[1] Anco, S., Bluman, G.: Direct construction method for conservation laws of partial differential equations. I. Examples of conservation law classifications. European J. Appl. Math., 13, 5, 2002, 545-566, DOI 10.1017/S095679250100465X | MR 1939160

[2] Anco, S., Bluman, G.: Direct construction method for conservation laws of partial differential equations. II. General treatment. European J. Appl. Math., 13, 5, 2002, 567-585, DOI 10.1017/S0956792501004661 | MR 1939161

[3] Anco, S., Silva, P.L. da, Freire, I.L.: A family of wave-breaking equations generalizing the Camassa--Holm and Novikov equations. J. Math. Phys., 56, 9, 2015, paper 091506, DOI 10.1063/1.4929661 | MR 3395277

[4] Bluman, G.W., Anco, S.: Symmetry and Integration Methods for Differential Equations. 2002, Applied Mathematical Sciences 154. Springer, New York, MR 1914342

[5] Bluman, G.W., Kumei, S.: Symmetries and Differential Equations. 1989, Applied Mathematical Sciences 81. Springer, New York, DOI 10.1007/978-1-4757-4307-4 | MR 1006433 | Zbl 0698.35001

[6] Bozhkov, Y., Freire, I.L., Ibragimov, N.: Group analysis of the Novikov equation. Comput. Appl. Math., 33, 1, 2014, 193-202, DOI 10.1007/s40314-013-0055-1 | MR 3187981

[7] Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. 2011, Universitext. Springer, New York, MR 2759829 | Zbl 1220.46002

[8] Camassa, R., Holm, D.D.: An integrable shallow water equation with peaked solitons. Phys. Rev. Lett., 71, 11, 1993, 1661-1664, DOI 10.1103/PhysRevLett.71.1661 | MR 1234453

[9] Clarkson, P.A., Mansfield, E.L., Priestley, T.J.: Symmetries of a class of nonlinear third-order partial differential equations. Math. Comput. Modelling., 25, 8-9, 1997, 195-212, DOI 10.1016/S0895-7177(97)00069-1 | MR 1465776

[10] Constantin, A., Escher, J.: Wave breaking for nonlinear nonlocal shallow water equations. Acta Math., 181, 2, 1998, 229-243, DOI 10.1007/BF02392586 | MR 1668586

[11] Constantin, A., Strauss, W.A.: Stability of peakons. Comm. Pure Appl. Math., 53, 5, 2000, 603-610, DOI 10.1002/(SICI)1097-0312(200005)53:5<603::AID-CPA3>3.0.CO;2-L | MR 1737505

[12] Constantin, A.: Existence of permanent and breaking waves for a shallow water equation: a geometric approach. Ann. Inst. Fourier, 50, 2, 2000, 321-362, DOI 10.5802/aif.1757 | MR 1775353

[13] Constantin, A., Escher, J.: Global existence and blow-up for a shallow water equation. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 26, 2, 1998, 303-328, MR 1631589

[14] Silva, P.L. da, Freire, I.L.: Strict self-adjointness and shallow water models. arXiv:, 1312.3992, 2013, Preprint..

[15] Silva, P.L. da, Freire, I.L.: On the group analysis of a modified Novikov equation. Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science, Springer Proceedings in Mathematics & Statistics, 117, 2015, 161-166, Springer, DOI: 10.1007/978-3-319-12307-3_23. DOI 10.1007/978-3-319-12307-3_23 | MR 3444170

[16] Silva, P.L. da, Freire, I.L.: An equation unifying both Camassa--Holm and Novikov equations. Dynamical Systems and Differential Equations, Proceedings of the 10th AIMS International Conference, 2015, 304-311, American Institute of Mathematical Sciences, DOI: 10.3934/proc.2015.0304. DOI 10.3934/proc.2015.0304 | MR 3462461

[17] Silva, P.L. da, Freire, I.L.: Uma nova equação unificando quatro modelos físicos. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 3, 2, 2015, In Portuguese..

[18] Silva, P.L. da, Freire, I.L., Sampaio, J.C.S.: A family of wave equations with some remarkable properties. Proc. A, 474, 2210, 2018, paper 20170763, MR 3782781

[19] Silva, P.L. da, Freire, I.L.: Well-posedness, travelling waves and geometrical aspects of generalizations of the Camassa--Holm equation. J. Differential Equations, 267, 9, 2019, 5318-5369, DOI 10.1016/j.jde.2019.05.033 | MR 3991561

[20] Degasperis, A., Procesi, M.: Asymptotic integrability. Symmetry and Perturbation Theory, World Scientific Publishing, River Edge, NJ, 1999, 23-37, MR 1844104

[21] Degasperis, A., Holm, D.D., Hone, A.N.W.: A new integrable equation with peakon solutions. Theoret. and Math. Phys., 133, 2, 2002, 1463-1474, Translated from Russian.. DOI 10.1023/A:1021186408422 | MR 2001531

[22] Degasperis, A., Holm, D.D., Hone, A.N.W.: Integrable and non-integrable equations with peakons. Nonlinear Physics: Theory and Experiment, II (Gallipoli, 2002), 2003, 37-43, World Scientific Publishing, River Edge, NJ, See arXiv:nlin/0209008.. MR 2028761

[23] Escher, J.: Breaking water waves. Nonlinear Water Waves, Lecture Notes in Mathematics, vol. 2158, 2016, 83-119, Springer, Switzerland, DOI: 10.1007/978-3-319-31462-4_2. DOI 10.1007/978-3-319-31462-4_2 | MR 3524896

[24] Fokas, A.S., Fuchssteiner, B.: Sympletic structures, their Bäcklund transformations and hereditary symmetries. Phys. D, 4, 1, 1981/82, 47-66, MR 0636470

[25] Folland, G.B.: Introduction to partial differential equations. Second edition. 1995, Princeton University Press, Princeton, NJ, MR 1357411

[26] Hay, M., Hone, A.N.W., Novikov, V.S., Wang, J.P.: Remarks on certain two-component systems with peakon solutions. J. Geom. Mech., 11, 4, 2019, 561-573, DOI 10.3934/jgm.2019028 | MR 4043678

[27] Himonas, A.A., Holliman, C.: The Cauchy problem for a generalized Camassa--Holm equation. Adv. Differential Equations, 19, 1-2, 2014, 161-200, MR 3161659

[28] Holm, D.D., Staley, M.F.: Wave structure and nonlinear balances in a family of evolutionary PDEs. SIAM J. Appl. Dyn. Syst., 2, 3, 2003, 323-380, DOI 10.1137/S1111111102410943 | MR 2031278

[29] Hone, A.N.W., Wang, J.P.: Integrable peakon equations with cubic nonlinearity. J. Phys. A, 41, 37, 2008, paper 372002, DOI 10.1088/1751-8113/41/37/372002 | MR 2430566

[30] Hone, A.N.W., Lundmark, H., Szmigielski, J.: Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa--Holm type equation. Dyn. Partial Differ. Equ., 6, 3, 2009, 253-289, DOI 10.4310/DPDE.2009.v6.n3.a3 | MR 2569508

[31] Hunter, J.K., Nachtergaele, B.: Applied Analysis. 2005, World Scientific Publishing, Singapore, MR 1829589

[32] Ibragimov, N.H.: Transformation Groups Applied to Mathematical Physics. 1985, Mathematics and its Applications (Soviet Series), D. Reidel Publishing Co., Dordrecht, Translated from Russian.. MR 0785566

[33] Ibragimov, N.H.: Elementary Lie Group Analysis and Ordinary Differential Equations. 1999, Wiley Series in Mathematical Methods in Practice, 4. John Wiley & Sons, Chichester, MR 1679646

[34] Krasil'shchik, J., Verbovetsky, A., Vitolo, R.: The Symbolic Computation of Integrability Structures for Partial Differential Equations. 2017, Texts and Monographs in Symbolic Computation. Springer, Cham, MR 3753682

[35] Lenells, J.: Conservation laws of the Camassa-Holm equation. J. Phys. A, 38, 4, 2005, 869-880, DOI 10.1088/0305-4470/38/4/007 | MR 2125239

[36] Lenells, J.: Traveling wave solutions of the Camassa-Holm equation. J. Differential Equations, 217, 2, 2005, 393-430, DOI 10.1016/j.jde.2004.09.007 | MR 2168830

[37] Mikhailov, A.V., Novikov, V.S.: Perturbative symmetry approach. J. Phys. A, 35, 22, 2002, 4775-4790, DOI 10.1088/0305-4470/35/22/309 | MR 1908645

[38] Mikhailov, A.V., Sokolov, V.V.: Symmetries of differential equations and the problem of integrability. Integrability, Lecture Notes in Phys., vol. 767, 2009, 19-88, Springer, Berlin, DOI 10.1007/978-3-540-88111-7_2 | MR 2867546

[39] Novikov, V.S.: Generalizations of the Camassa-Holm equation. J. Phys. A, 42, 34, 2009, 342002, DOI 10.1088/1751-8113/42/34/342002 | MR 2530232

[40] Olver, P.J.: Evolution equations possessing infinitely many symmetries. J. Mathematical Phys., 18, 6, 1977, 1212-1215, DOI 10.1063/1.523393 | MR 0521611

[41] Olver, P.J.: Applications of Lie Groups to Differential Equations. Second edition. 1993, Graduate Texts in Mathematics, 107. Springer-Verlag, New York, MR 1240056

[42] Popovych, R.O., Sergyeyev, A.: Conservation laws and normal forms of evolution equations. Phys. Lett. A, 374, 22, 2010, 2210-2217, DOI 10.1016/j.physleta.2010.03.033 | MR 2629731

[43] Popovych, R.O., Bihlo, A.: Inverse problem on conservation laws. Phys. D, 401, 2020, paper 132175, DOI 10.1016/j.physd.2019.132175 | MR 4034667

[44] M.E.Taylor: Partial Differential Equations I. Basic Theory. Second edition. 2011, Applied Mathematical Sciences, 115. Springer, New York, MR 2744150