Stability of a class of solitary waves in compressible elastic rods

By Adrian Constantin, Walter A. Strauss. 2000

204 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/50f0e9a5b511116ac9a524c225fba35fccb84c37

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In Applied Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Initial Boundary Value Problems of the Camassa–Holm Equation (2008, methodology): “They are orbitally stable (see Constantin and Strauss, 2000b).”
Blow-up of solutions to a nonlinear dispersive rod equation (2006, methodology): “The following theorem tells us that the solution blows up if and only if the first-order derivative blows up. Theorem 2.2 [ 10 , 28] Let u0(x) ∈ H s (S) ,s > 3/2, and u be the corresponding solution to problem (1.1) with lifespan T . Then”
Global weak solutions and blow-up structure for the Degasperis–Procesi equation (2006, background): “The Camassa–Holm equation is also a model for the propagation of axially symmetric waves in hyperelastic rods [17,19].”
Oscillation-induced blow-up to the modified Camassa–Holm equation with linear dispersion (2015, background): “which was proposed as a model describing the uni-directional propagation of shallow water waves [5, 10, 16] and axially symmetric waves in hyperelastic rods [9, 11].”
Inverse scattering transform for the Camassa–Holm equation (2006, background): “tom [5, 25, 1On leave from the Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Soﬁa, Bulgaria. 1 27] as well as that of axially symmetric waves in a hyperelastic rod [16, 18]. It ﬁrstly appeared in [20] as an equation with a bi-hamiltonian structure. CH is a complet”
Global Existence and Blow-Up Phenomena for the Degasperis-Procesi Equation (2006, methodology): “The Camassa-Holm equation is also a model for the propagation of axially symmetric waves in hyperelastic rods [ 17 , 19].”
Global weak solutions for a two-component Camassa–Holm shallow water system (2011, background): “The Camassa–Holm equation is also a model for the propagation of axially symmetric waves in hyperelastic rods [24,25].”
On the blow-up of solutions to the integrable modified Camassa–Holm equation (2014, background): “The Camassa-Holm (CH) equation mt + umx + 2mux = 0, m = u− uxx, (1.3) was also proposed [1] as a model describing the uni-directional propagation of shallow water waves.”
Infinite propagation speed for a two component Camassa-Holm equation (2009, background): “underlying shear flow [38]), and it also provides a model for nonlinear waves in cylindrical hyperelastic rods [ 23 , 25], with the solution u representing the radial stretch relative to a prestressed state.”