Stability of peakons

By Adrian Constantin, Walter A. Strauss. 2000

1,026 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ed96b7a4f5138c7c84b978ac4042221fe5ef1333

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Stability of the Camassa-Holm solitons (2002, result): “Our approach is completely different from the method used in [5] to prove the stability of the peakons.”
A note on the Cauchy problem of the Novikov equation (2013, background): “The Camassa–Holm equation has attracted a lot of interest for various reasons 9–16 .”
The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation (2010, background): “[18] A. Constantin, W. Strauss, Stability of the Camassa–Holm solitons, J. Nonlinear Sci. 12 (2002) 415–422.”
Cuspons and Smooth Solitons of the Degasperis–Procesi Equation Under Inhomogeneous Boundary Condition (2007, background): “In fact, the regular peakon u(x, t) = ce−|x−ct| ∈ H1 (c is the wave speed), which is a stable solution of the CH equation [5], also satisfies both the nonlocal equation (3.”
Riemann-Hilbert approach for the Camassa-Holm equation on the line (2006, background): “On the other hand, it has been observed [11,9] that if the parameters of an ω -soliton are changing appropriately with ω when ω → 0, then this soliton approaches a peakon, which is a piecewise smooth (weak), stable (cf. [2,7]) solution of (1a) with ω = 0: Theorem 3.1.”
Global existence and blow-up solutions for a nonlinear shallow water equation (2006, background): “[CaHo,BeSaSz,CoMo2] and are orbitally stable [CoMo, CoSt1 ], breaking waves occur [CaHo,Co1,Mc], and global solutions exist[Co1,CoEs].”
Breakdown for the Camassa-Holm Equation Using Decay Criteria and Persistence in Weighted Spaces (2012, background): “These solutions are orbitally stable: their shape is stable under small perturbations and therefore these waves are physically recognizable, see [9].”
A Note on the Degasperis-Procesi Equation (2005, background): “Also, both equations admit exact peaked solitary wave solutions which have to be understood as weak solutions [10, 8, 22].”
Wave Breaking and Global Existence for a Generalized Two-Component Camassa–Holm System (2010, background): “These peakons are shown to be stable [21, 22, 40].”
Blow-up of solutions to a nonlinear dispersive rod equation (2006, background): “Recently, the author [21] proved the stability of these solitary waves by applying a general theorem established by Grillakis, Shatah and Strauss [9].”