We prove that the existence of peakon as weak traveling wave solution and as global weak solution for the nonlinear surface wind waves equation, so as to correct the assertion that there exists no peakon solution for such an equation in the literature. Copyright © 2017 John Wiley & Sons, Ltd.

References

1Manna MA. Asymptotic dynamics of monochromatic short surface wind waves. Physica D 2001; 149(4): 231–236.
10.1016/S0167-2789(00)00205-0
Web of Science® Google Scholar
2Xie Y, Tang S, Zhong L, Chen A. Bifurcations and exact solutions for a nonlinear surface wind waves equation. Mathematical Methods in the Applied Sciences 2016; 39(6): 1289–1297.
10.1002/mma.3549
Web of Science® Google Scholar
3Camassa R, Holm D. An integrable shawllow water equation with peaked solitons. Physical Review Letters 1993; 71(11): 1661–1664.
10.1103/PhysRevLett.71.1661
CAS PubMed Web of Science® Google Scholar
4Wazwaz A. Peakon and solitonic solutions for KdV-like equations. Physical Scripta 2015; 90:045203 (9pp).
10.1088/0031-8949/90/4/045203
Web of Science® Google Scholar
5Li J, Liu Z. Smooth and non-smooth traveling waves in a nonlinearly dispersive equation. Applied Mathematical Modelling 2000; 25: 41s–56.
10.1016/S0307-904X(00)00031-7
PubMed Web of Science® Google Scholar
6Yin J, Tian L, Fan X. Classification of traveling waves in the Fornberg–Whitham equation. Journal of Mathematical Analysis and Applications 2010; 368: 133–143.
10.1016/j.jmaa.2010.03.037
Web of Science® Google Scholar
7Jiang B, Lu Y, Ma Q, Cao Y, Zhang YZ. Bifurcation of traveling wave solutions for the BBM-like B(2,2) equation. Applied Mathematics and Computation 2012; 218: 7375–7381.
10.1016/j.amc.2011.12.061
Web of Science® Google Scholar
8Grayshan K. Peakon solutions of the Novikov equation and properties of the data-to-solution map. Journal of Mathematical Analysis and Applications 2013; 397: 515–521.
10.1016/j.jmaa.2012.08.006
Web of Science® Google Scholar
9Lenells J. Traveling wave solutions of the Camassa–Holm equations. Journal of Differential Equations 2005; 217(2): 393–430.
10.1016/j.jde.2004.09.007
Web of Science® Google Scholar
10Constantin A, Escher J. Global weak solutions for a shallow water equation. Indiana University Mathematics Journal 1998; 47: 1527–1545.
10.1512/iumj.1998.47.1466
Web of Science® Google Scholar
11Constantin A, Molinet L. Global weak solutions for a shallow water equation. Communications in Mathematical Physics 2000; 211: 45–61.
10.1007/s002200050801
Web of Science® Google Scholar
12Bressan A, Constantin A. Global conservative solutions of the Camassa–Holm equation. Journal of Rational Mechanics and Analysis 2007; 183: 215–239.
10.1007/s00205-006-0010-z
Web of Science® Google Scholar
13Xin Z, Zhang P. On the weak solutions to a shallow water equation. Communications on Pure and Applied Mathematics 2000; 53: 1411–1433.
10.1002/1097-0312(200011)53:11<1411::AID-CPA4>3.0.CO;2-5
Web of Science® Google Scholar
14Isaza P. Unique continuation principle for the Ostrovsky equation with negative dispersion. Journal of Differential Equations 2013; 255: 796–811.
10.1016/j.jde.2013.04.034
Web of Science® Google Scholar

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Volume40, Issue15

October 2017

Pages 5419-5422

Remark on peakon solution to the nonlinear surface wind waves equation

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Remark on peakon solution to the nonlinear surface wind waves equation

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