Browse Journals

[1] R. Camassa and D. Holm, An integrable shallow water equation with peaked solitons, Physical Review Letters 71(11) (1993), 1661-1664.

DOI: https://doi.org/10.1103/PhysRevLett.71.1661

[2] A. Degasperis and M. Procesi, Asymptotic Integrqability, In: A. Degasperis and G. Gaeta, Editors, Symmetry and Perturbation Theory, Singapore: World Sientific, 1999, p. 23-37.

[3] A. Constantin and D. Lannes, The hydrodynamical relevans of the Camassa-Holm and Degasperis-Procesi equations, Archive for Rational Mechanics and Analysis 192(1) (2009), 165-186.

DOI: https://doi.org/10.1007/s00205-008-0128-2

[4] T. Benjamin, J. Bona and J. Mahony, Model equations for long waves in nonlinear dispersive systems, Philosophical Transactions of the Royal Society of London. Series A 272(1220) (1972), 47-78.

DOI: https://doi.org/10.1098/rsta.1972.0032

[5] A. Green and P. Naghdi, A derivation of equations for wave propagation in water of variable depth, Journal of Fluid Mechanics 78(2) (1976), 237-246.

DOI: https://doi.org/10.1017/S0022112076002425

[6] J. Esher, Y. Liu and Z. Yin, Global weak solutions and blow-up structure for the Degasperis-Procesi equation, Journal of Functional Analysis 241(2) (2006), 457-485.

DOI: https://doi.org/10.1016/j.jfa.2006.03.022

[7] O. Mustafa, Existence and uniqueness of low regularity solutions for the Dullin-Gottwald-Holm equation, Communications in Mathematical Physics 265(1) (2006), 189-200.

DOI: https://doi.org/10.1007/s00220-006-1532-9

[8] E. Wahlen, Gloobal existence of weak solutions to the Camassa-Holm equation, International Mathematics Research Notices (2006); Article 28976.

DOI: https://doi.org/10.1155/IMRN/2006/28976

[9] Y. Li and P. Olver, Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system I: Compactions and peakons, Discrete and Continuous Dynamical Systems 3(3) (1997), 419-432.

DOI: https://doi.org/10.3934/dcds.1997.3.419

[10] H. Lundmark and J. Szmigielski, Multi-peakon solutions of the Degasperis-Procesi equation, Inverse Problems 19(6) (2003), 1241.

DOI: https://doi.org/10.1088/0266-5611/19/6/001

[11] J. Lennels, Traveling wave solutions of the Camassa-Holm equation, Journal of Differential Equations 217(2) (2005), 393-430.

DOI: https://doi.org/10.1016/j.jde.2004.09.007

[12] R. Beels, D. Sattinger and J. Szmigielski, Multipeakons and the classical moment problem, Advances in Mathematics 154(2) (1999), 229-257.

DOI: https://doi.org/10.1006/aima.1999.1883

[13] K. Grunert and H. Holden, The general peakon-antipeakon solution for the Camassa-Holm equation, Journal of Hyperbolic Differential Equations 13(2) (2016), 353-380.

DOI: https://doi.org/10.1142/S0219891616500119

[14] H. Lundmark, Formation and dynamics of shock waves in the Degasperis-Procesi equation, Journal of Nonlinear Science 17(3) (2007), 169-198.

DOI: https://doi.org/10.1007/s00332-006-0803-3

[15] G. Omel’yanov, Asymptotics for peakon-antipeakon collision in a general Camassa-Holm model, Chaos, Solitons & Fractals: X 11 (2023), 100101.

DOI: https://doi.org/10.1016/j.csfx.2023.100101

[16] I. M. Gel’fand and G. E. Shilov, Generalized Functions, New York: Academic Press, 1964.

[17] J. Noyola Rodriguez and G. Omel’yanov, General Degasperis-Procesi equation and its solitary wave solutions, Chaos, Solitons & Fractals 118 (2019), 41-46.

DOI: https://doi.org/10.1016/j.chaos.2018.10.031

[18] G. Omel’yanov, Classical and nonclassical solitary waves in the general Degasperis-Procesi model, Russian Journal of Mathematical Physics 26(3) (2019), 384-390.

DOI: https://doi.org/10.1134/S1061920819030129

[19] G. Omel’yanov, Collision of solitons in non-integrable versions of the Degasperis-Procesi model, Chaos, Solitons & Fractals 136 (2020); 109802.

DOI: https://doi.org/10.1016/j.chaos.2020.109802

[20] J. Noyola Rodriguez and G. Omel’yanov, A finite difference scheme for smooth solutions of the general Degasperis-Procesi equation, Numerical Methods for Partial Differential Equations 36(4) (2020), 887-905.

DOI: https://doi.org/10.1002/num.22456

[21] O. A. Oleinik, On the construction of a generalized solution to the Cauchy problem for a quasi-linear equation by introducing the “vanishing viscosity”, Maer Math Coc Transl 23(2) (1963), 277-283.

[22] T. P. Liu, The entropy condition and the admissibility of shocks, Journal of Mathematical Analysis and Applications 53(1) (1976), 78-88.

DOI: https://doi.org/10.1016/0022-247X(76)90146-3

[23] V. G. Danilov, G. A. Omel’yanov and V. M. Shelkovich, Weak Asymptotics Method and Interaction of Nonlinear Waves, In: M. V. Karasev, Editor, Asymptotic Methods for Wave and Quantum Problems, Providence, RI: AMS “Advances in Mathematical Sciences” 208 (2003), 33-163.

[24] V. G. Danilov and D. Mitrovic, Shock wave formation process for a multidimensional scalar conservation law, Quarterly of Applied Mathematics 69(4) (2011), 613-634.

[25] G. A. Omel’yanov, About the stability problem for strictly hyperbolic systems of conservation laws, Rendiconti del Seminario Matematico 69(4) (2011), 377-392.

[26] M. G. García-Alvarado, R. Flores-Espinoza and G. A. Omel’yanov, Interaction of shock waves in gas dynamics: Uniform in time asymptotics, International Journal of Mathematics and Mathematical Sciences (2005); Article ID 709309.

DOI: https://doi.org/10.1155/IJMMS.2005.3111

[27] R. F. Espinoza and G. A. Omel’yanov, Asymptotic behavior for the centered-rarefaction appearance problem, Electronic Journal of Differential Equations 148 (2005), 1-25.