Solitary shock waves and other travelling waves in a general compressible hyperelastic rod

By Hui-hui Dai, Y. Huo. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2000

183 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e7d14ddf8c9ff67d34a014fde7ee830befc7e90b

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Citations in the corpus

Local-in-Space Criteria for Blowup in Shallow Water and Dispersive Rod Equations (2012, background): “, [1,10,25]) and for the examples of smooth solitary waves constructed in [16] for 0 < γ < 1.”
Local well‐posedness and blow‐up criteria of solutions for a rod equation (2005, background): “Dai and Hou investigated the solitary waves for the rod equation in [8] for γ ∈ R.”
Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View (2007, unknown): “With g u = 3− 2 u 2 and f u = 2u2, Dai (Dai, 1998a,b; Dai and Huo, 2000) derived (1.8) as an equation describing finite length, small amplitude radial deformation waves in cylindrical compressible hyperelastic rods, and the equation is often referred to as the hyperelastic-rod wave equation.”
Blow-up of solutions to a nonlinear dispersive rod equation (2006, background): “It should be mentioned that for γ 1, (1.1) admits smooth solitary waves observed by Dai and Huo [7].”
On the well-posedness of the Degasperis-Procesi equation (2006, methodology): “In another interpretation, the Camassa–Holm equation was derived by Dai [14] as a model for finite length, small amplitude radial deformation waves in cylindrical compressible hyperelastic rods.”
Global conservative solutions of the generalized hyperelastic-rod wave equation ✩ (2007, unknown): “For f(u) = γu 2 2 and g(u) = 3−γ 2 u (2), we obtain the hyperelastic-rod wave equation: ut − utxx + 3uux − γ(2uxuxx + uuxxx) = 0, which was introduced by Dai [11, 10, 12] in 1998.”
A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation (2006, unknown): “In another interpretation, Dai and Huo (2000) derived (1.5) (in a more general form) as an equation describing finite length, small amplitude radial deformation waves in cylindrical compressible hyperelastic rods.”
WELLPOSEDNESS FOR A PARABOLIC-ELLIPTIC SYSTEM (2005, unknown): “Furthermore, Dai [6] derived the equation ut − utxx + 3uux = γ(2uxuxx + uuxxx) as a model for small amplitude radial deformation waves in cylindrical compressible hyperelastic rods.”