Some More Solutions of Caudrey–Dodd–Gibbon Equation Using Optimal System of Lie Symmetries

Abstract

This paper investigates ( $$1+1$$ )-dimensional Caudrey–Dodd–Gibbon equation (CDG) for the invariance properties, optimal system and group invariant solutions. The Lie point symmetries, geometric vector field, commutation table of Lie algebra and various similarity reductions are obtained by virtue of the invariance criteria of the Lie symmetry analysis. By utilizing the Lie symmetry reduction, the ( $$1+1$$ )-dimensional Caudrey–Dodd–Gibbon equation (CDG) will be reduced to a number of ordinary differential equations. The group invariant solutions and new closed form solutions are obtained in the shapes of dynamical structures of solitary waves. Some of the obtained closed form solutions are absolutely new in formulation and entirely different from the earlier studies (Wazwaz in Appl Math Comput 174:289–299, 2006; Bibi et al. in Adv Differ Equ 2019:89, 2019). The dynamical behavior of the derived solutions is analyzed physically through 3D, 2D-graphics and corresponding contour plots.