References
- Chen RM, Hu TQ, Liu Y. The shallow-water models with cubic nonlinearity. J Math Fluid Mech. 2022;24(1):1–31.
- Mi YS, Liu Y, Huang DW, et al. Qualitative analysis for the new shallow-water model with cubic nonlinearity. J Differ Equ. 2020;269(6):5228–5279.
- Camassa R, Holm DD. An integrable shallow water equation with peaked solitons. Phys Rev Lett. 1993;71(11):1661–1664.
- Constantin A, Strauss W. Stability of a class of solitary waves in compressible elastic rods. Phys Lett A. 2000;270(3-4):140–148.
- Fuchssteiner B, Fokas AS. Symplectic structures their Backlund transformations and hereditary symmetries. Phys D: Nonlinear Phenom. 1981;4(1):47–66.
- Constantin A, Escher J. Wave breaking for nonlinear nonlocal shallow water equations. Acta Math. 1998;181(2):229–243.
- Constantin A. Global existence of solutions and wave breaking waves for a shallow water equation: a geometric approach. Ann Inst Fourier (Grenoble). 2000;50(2):321–362.
- Constantin A, Escher J. Global existence and blow-up for a shallow water equation. Ann Sc Norm Super Pisa. 1998;26:303–328.
- Constantin A, Kolev B. Integrability of invariant metrics on the diffeomorphism group of the circle. J Nonlinear Sci. 2006;16(2):109–122.
- Kolev B. Poisson brackets in hydrodynamics. Discrete Contin Dyn Syst. 2007;19(3):555–574.
- Liu ZR, Qian TF. Peakons of the Camassa–Holm equation. Appl Math Model. 2002;26(3):473–480.
- Cao CS, Holm DD, Titi E. Traveling wave solutions for a class of one-dimensional nonlinear shallow water wave models. J Dyn Differ Equ. 2004;16(1):167–178.
- Constantin A, Strauss W. Stability of peakons. Comm Pure Appl Math. 2000;53:603–610.
- Constantin A, Molinet L. Orbital stability of solitary waves for a shallow water equation. Phys D Nonlinear Phenom. 2001;157(1-2):75–89.
- Chen RM, Liu XC, Liu Y. Stability of the Camassa–Holm peakons in the dynamics of a shallow-water-type system. Calc Var Partial Differ Equ. 2016;55(1):1–22.
- Dika K, Molinet L. Stability of multipeakons. Ann Inst H Poincaré-An. 2009;26(4):1517–1532.
- Qin GQ, Yan ZY, Guo BL. Orbital stability of peakon solutions for a generalized higher-order Camassa–Holm equation. Z Angew Math Phys. 2022;73(3):1–19.
- Deng TJ, Chen AY. Orbital stability of the sum of N peakons for the generalized higher-order Camassa–Holm equation. Z Angew Math Phys. 2022;73(4):1–28.
- Qu CZ, Liu XC, Liu Y. Stability of peakons for an integrable modified Camassa–Holm equation with cubic nonlinearity. Commun Math Phys. 2013;322(3):967–997.
- Liu XC, Liu Y, Qu CZ. Stability of the train of peakons for an integrable modified Camassa–Holm equation. Adv Math. 2014;255:1–37.
- Liu XC, Liu Y, Qu CZ. Stability of peakons for the Novikov equation. J Math Pures Et Appl. 2014;101(2):172–187.
- Palacios, José M. Orbital and asymptotic stability of a train of peakons for the Novikov equation. Discrete Contin Dyn Sys-Ser B. 2020;41:1–43.
- Liu XX. Orbital stability of peakons for a modified Camassa–Holm equation with higher-order nonlinearity. Discrete Contin Dyn Syst. 2018;38(11):5505–5521.
- Liu XX. Stability in the energy space of the sum of N peakons for a modified Camassa–Holm equation with higher-order nonlinearity. J Math Phys. 2018;59(12):Article ID 121505.
- Guo ZH, Liu XC, Liu XX, et al.Stability of peakons for the generalized modified Camassa–Holm equation. J Differ Equ. 2019;266(12):7749–7779.
- Anco S, Recio E. A general family of multi-peakon equations and their properties. J Phys A Math Theor. 2019;52(12):Article ID 125203.
- Yang ML, Li YS, Zhao YY. On the Cauchy problem of generalized Fokas–Olver–Resenau–Qiao equation. Appl Anal. 2018;97(13):2246–2268.
- Deng TJ, Chen AY. Orbital stability of the sum of N peakons for the generalized modified Camassa–Holm equation. Monatsh Math. 2022. DOI:10.1007/s00605-022-01766-2
- Chen RM, Di HF, Liu Y. Stability of peaked solitary waves for a class of cubic quasilinear shallow-water equations. Int Math Res Not. 2023;2023(7):6186–6218.
- Qin GQ, Yan ZY, Guo BL. The Cauchy problem and multi-peakons for the mCH-Novikov-CH equation with quadratic and cubic nonlinearities. J Dyn Differ Equ. 2022. DOI:10.1007/s10884-021-10115-0