Global conservative solutions of the generalized hyperelastic-rod wave equation ✩

73 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View (2007, methodology): “By suitably modifying the techniques described in this paper, the results can be extended, see Holden and Raynaud ( 2007b ), to show global existence of conservative solutions for the generalized hyperelastic-rod wave equation where f , g ∈ C ∞ (ℝ) and f is strictly convex.”
Local-in-Space Criteria for Blowup in Shallow Water and Dispersive Rod Equations (2012, background): “on (2.1) is a particular case (corresponding to f(u) = γ−3 2 u 2, g(u) = γu ) of the so called “generalized hyperelastic rod equation”, ut +f′(u)ux +∂xp∗ g(u) + f ′′(u) 2 u 2 x = 0, studied, e.g., in [19]. The choice f(u) = u2 and g(u) = κu + u2, with κ ≥ 0, would correspond to the Camassa–Holm equa”