References
- Li H, Li Y, Chen Y. Bi-Hamiltonian structure of multi-component Novikov system. J Nonlinear Math Phys. 2014;21:509–520.
- Qu C, Fu Y. On the Cauchy problem and peakons of a two-component Novikov system. Sci China Math. 2020;63:1965–1996.
- Novikov V. Generalizations of Camassa-Holm equation. J Phys A. 2009;42:342002.
- Hone A, Wang J. Integrable peakon equations with cubic nonlinearity. J Phys A. 2008;41:372002.
- Himonas A, Holliman C. The Cauchy problem of the Novikov equation. Nonlinearity. 2012;25:449–479.
- Ni L, Zhou Y. Well-posedness and persistence properties for the Novikov equation. J Differential Equations. 2011;250:3002–3021.
- Wu X, Yin Z. Well-posedness and global existence for the Novikov equation. Ann Sc Norm Super Pisa CI Sci. 2012;11:707–727.
- Yan W, Li Y, Zhang Y. The Cauchy problem of the integrable Novikov equation. J Differential Equations. 2012;253:298–318.
- Himonas A, Holmes J. Hölder continuity of the solution map for the Novikov equation. J Math Phys. 2013;54:061501.
- Wang H, Fu Y. A note on the Cauchy problem for the periodic two-component Novikov system. Appl Anal. 2020;99:1042–1065.
- Fuchssteiner B, Fokas A. Symplectic structures, their Bäklund transformation and hereditary symmetries. Phys D. 1981/1982;4:47–66.
- Camassa R, Holm D. An integrable shallow water equation with peaked solitons. Phys Rev Lett. 1993;71:1661–1664.
- Camassa R, Holm D, Hyman J. A new integrable shallow water equation. Adv Appl Mech. 1994;31:1–33.
- Constantin A. Existence of permanent and breaking waves for a shallow water equation: a geometric approach. Ann Inst Fourier (Grenoble). 2000;50:321–362.
- Constantin A, Escher J. Wave breaking for nonlinear nonlocal shallow water equations. Acta Math. 1998;181:229–243.
- Constantin A, Escher J. On the blow-up rate and the blow-up set of breaking waves for a shallow water equation. Math Z. 2000;233:75–91.
- Danchin R. A few remarks on the Camassa-Holm equation. Differential Integral Equations. 2001;14:953–988.
- Danchin R. A note on well-posedness for Camassa-Holm equation. J Differential Equations. 2003;192:429–444.
- Danchin R. Fourier analysis method for PDEs. Lecture Notes; 2005 Nov 14. https://m.doc88.com/p-9079718125760.html.
- 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.
- Himonas A, Kenig C. Non-uniform dependence on initial data for the CH equation on the line. Differential Integral Equations. 2009;22:201–224.
- Himonas A, Kenig C, Misiołek G. Non-uniform dependence for the periodic CH equation. Comm Partial Differential Equations. 2010;35:1145–1162.
- Chen M, Liu Y, Zhang P. The Hölder continuity of the solution map to the b-family equation. Math Ann. 2013;357:1245–1289.
- Tang H, Zhao Y. A note on the solution map for the periodic Camassa-Holm equation. Appl Anal. 2014;93:1745–1760.
- Pastrana J. Non-uniform dependence for Euler equations in Besov spaces. J Differential Equations. 2021;273:40–57.
- Himonas A, Misiołek G, Ponce G, et al. Persistence properties and unique continuation of solutions of the Camassa-Holm equation. Commun Math Phys. 2007;271:511–522.
- Luo W, Yin Z. Gevrey regularity and analyticity for Camassa-Holm type systems. Ann Sc Norm Super Pisa CI Sci. 2018;18:1061–1079.
- Constantin A, Ivanov R. On an integrable two-component Camassa-Holm shallow water system. Phys Lett A. 2008;372:7129–7132.
- Chen M, Liu S, Zhang Y. A two-component generalization of the Camassa-Holm equation and its solutions. Lett Math Phys. 2006;75:1–15.
- Shabat A, Alonso M. On the prolongation of a hierarchy of hydrodynamic chains. In: Proceedings of the NATO advanced research workshop; 2002, Cadiz, Spain. Dordrecht: Kluwer Academic Publishers; 2004, p. 263–280. (NATO Science Series).
- Fu Y, Wang H. A note on the solution map for the periodic multi-dimensional Camassa-Holm-type system. Monatsh Math. 2022;197:435–461.
- Guan C, Yin Z. Global existence and blow-up phenomenon for the 2-component Camassa-Holm system. J Differential Equations. 2010;248:2003–2014.
- Gui G, Liu Y. On the global existence and wave-breaking criterion for the two-component Camassa-Holm system. J Funct Anal. 2010;258:4251–4278.
- Gui G, Liu Y. On the Cauchy problem for the two-component Camassa-Holm system. Math Z. 2011;268:45–66.
- Lv G, Wang X. On the Cauchy problem for a two-component b-family system. Nonlinear Anal. 2014;111:1–14.
- Geng X, Xue B. An extension of integrable peakon equations with cubic nonlinearity. Nonlinearity. 2009;22:1847–1856.
- Mi Y, Mu C, Tao W. On the Cauchy problem for the two-component Novikov equation. Adv Math Phys. 2013;2:105–121.
- Tang H, Liu Z. The Cauchy problem for a two-component Novikov equation in the critical Besov spaces. J Math Anal Appl. 2015;423:120–135.
- Wang H, Chong G, Wu L. A note on the Cauchy problem for the two-component Novikov system. J Evol Equ. 2021;21:1809–1843.
- Bahouri H, Chemin J, Danchin R. Fourier analysis and nonlinear partial differential equations. Berlin: Springer-Verlag; 2011. (Grundlehren der mathematischen Wissenschaften; 343).
- Li J, Yin Z. Well-posedness and analytic solutions of the two-component Euler-Poincaré system. Monatsh Math. 2017;183:509–537.
- Taylor M. Commutator estimates. Proc Amer Math Soc. 2003;131:1501–1507.
- Wang F, Li F. Continuity properties of the data-to-solution map for the two-component higher order Camassa-Holm system. Nonlinear Anal Real World Appl. 2019;45:866–876.