TY - BOOK AU - Bahouri, H. AU - Chemin, J. Y. AU - Danchin, R. PY - 2011 DA - 2011// TI - Fourier Analysis and Nonlinear Partial Differential Equations PB - Springer CY - Heidelberg UR - https://doi.org/10.1007/978-3-642-16830-7 DO - 10.1007/978-3-642-16830-7 ID - Bahouri2011 ER - TY - JOUR AU - Cai, H. AU - Chen, G. AU - Chen, R. M. AU - Shen, Y. N. PY - 2018 DA - 2018// TI - Lipschitz metric for the Novikov equation JO - Arch. Ration. Mech. Anal. VL - 229 UR - https://doi.org/10.1007/s00205-018-1234-4 DO - 10.1007/s00205-018-1234-4 ID - Cai2018 ER - TY - JOUR AU - Constantin, A. PY - 2000 DA - 2000// TI - Global existence of solutions and breaking waves for a shallow water equation: a geometric approach JO - Ann. Inst. Fourier (Grenoble) VL - 50 UR - https://doi.org/10.5802/aif.1757 DO - 10.5802/aif.1757 ID - Constantin2000 ER - TY - JOUR AU - Constantin, A. AU - Escher, J. PY - 1998 DA - 1998// TI - Wave breaking for nonlinear nonlocal shallow water equations JO - Acta Math. VL - 181 UR - https://doi.org/10.1007/BF02392586 DO - 10.1007/BF02392586 ID - Constantin1998 ER - TY - JOUR AU - Danchin, R. PY - 2012 DA - 2012// TI - A survey on Fourier analysis methods for solving the compressible Navier-Stokes equations JO - Sci. China Math. VL - 55 UR - https://doi.org/10.1007/s11425-011-4357-8 DO - 10.1007/s11425-011-4357-8 ID - Danchin2012 ER - TY - JOUR AU - Freire, I. L. PY - 2020 DA - 2020// TI - Wave breaking for shallow water models with time decaying solutions JO - J. Differ. Equ. VL - 267 ID - Freire2020 ER - TY - JOUR AU - Fu, Y. AU - Qu, C. Z. PY - 2017 DA - 2017// TI - Well-posedness and wave breaking of the degenerate Novikov equation JO - J. Differ. Equ. VL - 263 UR - https://doi.org/10.1016/j.jde.2017.05.027 DO - 10.1016/j.jde.2017.05.027 ID - Fu2017 ER - TY - JOUR AU - Gao, Y. AU - Li, L. AU - Liu, J. G. PY - 2018 DA - 2018// TI - A dispersive regularization for the modified Camassa-Holm equation JO - SIAM J. Math. Anal. VL - 50 UR - https://doi.org/10.1137/17M1132756 DO - 10.1137/17M1132756 ID - Gao2018 ER - TY - JOUR AU - Guo, Y. X. AU - Lai, S. Y. PY - 2010 DA - 2010// TI - New exact solutions for an N+1$N+1$ dimensional generalized Boussineq equation JO - Nonlinear Anal. VL - 72 UR - https://doi.org/10.1016/j.na.2009.11.030 DO - 10.1016/j.na.2009.11.030 ID - Guo2010 ER - TY - JOUR AU - Guo, Z. G. AU - Li, X. G. AU - Yu, C. PY - 2018 DA - 2018// TI - Some properties of solutions to the Camassa-Holm-type equation with higher order nonlinearities JO - J. Nonlinear Sci. VL - 28 UR - https://doi.org/10.1007/s00332-018-9469-7 DO - 10.1007/s00332-018-9469-7 ID - Guo2018 ER - TY - JOUR AU - Himonas, A. AU - Holliman, C. AU - Kenig, C. PY - 2018 DA - 2018// TI - Construction of 2-peakon solutions and ill-posedness for the Novikov equation JO - SIAM J. Math. Anal. VL - 50 UR - https://doi.org/10.1137/17M1151201 DO - 10.1137/17M1151201 ID - Himonas2018 ER - TY - JOUR AU - Himonas, A. AU - Misiolek, G. PY - 2003 DA - 2003// TI - Analyticity of the Cauchy problem for an integrable evolution equation JO - Math. Ann. VL - 327 UR - https://doi.org/10.1007/s00208-003-0466-1 DO - 10.1007/s00208-003-0466-1 ID - Himonas2003 ER - TY - JOUR AU - Hone, A. N. W. AU - Wang, J. P. PY - 2008 DA - 2008// TI - Integrable peakon equations with cubic nonlinearities JO - J. Phys. A, Math. Theor. VL - 41 UR - https://doi.org/10.1088/1751-8113/41/37/372002 DO - 10.1088/1751-8113/41/37/372002 ID - Hone2008 ER - TY - JOUR AU - Huang, Y. Z. AU - Yu, X. PY - 2019 DA - 2019// TI - Solitons and peakons of a nonautonomous Camassa-Holm equation JO - Appl. Math. Lett. VL - 98 UR - https://doi.org/10.1016/j.aml.2019.06.040 DO - 10.1016/j.aml.2019.06.040 ID - Huang2019 ER - TY - JOUR AU - Lai, S. Y. AU - Wu, Y. H. PY - 2011 DA - 2011// TI - A model containing both the Camassa-Holm and Degasperis-Procesi equations JO - J. Math. Anal. Appl. VL - 374 UR - https://doi.org/10.1016/j.jmaa.2010.09.012 DO - 10.1016/j.jmaa.2010.09.012 ID - Lai2011 ER - TY - JOUR AU - Lenells, J. AU - Wunsch, M. PY - 2013 DA - 2013// TI - On the weakly dissipative Camassa-Holm, Degasperis-Procesi and Novikov equations JO - J. Differ. Equ. VL - 255 UR - https://doi.org/10.1016/j.jde.2013.04.015 DO - 10.1016/j.jde.2013.04.015 ID - Lenells2013 ER - TY - JOUR AU - Li, H. Y. AU - Yan, W. P. PY - 2019 DA - 2019// TI - Asymptotic stability and instability of explicit self-similar waves for a class of nonlinear shallow water equations JO - Commun. Nonlinear Sci. Numer. Simul. VL - 79 UR - https://doi.org/10.1016/j.cnsns.2019.104928 DO - 10.1016/j.cnsns.2019.104928 ID - Li2019 ER - TY - JOUR AU - Li, M. G. AU - Zhang, Q. T. PY - 2017 DA - 2017// TI - Generic regularity of conservative solutions to Camassa-Holm type equations JO - SIAM J. Math. Anal. VL - 49 UR - https://doi.org/10.1137/16M1063009 DO - 10.1137/16M1063009 ID - Li2017 ER - TY - JOUR AU - Luo, W. AU - Yin, Z. Y. PY - 2015 DA - 2015// TI - Local well-posedness and blow-up criteria for a two-component Novikov system in the critical Besov space JO - Nonlinear Anal. VL - 122 UR - https://doi.org/10.1016/j.na.2015.03.022 DO - 10.1016/j.na.2015.03.022 ID - Luo2015 ER - TY - JOUR AU - Mi, Y. S. AU - Liu, Y. AU - Guo, B. L. AU - Luo, T. PY - 2019 DA - 2019// TI - The Cauchy problem for a generalized Camassa-Holm equation JO - J. Differ. Equ. VL - 266 UR - https://doi.org/10.1016/j.jde.2018.11.019 DO - 10.1016/j.jde.2018.11.019 ID - Mi2019 ER - TY - JOUR AU - Ming, S. AU - Lai, S. Y. AU - Su, Y. Q. PY - 2019 DA - 2019// TI - The Cauchy problem of a weakly dissipative shallow water equation JO - Appl. Anal. VL - 98 UR - https://doi.org/10.1080/00036811.2017.1422728 DO - 10.1080/00036811.2017.1422728 ID - Ming2019 ER - TY - JOUR AU - Molinet, L. PY - 2018 DA - 2018// TI - A Liouville property with application to asymptotic stability for the Camassa-Holm equation JO - Arch. Ration. Mech. Anal. VL - 230 UR - https://doi.org/10.1007/s00205-018-1243-3 DO - 10.1007/s00205-018-1243-3 ID - Molinet2018 ER - TY - JOUR AU - Molinet, L. PY - 2019 DA - 2019// TI - A rigidity result for the Holm-Staley b-family of equations with application to the asymptotic stability of the Degasperis-Procesi peakon JO - Nonlinear Anal., Real World Appl. VL - 50 UR - https://doi.org/10.1016/j.nonrwa.2019.06.004 DO - 10.1016/j.nonrwa.2019.06.004 ID - Molinet2019 ER - TY - JOUR AU - Novikov, V. PY - 2009 DA - 2009// TI - Generalizations of the Camassa-Holm equation JO - J. Phys. A VL - 42 ID - Novikov2009 ER - TY - JOUR AU - Novruzova, E. AU - Hagverdiyevb, A. PY - 2014 DA - 2014// TI - On the behavior of the solution of the dissipative Camassa-Holm equation with the arbitrary dispersion coefficient JO - J. Differ. Equ. VL - 257 UR - https://doi.org/10.1016/j.jde.2014.08.016 DO - 10.1016/j.jde.2014.08.016 ID - Novruzova2014 ER - TY - JOUR AU - Silva, P. L. AU - Freire, I. L. PY - 2019 DA - 2019// TI - Well-posedness, traveling waves and geometrical aspects of generalizations of the Camassa-Holm equation JO - J. Differ. Equ. VL - 267 UR - https://doi.org/10.1016/j.jde.2019.05.033 DO - 10.1016/j.jde.2019.05.033 ID - Silva2019 ER - TY - JOUR AU - Tu, X. AU - Yin, Z. Y. PY - 2015 DA - 2015// TI - Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation in the critical Besov space JO - Nonlinear Anal. VL - 128 UR - https://doi.org/10.1016/j.na.2015.07.017 DO - 10.1016/j.na.2015.07.017 ID - Tu2015 ER - TY - JOUR AU - Wang, Y. AU - Zhu, M. PY - 2020 DA - 2020// TI - On the singularity formation for a class of periodic higher order Camassa-Holm equations JO - J. Differ. Equ. VL - 269 UR - https://doi.org/10.1016/j.jde.2020.05.040 DO - 10.1016/j.jde.2020.05.040 ID - Wang2020 ER - TY - JOUR AU - Yan, W. AU - Li, Y. S. AU - Zhai, X. P. AU - Zhang, Y. M. PY - 2019 DA - 2019// TI - The Cauchy problem for higher order modified Camassa-Holm equations on the circle JO - Nonlinear Anal. VL - 187 UR - https://doi.org/10.1016/j.na.2019.05.009 DO - 10.1016/j.na.2019.05.009 ID - Yan2019 ER - TY - JOUR AU - Zhang, L. PY - 2019 DA - 2019// TI - Non-uniform dependence and well-posedness for the rotation Camassa-Holm equation on the torus JO - J. Differ. Equ. VL - 267 UR - https://doi.org/10.1016/j.jde.2019.05.023 DO - 10.1016/j.jde.2019.05.023 ID - Zhang2019 ER - TY - JOUR AU - Zhang, Y. Y. AU - Hu, Q. Y. PY - 2020 DA - 2020// TI - Weak well-posedness for the integrable modified Camassa-Holm equation with the cubic nonlinearity JO - J. Math. Anal. Appl. VL - 483 UR - https://doi.org/10.1016/j.jmaa.2019.123633 DO - 10.1016/j.jmaa.2019.123633 ID - Zhang2020 ER - TY - JOUR AU - Zheng, R. D. AU - Yin, Z. Y. PY - 2020 DA - 2020// TI - Wave breaking and solitary wave solutions for a generalized Novikov equation JO - Appl. Math. Lett. VL - 100 UR - https://doi.org/10.1016/j.aml.2019.106014 DO - 10.1016/j.aml.2019.106014 ID - Zheng2020 ER - TY - JOUR AU - Zhou, Y. AU - Chen, H. P. PY - 2011 DA - 2011// TI - Wave breaking and propagation speed for the Camassa-Holm equation with k≠0$k\neq 0$ JO - Nonlinear Anal., Real World Appl. VL - 12 UR - https://doi.org/10.1016/j.nonrwa.2010.12.005 DO - 10.1016/j.nonrwa.2010.12.005 ID - Zhou2011 ER -