Generating new symmetric bi-peakon and singular bi-periodic profile solutions to the generalized doubly dispersive equation

摘要

Abstract This work aims to explore new bidirectional-wave solutions to the generalized doubly dispersive equation through the use of two effective integration schemes: the modified rational sine–cosine and sinh–cosh functions, and the unified method. The proposed model is a type of nonlinear partial differential equation that includes a second-order temporal derivative and exhibits the property of propagating wave solutions as symmetric binary waves in a like manner to the Boussinesq equation. The new solutions are derived in detail, and graphical representations are provided to illustrate their physical structures. The results of this study are valuable for enhancing our understanding of the generalized doubly dispersive equation, which has diverse practical applications.