Compactons in a general compressible hyperelastic rod

There is much work in the area of solitons, but there appears very little in the way of compactons. After the approach of Adomian decomposition applied successfully (e.g. [Chaos, Solitons & Fractals 13 (2002) 321; Chaos, Solitons & Fractals 13 (2002) 1053; Appl. Math. Comput. 134 (2003) 487; Chaos, Solitons & Fractals 14 (2002) 1151]), we develop a new method to enlarge the window of compacton research, that is, the bifurcation method of traveling wave systems and numerical simulation of traveling wave equation. As above mentioned, we employ both bifurcation method and numerical simulation to investigate bounded traveling waves in a general compressible hyperelastic rod in this paper. We find some new bounded traveling waves, which are defined on finite core regions. Their planar simulative graphs and implicit expressions imply that they possess the properties of compactons.