TY - JOUR
T1 - Wave-Breaking and Peakons for a Modified Camassa-Holm Equation
AU - Gui, Guilong
AU - Liu, Yue
AU - Olver, Peter J.
AU - Qu, Changzheng
PY - 2013/5
Y1 - 2013/5
N2 - In this paper, we investigate the formation of singularities and the existence of peaked traveling-wave solutions for a modified Camassa-Holm equation with cubic nonlinearity. The equation is known to be integrable, and is shown to admit a single peaked soliton and multi-peakon solutions, of a different character than those of the Camassa-Holm equation. Singularities of the solutions can occur only in the form of wave-breaking, and a new wave-breaking mechanism for solutions with certain initial profiles is described in detail.
AB - In this paper, we investigate the formation of singularities and the existence of peaked traveling-wave solutions for a modified Camassa-Holm equation with cubic nonlinearity. The equation is known to be integrable, and is shown to admit a single peaked soliton and multi-peakon solutions, of a different character than those of the Camassa-Holm equation. Singularities of the solutions can occur only in the form of wave-breaking, and a new wave-breaking mechanism for solutions with certain initial profiles is described in detail.
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U2 - 10.1007/s00220-012-1566-0
DO - 10.1007/s00220-012-1566-0
M3 - Article
AN - SCOPUS:84876127782
SN - 0010-3616
VL - 319
SP - 731
EP - 759
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 3
ER -