| 1 |
R. M. Chen, Y. Liu, C. Qu, and S. Zhang, Oscillation-induced blow-up to the modified Camassa-Holm equation with linear dispersion, Adv. Math. 272 (2015), 225-251.
DOI
|
| 2 |
K. El Dika and L. Molinet, Stability of multipeakons, Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009), no. 4, 1517-1532.
DOI
|
| 3 |
K. El Dika and L. Molinet, Stability of multi antipeakon-peakons profile, Discrete Contin. Dyn. Syst. Ser. B 12 (2009), no. 3, 561-577.
DOI
|
| 4 |
A. S. Fokas, The Korteweg-de Vries equation and beyond, Acta Appl. Math. 39 (1995), no. 1-3, 295-305.
DOI
|
| 5 |
B. Fuchssteiner and A. S. Fokas, Symplectic structures, their Backlund transformations and hereditary symmetries, Phys. D 4 (1981/82), no. 1, 47-66.
DOI
|
| 6 |
Y. Fu, G. Gui, C. Qu, and Y. Liu, On the Cauchy problem for the integrable modified Camassa-Holm equation with cubic nonlinearity, J. Differential Equations 255 (2013), no. 7, 1905-1938.
DOI
|
| 7 |
B. Fuchssteiner, Some tricks from the symmetry-toolbox for nonlinear equations: generalizations of the Camassa-Holm equation, Phys. D 95 (1996), no. 3-4, 229-243.
DOI
|
| 8 |
G. Gui, Y. Liu, P. J. Olver, and C. Qu, Wave-breaking and peakons for a modified Camassa-Holm equation, Comm. Math. Phys. 319 (2013), no. 3, 731-759.
DOI
|
| 9 |
A. A. Himonas and C. Holliman, The Cauchy problem for the Novikov equation, Non-linearity 25 (2012), no. 2, 449-479.
|
| 10 |
A. N. W. Hone and J. P. Wang, Integrable peakon equations with cubic nonlinearity, J. Phys. A 41 (2008), no. 37, 372002, 10 pp.
|
| 11 |
X. X. Liu, Stability of peakons for a Camassa-Holm-type equation with quartic nonlinearity , submitted.
|
| 12 |
R. S. Johnson, Camassa-Holm, Korteweg-de Vries and related models for water waves, J. Fluid Mech. 455 (2002), 63-82.
DOI
|
| 13 |
X. Liu, Y. Liu, and C. Qu, Stability of peakons for the Novikov equation, J. Math. Pures Appl. (9) 101 (2014), no. 2, 172-187.
DOI
|
| 14 |
X. Liu, Y. Liu, and C. Qu, Orbital stability of the train of peakons for an integrable modified Camassa-Holm equation, Adv. Math. 255 (2014), 1-37.
DOI
|
| 15 |
P. J. Olver and P. Rosenau, Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support, Phys. Rev. E (3) 53 (1996), no. 2, 1900-1906.
|
| 16 |
Y. Liu, P. J. Olver, C. Qu, and S. Zhang, On the blow-up of solutions to the integrable modified Camassa-Holm equation, Anal. Appl. (Singap.) 12 (2014), no. 4, 355-368.
DOI
|
| 17 |
Y. Martel, F. Merle, and T.-P. Tsai, Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations, Comm. Math. Phys. 231 (2002), no. 2, 347-373.
DOI
|
| 18 |
V. Novikov, Generalizations of the Camassa-Holm equation, J. Phys. A 42 (2009), no. 34, 342002, 14 pp.
|
| 19 |
Z. Qiao, A new integrable equation with cuspons and W/M-shape-peaks solitons, J. Math. Phys. 47 (2006), no. 11, 112701, 9 pp.
DOI
|
| 20 |
Z. Qiao and X. Li, An integrable equation with nonsmooth solitons, Theoret. and Math. Phys. 167 (2011), no. 2, 584-589.
DOI
|
| 21 |
C. Qu, X. Liu, and Y. Liu, Stability of peakons for an integrable modified Camassa-Holm equation with cubic nonlinearity, Comm. Math. Phys. 322 (2013), no. 3, 967-997.
DOI
|
| 22 |
X. Wu and Z. Yin, Global weak solutions for the Novikov equation, J. Phys. A 44 (2011), no. 5, 055202, 17 pp.
|
| 23 |
E. Recio and S. C. Anco, A general family of multi-peakon equations, https://arxiv.org/abs/1609.04354.
|
| 24 |
J. F. Toland, Stokes waves, Topol. Methods Nonlinear Anal. 7 (1996), no. 1, 1-48.
DOI
|
| 25 |
G. B. Whitham, Linear and Nonlinear Waves, reprint of the 1974 original, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1999.
|
| 26 |
R. Camassa, D. D. Holm, and J. Hyman, A new integrable shallow water equation, Adv. Appl. Mech. 31 (1994), 1-33.
DOI
|
| 27 |
R. Beals, D. H. Sattinger, and J. Szmigielski, Acoustic scattering and the extended Korteweg-de Vries hierarchy, Adv. Math. 140 (1998), no. 2, 190-206.
DOI
|
| 28 |
R. Beals, D. H. Sattinger, and J. Szmigielski, Multi-peakons and a theorem of Stieltjes, Inverse Problems 15 (1999), no. 1, L1-L4.
DOI
|
| 29 |
R. Camassa and D. D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett. 71 (1993), no. 11, 1661-1664.
DOI
|
| 30 |
A. Constantin, Existence of permanent and breaking waves for a shallow water equation: a geometric approach, Ann. Inst. Fourier (Grenoble) 50 (2000), no. 2, 321-362.
DOI
|
| 31 |
A. Constantin, On the scattering problem for the Camassa-Holm equation, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 457 (2001), no. 2008, 953-970.
DOI
|
| 32 |
A. Constantin, The trajectories of particles in Stokes waves, Invent. Math. 166 (2006), no. 3, 523-535.
DOI
|
| 33 |
A. Constantin and J. Escher, Global existence and blow-up for a shallow water equation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 26 (1998), no. 2, 303-328.
|
| 34 |
A. Constantin and J. Escher, Well-posedness, global existence, and blowup phenomena for a periodic quasilinear hyperbolic equation, Comm. Pure Appl. Math. 51 (1998), no. 5, 475-504.
DOI
|
| 35 |
A. Constantin and J. Escher, Wave breaking for nonlinear nonlocal shallow water equations, Acta Math. 181 (1998), no. 2, 229-243.
DOI
|
| 36 |
A. Constantin and J. Escher, Analyticity of periodic traveling free surface water waves with vorticity, Ann. of Math. (2) 173 (2011), no. 1, 559-568.
DOI
|
| 37 |
A. Constantin and D. Lannes, The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations, Arch. Ration. Mech. Anal. 192 (2009), no. 1, 165-186.
DOI
|
| 38 |
A. Constantin and W. A. Strauss, Stability of peakons, Comm. Pure Appl. Math. 53 (2000), no. 5, 603-610.
DOI
|
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