On solutions of the Camassa-Holm equation

By R. Johnson. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2003

175 citations recorded by the source corpus.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2273e58c2d667b1a37b9059fe339fcecc53ce913

How researchers see this paper

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

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation (2010, background): “[27] R.S. Johnson, On solutions of the Camassa–Holm equation, Proc.”
A three-component generalization of Camassa–Holm equation with N-peakon solutions (2011, background): “For example, it is shown that the CH equation is integrable by the inverse scattering transformation, it possesses the Lax pair formalism, multi-soliton solutions, algebro-geometric solutions and other remarkable properties of integrable equations [8,21,16,22,17,19,10,13,35,32,34,38,25, 26].”
A Two-component Generalization of the Camassa-Holm Equation and its Solutions (2005, background): “Since the works of Camassa and Holm, this equation has become a well known example of integrable systems and has been studied from various point views in, for example, [1, 3, 9, 10, 14, 15, 18, 20, 26, 27, 28] and references therein.”
On the Camassa–Holm equation and a direct method of solution. III. N-soliton solutions (2005, methodology): “Of course, we may use mathematical software (such as MATHEMATICA) to aid our calculations; yet, the work of Johnson (2003) offers a cautionary note against an undue reliance on symbolic manipulation tools.”
Inverse scattering transform for the Camassa–Holm equation (2006, methodology): “The inverse scattering based on a Liouville transform, which leads to a spectral problem of the standard form −Ψyy +Q(y)Ψ = μΨ (the Schrödinger equation) is developed in series of works [9, 26, 31, 32].”
On the Camassa-Holm equation and a direct method of solution I. Bilinear form and solitary waves (2004, methodology): “For our part, we will follow closely the work of Constantin (2001) and Johnson (2003b) which is most consonant with our own (aside from changes in notation).”