Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa-Holm type equation
By Andrew N. W. Hone, Hans Lundmark, Jacek Szmigielski. 2009
225 citations recorded by the source corpus.
Recently Vladimir Novikov found a new integrable analogue of the Camassa-Holm equation, admitting peaked soliton (peakon) solutions, which has nonlinear terms that are cubic, rather than quadratic. In this paper, the explicit formulas for multipeakon solutions of Novikov's cubically nonlinear equation are calculated, using the matrix Lax pair found by Hone and Wang. By a transformation of Liouville type, the associated spectral problem is related to a cubic string equation, which is dual to the cubic string that was previously found in the work of Lundmark and Szmigielski on the multipeakons of the Degasperis-Procesi equation.
Subfields: Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/c58d43f3fe3befa0d4ea647bf3386054a4c25b72
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In Geometry and Topology
In Statistical and Nonlinear Physics
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Citations in the corpus
- Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems (2016, unknown): “properties for CH type and related nonlinear evolution equations, we refer the reader to [12], [13], [11], [15], [16], [6], [23], [49], [53], [50], [17], [45], [8], [42], [43], [44], [4], [3], [64], [18], [5], [47], [48], [10], [9], [70], and the references therein.”
- A note on the Cauchy problem of the Novikov equation (2013, result): “Thus, some results of the Novikov equation are truly different with the Camassa–Holm and Degasperis–Procesi equation 1 , 25 , 26 .”
- The Cauchy problem for the Novikov equation (2012, background): “[9] derived the explicit formulas for multipeakon solutions of (1.”
- Well-posedness, wave breaking and peakons for a modified μ-Camassa-Holm equation (2014, unknown): “7) have been studied respectively in [26,27,37,42,43].”
- The periodic Cauchy problem for Novikov's equation (2010, background): “Novikov in [17] has attracted some attention in the litterature [10, 11].”
- Global weak solutions for the Novikov equation (2011, result): “(u, x) (−u,−x); some results of the Novikov equation are truly different with the Camassa–Holm and Degasperis–Procesi equation [17, 19, 26, 27].”