper studied shallow water waves with IKdV equation, mIKdV equation and finally the IKdV equation with power law nonlinearity.•Solitary wave solutions are obtained by ansatz method that is not of the usual norm.•There are several numerical simulations that are obtained in this paper along with the interaction of solitary waves.•The numerical simulations employed quintic B-spline collocation method.•The results of this paper come with a lot of encouragement for further future investigations in this paper.