References
- Novikov V. Generalization of the Camassa--Holm equation. J. Phys. A. 2009;42:342002, 14 p.
- Tu X, Yin Z. Local well-posedness and blow-up phenomena for a generalized Camassa--Holm equation with peakon solutions. Discrete Contin. Dyn. Syst. A. 2016;128:1–19.
- Tu X, Yin Z. Blow-up phenomena and local well-posedness for a generalized Camassa--Holm equation in the critical Besov space. Nonlinear Anal. TMA. 2015;128:1–19.
- Tu X, Yin Z. Global weak solutions for a generalized Camassa--Holm equation. 2016. arXiv:1511.02848v2 [math.AP].
- Tu X, Yin Z. Analyticity of the Cauchy problem and persistence properties for a generalized Camassa--Holm equation. 2015. arXiv:1511.02316v1 [math.AP].
- Geng X, Xue B. An extension of integrable peakon equations with cubic nonlinearity. Nonlinearity. 2009;22:1847–1856.
- Fokas A, Fuchssteiner B. Symplectic structures, their Backlund transformation and hereditary symmetries. Physica D. 1981;4:47–66.
- Camassa R, Holm D. An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 1993;71:1661–1664.
- Constantin A. On the scattering problem for the Camassa--Holm equation. Proc. R. Soc. London A. 2001;457:953–970.
- Constantin A. The trajectories of particles in Stokes waves. Invent. Math. 2006;166:523–535.
- Constantin A, Escher J. Particle trajectores in solitary water waves. Bull. Am. Math. Soc. 2007;44:423–431.
- Constantin A, Strauss W. Stability of peakons. Comm. Pure Appl. Math. 2000;53:603–610.
- Constantin A, Escher J. Analyticity of periodic traveling free surface water waves with vorticity. Ann. Math. 2011;173:559–568.
- Amick CJ, Fraenkel LE, Toland JF. On the Stokes conjecture for the wave of extreme form. Acta Math. 1982;148:193–214.
- Constantin A, McKean HP. A shallow water equation on the circle. Comm. Pure Appl. Math. 1999;52:949–982.
- Constantin A. On the inverse spectral problem for the Camassa--Holm equation. J. Funct. Anal. 1998;155:352–363.
- Constantin A, Gerdjikov V, Ivanov RI. Inverse scattering transform for the Camassa--Holm equation. Inverse Probl. 2006;22:2197–2207.
- Constantin A, Kappeler T, Kolev B, et al. On Geodesic exponential maps of the Virasoro group. Ann. Global Anal. Geom. 2007;31:155–180.
- Misiolek GA. Shallow water equation as a geodesic flow on the Bott-Virasoro group. J. Geom. Phys. 1998;24:203–208.
- Constantin A, Escher J. Wave breaking for nonlinear nonlocal shallow water equations. Acta Math. 1998;181:229–243.
- Bressan A, Constantin A. Global conservative solutions of the Camassa--Holm equation. Arch. Ration. Mech. Anal. 2007;183:215–239.
- Holden H, Raynaud X. Global conservative solutions of the Camassa--Holm equations-a Lagrangianpoiny of view. Comm. Partial Differ. Equ. 2007;32:1511–1549.
- Bressan A, Constantin A. Global dissipative solutions of the Camassa--Holm equation. Anal. Appl. 2007;5:1–27.
- Holden H, Raynaud X. Dissipative solutions for the Camassa--Holm equation. Discrete Contin. Dyn. Syst. 2009;24:1047–1112.
- Degasperis A, Procesi M. Asymptotic integrability. Symmetry Perturbation Theory. 1999;1:23–37.
- Degasperis A, Holm DD, Hone ANW. A new integrable equation with peakon solutions. Theor. Math. Phys. 2002;133:1461–1472.
- Constantin A, Ivanov R, Lenells J. Inverse scattering transform for the Degasperis--Procesi equation. Nonlinearity. 2010;23:2559–2575.
- Degasperis A, Procesi M. Asymptotic integrability. In: Degasperis A, Gaeta G, editors. Symmetry and perturbation theory. Singapore: World Scientific; 1999. p. 23–37.
- Toland JF. Stokes waves. Topol. Methods Nonlinear Anal. 1996;7:1–48.
- Holm DD, Staley MF. Wave structure and nonlinear balances in a family of evolutionary PDEs. SIAM J. Appl. Dyn. Syst. 2003;2:323–380.
- Lundmark H, Szmigielski J. Multi-peakon solutions of the Degasperis--Procesi equation. Inverse Probl. 2005;21:1553–1570.
- Matsuno Y. Multisoliton solutions of the Degasperis--Procesi equation and their peakon limit. Inverse Probl. 2003;19:1241–1245.
- Lenells J. Traveling wave solutions of the Degasperis--Procesi equation. J. Math. Anal. Appl. 2005;306:72–82.
- Vakhnenko VO, Parkes EJ. Periodic and solitary-wave solutions of the Degasperis--Procesi equation. Chaos Solitons Fractals. 2004;20:1059–1073.
- Home ANW, Wang JP. Integrable peakon equations with cubic nonlinearity. J. Phys. A. 2008;41:41–68.
- Wu X, Yin Z. Well-posedness and global existence for the Novikov equation. Annali della Scuola Normale Superiore di Pisa Classe di Sci. 2012;11:707–727.
- Ni L, Zhou Y. Well-posedness and persistence properties for the Novikov equation. J. Differ. Equ. 2011;250:3002–3021.
- Wu X, Yin Z. A note on the Cauchy problem of the Novikov equation. Appl. Anal. 2013;92:1116–1137.
- Himonas A, Holliman C. The Cauchy problem for the Novikov equation. Nonlinearity. 2012;25:449–479.
- Jiang Z, Ni L. Blow-up phenomenon for the integrable Novikov equation. J. Math. Anal. Appl. 2012;385:551–558.
- Yan W, Li Y, Zhang Y. Global existence and blow-up phenomena for the weakly dissipative Novikov equation. Nonlinear Anal. 2012;75:2464–2473.
- Hone W, Lundmark H, Szmigielski J. Explicit multipeakon solutions of Novikov cubically nonlinear integrable Camassa--Holm type equation. Dyn. Partial Differ. Equ. 2009;6:253–289.
- Kato T, Ponce G. Commutator estimates and the Euler and Navier--Stokes equations. Comm. Pure Appl. Math. 1988;41:891–907.
- Bona J, Smith R. The initial value problem for the Korteweg-de Vries equation. Philos. Trans. R. Soc. London Ser. A. 1975;278:555–601.
- Li Y, Olver P. Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation. J. Differential Equations. 2000;162:27–63.
- Walter W. Differential and integral inequalities. New York (NY): Springer-Verlag; 1970.