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Compactons in a general compressible hyperelastic rod. (English) Zbl 1116.74374
Summary: 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. [A. M. Wazwaz, Chaos, Solitons Fractals 13, No. 2, 321–330 (2002; Zbl 1028.35131); 13, No. 5, 1053–1062 (2002; Zbl 0997.35083); Appl. Math. Comput. 134, No. 2-3, 487–500 (2003; Zbl 1027.35119); Z. Yan, Chaos, Solitons Fractals 14, No. 8, 1151–1158 (2002; Zbl 1038.35082)]), 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.

MSC:
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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