Soliton solutions to KdV equation with spatio-temporal dispersion

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.