On the Camassa-Holm equation and a direct method of solution I. Bilinear form and solitary waves

By A. Parker. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2004

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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.”
On the Camassa–Holm equation and a direct method of solution. III. N-soliton solutions (2005, methodology): “For the case kZ0, only non-analytic multipeakon solutions (Camasa and Holm 1993) and analytic solitary and anti-solitary waves (Dai 1998; Parker 2004) were previously known.”
Inverse scattering transform for the Camassa–Holm equation (2006, methodology): “The construction of the soliton solutions based on the bilinear representation of the CH equation (Hirota’s method) is presented in [36, 37, 38], see also [33] for a parametric representation of the N -soliton solution.”