Fig. 1

Graphical representation of \(q_{1}(x,t)\) in peakon dark and periodic wave soliton structure visualized in contour, two and three dimensional plotting with \(\nabla _{1}=2, \nabla _{2}=4, \nabla _{3}=2, \kappa =2, \nu =1.5, \epsilon =1.5, \omega =1, \gamma =1\).