Degasperis–Procesi equation (English Wikipedia)

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arxiv.org

Degasperis & Procesi 1999; Degasperis, Holm & Hone 2002; Mikhailov & Novikov 2002; Hone & Wang 2003; Ivanov 2005. Degasperis, Antonio; Procesi, Michela (1999), "Asymptotic integrability", in Degasperis, Antonio; Gaeta, Giuseppe (eds.), Symmetry and Perturbation Theory (Rome, 1998), River Edge, NJ: World Scientific, pp. 23–37 Degasperis, Antonio; Holm, Darryl D.; Hone, Andrew N. W. (2002), "A new integrable equation with peakon solutions", Theoret. And Math. Phys., vol. 133, no. 2, pp. 1463–1474, arXiv:nlin.SI/0205023, doi:10.1023/A:1021186408422, S2CID 121862973 Mikhailov, Alexander V.; Novikov, Vladimir S. (2002), "Perturbative symmetry approach", J. Phys. A: Math. Gen., vol. 35, no. 22, pp. 4775–4790, arXiv:nlin.SI/0203055v1, Bibcode:2002JPhA...35.4775M, doi:10.1088/0305-4470/35/22/309, S2CID 6976529 Hone, Andrew N. W.; Wang, Jing Ping (2003), "Prolongation algebras and Hamiltonian operators for peakon equations", Inverse Problems, vol. 19, no. 1, pp. 129–145, Bibcode:2003InvPr..19..129H, doi:10.1088/0266-5611/19/1/307, S2CID 250876439 Ivanov, Rossen (2005), "On the integrability of a class of nonlinear dispersive wave equations", J. Nonlin. Math. Phys., vol. 12, no. 4, pp. 462–468, arXiv:nlin/0606046, Bibcode:2005JNMP...12..462R, doi:10.2991/jnmp.2005.12.4.2, S2CID 248410128
Johnson 2003; Dullin, Gottwald & Holm 2004; Constantin & Lannes 2007; Ivanov 2007. Johnson, Robin S. (2003), "The classical problem of water waves: a reservoir of integrable and nearly-integrable equations", J. Nonlin. Math. Phys., vol. 10, no. Supplement 1, pp. 72–92, Bibcode:2003JNMP...10S..72J, doi:10.2991/jnmp.2003.10.s1.6 Dullin, Holger R.; Gottwald, Georg A.; Holm, Darryl D. (2004), "On asymptotically equivalent shallow water wave equations", Physica D, vol. 190, no. 1–2, pp. 1–14, arXiv:nlin.PS/0307011, Bibcode:2004PhyD..190....1D, doi:10.1016/j.physd.2003.11.004, S2CID 16100694 Constantin, Adrian; Lannes, David (2007), "The hydrodynamical relevance of the Camassa–Holm and Degasperis–Procesi equations", Archive for Rational Mechanics and Analysis, 192 (1): 165–186, arXiv:0709.0905, Bibcode:2009ArRMA.192..165C, doi:10.1007/s00205-008-0128-2, S2CID 17294466 Ivanov, Rossen (2007), "Water waves and integrability", Phil. Trans. R. Soc. A, vol. 365, no. 1858, pp. 2267–2280, arXiv:0707.1839, Bibcode:2007RSPTA.365.2267I, doi:10.1098/rsta.2007.2007, PMID 17360266, S2CID 11248237
Degasperis, Holm & Hone 2002. Degasperis, Antonio; Holm, Darryl D.; Hone, Andrew N. W. (2002), "A new integrable equation with peakon solutions", Theoret. And Math. Phys., vol. 133, no. 2, pp. 1463–1474, arXiv:nlin.SI/0205023, doi:10.1023/A:1021186408422, S2CID 121862973
Lundmark & Szmigielski 2003; Lundmark & Szmigielski 2005. Lundmark, Hans; Szmigielski, Jacek (2003), "Multi-peakon solutions of the Degasperis–Procesi equation", Inverse Problems, vol. 19, no. 6, pp. 1241–1245, arXiv:nlin.SI/0503033, Bibcode:2003InvPr..19.1241L, doi:10.1088/0266-5611/19/6/001, S2CID 250887009 Lundmark, Hans; Szmigielski, Jacek (2005), "Degasperis–Procesi peakons and the discrete cubic string", Internat. Math. Res. Papers, vol. 2005, no. 2, pp. 53–116, arXiv:nlin.SI/0503036, doi:10.1155/IMRP.2005.53
Matsuno 2005a; Matsuno 2005b. Matsuno, Yoshimasa (2005a), "Multisoliton solutions of the Degasperis–Procesi equation and their peakon limit", Inverse Problems, vol. 21, no. 5, pp. 1553–1570, arXiv:nlin/0511029, Bibcode:2005InvPr..21.1553M, doi:10.1088/0266-5611/21/5/004, S2CID 122820100 Matsuno, Yoshimasa (2005b), "The N-soliton solution of the Degasperis–Procesi equation", Inverse Problems, vol. 21, no. 6, pp. 2085–2101, arXiv:nlin.SI/0511029, Bibcode:2005InvPr..21.2085M, doi:10.1088/0266-5611/21/6/018

dissem.in

Coclite & Karlsen 2006; Coclite & Karlsen 2007; Lundmark 2007; Escher, Liu & Yin 2007. Coclite, Giuseppe Maria; Karlsen, Kenneth Hvistendahl (2007), "On the uniqueness of discontinuous solutions to the Degasperis–Procesi equation" (PDF), J. Differential Equations, vol. 234, no. 1, pp. 142–160, Bibcode:2007JDE...234..142C, doi:10.1016/j.jde.2006.11.008 Lundmark, Hans (2007), "Formation and dynamics of shock waves in the Degasperis–Procesi equation", J. Nonlinear Sci., vol. 17, no. 3, pp. 169–198, Bibcode:2007JNS....17..169L, doi:10.1007/s00332-006-0803-3, S2CID 28451735 Escher, Joachim; Liu, Yue; Yin, Zhaoyang (2007), "Shock waves and blow-up phenomena for the periodic Degasperis–Procesi equation", Indiana Univ. Math. J., vol. 56, no. 1, pp. 87–117, doi:10.1512/iumj.2007.56.3040

doi.org

Degasperis & Procesi 1999; Degasperis, Holm & Hone 2002; Mikhailov & Novikov 2002; Hone & Wang 2003; Ivanov 2005. Degasperis, Antonio; Procesi, Michela (1999), "Asymptotic integrability", in Degasperis, Antonio; Gaeta, Giuseppe (eds.), Symmetry and Perturbation Theory (Rome, 1998), River Edge, NJ: World Scientific, pp. 23–37 Degasperis, Antonio; Holm, Darryl D.; Hone, Andrew N. W. (2002), "A new integrable equation with peakon solutions", Theoret. And Math. Phys., vol. 133, no. 2, pp. 1463–1474, arXiv:nlin.SI/0205023, doi:10.1023/A:1021186408422, S2CID 121862973 Mikhailov, Alexander V.; Novikov, Vladimir S. (2002), "Perturbative symmetry approach", J. Phys. A: Math. Gen., vol. 35, no. 22, pp. 4775–4790, arXiv:nlin.SI/0203055v1, Bibcode:2002JPhA...35.4775M, doi:10.1088/0305-4470/35/22/309, S2CID 6976529 Hone, Andrew N. W.; Wang, Jing Ping (2003), "Prolongation algebras and Hamiltonian operators for peakon equations", Inverse Problems, vol. 19, no. 1, pp. 129–145, Bibcode:2003InvPr..19..129H, doi:10.1088/0266-5611/19/1/307, S2CID 250876439 Ivanov, Rossen (2005), "On the integrability of a class of nonlinear dispersive wave equations", J. Nonlin. Math. Phys., vol. 12, no. 4, pp. 462–468, arXiv:nlin/0606046, Bibcode:2005JNMP...12..462R, doi:10.2991/jnmp.2005.12.4.2, S2CID 248410128
Johnson 2003; Dullin, Gottwald & Holm 2004; Constantin & Lannes 2007; Ivanov 2007. Johnson, Robin S. (2003), "The classical problem of water waves: a reservoir of integrable and nearly-integrable equations", J. Nonlin. Math. Phys., vol. 10, no. Supplement 1, pp. 72–92, Bibcode:2003JNMP...10S..72J, doi:10.2991/jnmp.2003.10.s1.6 Dullin, Holger R.; Gottwald, Georg A.; Holm, Darryl D. (2004), "On asymptotically equivalent shallow water wave equations", Physica D, vol. 190, no. 1–2, pp. 1–14, arXiv:nlin.PS/0307011, Bibcode:2004PhyD..190....1D, doi:10.1016/j.physd.2003.11.004, S2CID 16100694 Constantin, Adrian; Lannes, David (2007), "The hydrodynamical relevance of the Camassa–Holm and Degasperis–Procesi equations", Archive for Rational Mechanics and Analysis, 192 (1): 165–186, arXiv:0709.0905, Bibcode:2009ArRMA.192..165C, doi:10.1007/s00205-008-0128-2, S2CID 17294466 Ivanov, Rossen (2007), "Water waves and integrability", Phil. Trans. R. Soc. A, vol. 365, no. 1858, pp. 2267–2280, arXiv:0707.1839, Bibcode:2007RSPTA.365.2267I, doi:10.1098/rsta.2007.2007, PMID 17360266, S2CID 11248237
Degasperis, Holm & Hone 2002. Degasperis, Antonio; Holm, Darryl D.; Hone, Andrew N. W. (2002), "A new integrable equation with peakon solutions", Theoret. And Math. Phys., vol. 133, no. 2, pp. 1463–1474, arXiv:nlin.SI/0205023, doi:10.1023/A:1021186408422, S2CID 121862973
Lundmark & Szmigielski 2003; Lundmark & Szmigielski 2005. Lundmark, Hans; Szmigielski, Jacek (2003), "Multi-peakon solutions of the Degasperis–Procesi equation", Inverse Problems, vol. 19, no. 6, pp. 1241–1245, arXiv:nlin.SI/0503033, Bibcode:2003InvPr..19.1241L, doi:10.1088/0266-5611/19/6/001, S2CID 250887009 Lundmark, Hans; Szmigielski, Jacek (2005), "Degasperis–Procesi peakons and the discrete cubic string", Internat. Math. Res. Papers, vol. 2005, no. 2, pp. 53–116, arXiv:nlin.SI/0503036, doi:10.1155/IMRP.2005.53
Matsuno 2005a; Matsuno 2005b. Matsuno, Yoshimasa (2005a), "Multisoliton solutions of the Degasperis–Procesi equation and their peakon limit", Inverse Problems, vol. 21, no. 5, pp. 1553–1570, arXiv:nlin/0511029, Bibcode:2005InvPr..21.1553M, doi:10.1088/0266-5611/21/5/004, S2CID 122820100 Matsuno, Yoshimasa (2005b), "The N-soliton solution of the Degasperis–Procesi equation", Inverse Problems, vol. 21, no. 6, pp. 2085–2101, arXiv:nlin.SI/0511029, Bibcode:2005InvPr..21.2085M, doi:10.1088/0266-5611/21/6/018
Coclite & Karlsen 2006; Coclite & Karlsen 2007; Lundmark 2007; Escher, Liu & Yin 2007. Coclite, Giuseppe Maria; Karlsen, Kenneth Hvistendahl (2007), "On the uniqueness of discontinuous solutions to the Degasperis–Procesi equation" (PDF), J. Differential Equations, vol. 234, no. 1, pp. 142–160, Bibcode:2007JDE...234..142C, doi:10.1016/j.jde.2006.11.008 Lundmark, Hans (2007), "Formation and dynamics of shock waves in the Degasperis–Procesi equation", J. Nonlinear Sci., vol. 17, no. 3, pp. 169–198, Bibcode:2007JNS....17..169L, doi:10.1007/s00332-006-0803-3, S2CID 28451735 Escher, Joachim; Liu, Yue; Yin, Zhaoyang (2007), "Shock waves and blow-up phenomena for the periodic Degasperis–Procesi equation", Indiana Univ. Math. J., vol. 56, no. 1, pp. 87–117, doi:10.1512/iumj.2007.56.3040

harvard.edu

ui.adsabs.harvard.edu

Degasperis & Procesi 1999; Degasperis, Holm & Hone 2002; Mikhailov & Novikov 2002; Hone & Wang 2003; Ivanov 2005. Degasperis, Antonio; Procesi, Michela (1999), "Asymptotic integrability", in Degasperis, Antonio; Gaeta, Giuseppe (eds.), Symmetry and Perturbation Theory (Rome, 1998), River Edge, NJ: World Scientific, pp. 23–37 Degasperis, Antonio; Holm, Darryl D.; Hone, Andrew N. W. (2002), "A new integrable equation with peakon solutions", Theoret. And Math. Phys., vol. 133, no. 2, pp. 1463–1474, arXiv:nlin.SI/0205023, doi:10.1023/A:1021186408422, S2CID 121862973 Mikhailov, Alexander V.; Novikov, Vladimir S. (2002), "Perturbative symmetry approach", J. Phys. A: Math. Gen., vol. 35, no. 22, pp. 4775–4790, arXiv:nlin.SI/0203055v1, Bibcode:2002JPhA...35.4775M, doi:10.1088/0305-4470/35/22/309, S2CID 6976529 Hone, Andrew N. W.; Wang, Jing Ping (2003), "Prolongation algebras and Hamiltonian operators for peakon equations", Inverse Problems, vol. 19, no. 1, pp. 129–145, Bibcode:2003InvPr..19..129H, doi:10.1088/0266-5611/19/1/307, S2CID 250876439 Ivanov, Rossen (2005), "On the integrability of a class of nonlinear dispersive wave equations", J. Nonlin. Math. Phys., vol. 12, no. 4, pp. 462–468, arXiv:nlin/0606046, Bibcode:2005JNMP...12..462R, doi:10.2991/jnmp.2005.12.4.2, S2CID 248410128
Johnson 2003; Dullin, Gottwald & Holm 2004; Constantin & Lannes 2007; Ivanov 2007. Johnson, Robin S. (2003), "The classical problem of water waves: a reservoir of integrable and nearly-integrable equations", J. Nonlin. Math. Phys., vol. 10, no. Supplement 1, pp. 72–92, Bibcode:2003JNMP...10S..72J, doi:10.2991/jnmp.2003.10.s1.6 Dullin, Holger R.; Gottwald, Georg A.; Holm, Darryl D. (2004), "On asymptotically equivalent shallow water wave equations", Physica D, vol. 190, no. 1–2, pp. 1–14, arXiv:nlin.PS/0307011, Bibcode:2004PhyD..190....1D, doi:10.1016/j.physd.2003.11.004, S2CID 16100694 Constantin, Adrian; Lannes, David (2007), "The hydrodynamical relevance of the Camassa–Holm and Degasperis–Procesi equations", Archive for Rational Mechanics and Analysis, 192 (1): 165–186, arXiv:0709.0905, Bibcode:2009ArRMA.192..165C, doi:10.1007/s00205-008-0128-2, S2CID 17294466 Ivanov, Rossen (2007), "Water waves and integrability", Phil. Trans. R. Soc. A, vol. 365, no. 1858, pp. 2267–2280, arXiv:0707.1839, Bibcode:2007RSPTA.365.2267I, doi:10.1098/rsta.2007.2007, PMID 17360266, S2CID 11248237
Lundmark & Szmigielski 2003; Lundmark & Szmigielski 2005. Lundmark, Hans; Szmigielski, Jacek (2003), "Multi-peakon solutions of the Degasperis–Procesi equation", Inverse Problems, vol. 19, no. 6, pp. 1241–1245, arXiv:nlin.SI/0503033, Bibcode:2003InvPr..19.1241L, doi:10.1088/0266-5611/19/6/001, S2CID 250887009 Lundmark, Hans; Szmigielski, Jacek (2005), "Degasperis–Procesi peakons and the discrete cubic string", Internat. Math. Res. Papers, vol. 2005, no. 2, pp. 53–116, arXiv:nlin.SI/0503036, doi:10.1155/IMRP.2005.53
Matsuno 2005a; Matsuno 2005b. Matsuno, Yoshimasa (2005a), "Multisoliton solutions of the Degasperis–Procesi equation and their peakon limit", Inverse Problems, vol. 21, no. 5, pp. 1553–1570, arXiv:nlin/0511029, Bibcode:2005InvPr..21.1553M, doi:10.1088/0266-5611/21/5/004, S2CID 122820100 Matsuno, Yoshimasa (2005b), "The N-soliton solution of the Degasperis–Procesi equation", Inverse Problems, vol. 21, no. 6, pp. 2085–2101, arXiv:nlin.SI/0511029, Bibcode:2005InvPr..21.2085M, doi:10.1088/0266-5611/21/6/018
Coclite & Karlsen 2006; Coclite & Karlsen 2007; Lundmark 2007; Escher, Liu & Yin 2007. Coclite, Giuseppe Maria; Karlsen, Kenneth Hvistendahl (2007), "On the uniqueness of discontinuous solutions to the Degasperis–Procesi equation" (PDF), J. Differential Equations, vol. 234, no. 1, pp. 142–160, Bibcode:2007JDE...234..142C, doi:10.1016/j.jde.2006.11.008 Lundmark, Hans (2007), "Formation and dynamics of shock waves in the Degasperis–Procesi equation", J. Nonlinear Sci., vol. 17, no. 3, pp. 169–198, Bibcode:2007JNS....17..169L, doi:10.1007/s00332-006-0803-3, S2CID 28451735 Escher, Joachim; Liu, Yue; Yin, Zhaoyang (2007), "Shock waves and blow-up phenomena for the periodic Degasperis–Procesi equation", Indiana Univ. Math. J., vol. 56, no. 1, pp. 87–117, doi:10.1512/iumj.2007.56.3040

indiana.edu

iumj.indiana.edu

Coclite & Karlsen 2006; Coclite & Karlsen 2007; Lundmark 2007; Escher, Liu & Yin 2007. Coclite, Giuseppe Maria; Karlsen, Kenneth Hvistendahl (2007), "On the uniqueness of discontinuous solutions to the Degasperis–Procesi equation" (PDF), J. Differential Equations, vol. 234, no. 1, pp. 142–160, Bibcode:2007JDE...234..142C, doi:10.1016/j.jde.2006.11.008 Lundmark, Hans (2007), "Formation and dynamics of shock waves in the Degasperis–Procesi equation", J. Nonlinear Sci., vol. 17, no. 3, pp. 169–198, Bibcode:2007JNS....17..169L, doi:10.1007/s00332-006-0803-3, S2CID 28451735 Escher, Joachim; Liu, Yue; Yin, Zhaoyang (2007), "Shock waves and blow-up phenomena for the periodic Degasperis–Procesi equation", Indiana Univ. Math. J., vol. 56, no. 1, pp. 87–117, doi:10.1512/iumj.2007.56.3040

nih.gov

pubmed.ncbi.nlm.nih.gov

Johnson 2003; Dullin, Gottwald & Holm 2004; Constantin & Lannes 2007; Ivanov 2007. Johnson, Robin S. (2003), "The classical problem of water waves: a reservoir of integrable and nearly-integrable equations", J. Nonlin. Math. Phys., vol. 10, no. Supplement 1, pp. 72–92, Bibcode:2003JNMP...10S..72J, doi:10.2991/jnmp.2003.10.s1.6 Dullin, Holger R.; Gottwald, Georg A.; Holm, Darryl D. (2004), "On asymptotically equivalent shallow water wave equations", Physica D, vol. 190, no. 1–2, pp. 1–14, arXiv:nlin.PS/0307011, Bibcode:2004PhyD..190....1D, doi:10.1016/j.physd.2003.11.004, S2CID 16100694 Constantin, Adrian; Lannes, David (2007), "The hydrodynamical relevance of the Camassa–Holm and Degasperis–Procesi equations", Archive for Rational Mechanics and Analysis, 192 (1): 165–186, arXiv:0709.0905, Bibcode:2009ArRMA.192..165C, doi:10.1007/s00205-008-0128-2, S2CID 17294466 Ivanov, Rossen (2007), "Water waves and integrability", Phil. Trans. R. Soc. A, vol. 365, no. 1858, pp. 2267–2280, arXiv:0707.1839, Bibcode:2007RSPTA.365.2267I, doi:10.1098/rsta.2007.2007, PMID 17360266, S2CID 11248237

ntnu.no

math.ntnu.no

Coclite & Karlsen 2006; Coclite & Karlsen 2007; Lundmark 2007; Escher, Liu & Yin 2007. Coclite, Giuseppe Maria; Karlsen, Kenneth Hvistendahl (2007), "On the uniqueness of discontinuous solutions to the Degasperis–Procesi equation" (PDF), J. Differential Equations, vol. 234, no. 1, pp. 142–160, Bibcode:2007JDE...234..142C, doi:10.1016/j.jde.2006.11.008 Lundmark, Hans (2007), "Formation and dynamics of shock waves in the Degasperis–Procesi equation", J. Nonlinear Sci., vol. 17, no. 3, pp. 169–198, Bibcode:2007JNS....17..169L, doi:10.1007/s00332-006-0803-3, S2CID 28451735 Escher, Joachim; Liu, Yue; Yin, Zhaoyang (2007), "Shock waves and blow-up phenomena for the periodic Degasperis–Procesi equation", Indiana Univ. Math. J., vol. 56, no. 1, pp. 87–117, doi:10.1512/iumj.2007.56.3040

semanticscholar.org

api.semanticscholar.org

Degasperis & Procesi 1999; Degasperis, Holm & Hone 2002; Mikhailov & Novikov 2002; Hone & Wang 2003; Ivanov 2005. Degasperis, Antonio; Procesi, Michela (1999), "Asymptotic integrability", in Degasperis, Antonio; Gaeta, Giuseppe (eds.), Symmetry and Perturbation Theory (Rome, 1998), River Edge, NJ: World Scientific, pp. 23–37 Degasperis, Antonio; Holm, Darryl D.; Hone, Andrew N. W. (2002), "A new integrable equation with peakon solutions", Theoret. And Math. Phys., vol. 133, no. 2, pp. 1463–1474, arXiv:nlin.SI/0205023, doi:10.1023/A:1021186408422, S2CID 121862973 Mikhailov, Alexander V.; Novikov, Vladimir S. (2002), "Perturbative symmetry approach", J. Phys. A: Math. Gen., vol. 35, no. 22, pp. 4775–4790, arXiv:nlin.SI/0203055v1, Bibcode:2002JPhA...35.4775M, doi:10.1088/0305-4470/35/22/309, S2CID 6976529 Hone, Andrew N. W.; Wang, Jing Ping (2003), "Prolongation algebras and Hamiltonian operators for peakon equations", Inverse Problems, vol. 19, no. 1, pp. 129–145, Bibcode:2003InvPr..19..129H, doi:10.1088/0266-5611/19/1/307, S2CID 250876439 Ivanov, Rossen (2005), "On the integrability of a class of nonlinear dispersive wave equations", J. Nonlin. Math. Phys., vol. 12, no. 4, pp. 462–468, arXiv:nlin/0606046, Bibcode:2005JNMP...12..462R, doi:10.2991/jnmp.2005.12.4.2, S2CID 248410128
Johnson 2003; Dullin, Gottwald & Holm 2004; Constantin & Lannes 2007; Ivanov 2007. Johnson, Robin S. (2003), "The classical problem of water waves: a reservoir of integrable and nearly-integrable equations", J. Nonlin. Math. Phys., vol. 10, no. Supplement 1, pp. 72–92, Bibcode:2003JNMP...10S..72J, doi:10.2991/jnmp.2003.10.s1.6 Dullin, Holger R.; Gottwald, Georg A.; Holm, Darryl D. (2004), "On asymptotically equivalent shallow water wave equations", Physica D, vol. 190, no. 1–2, pp. 1–14, arXiv:nlin.PS/0307011, Bibcode:2004PhyD..190....1D, doi:10.1016/j.physd.2003.11.004, S2CID 16100694 Constantin, Adrian; Lannes, David (2007), "The hydrodynamical relevance of the Camassa–Holm and Degasperis–Procesi equations", Archive for Rational Mechanics and Analysis, 192 (1): 165–186, arXiv:0709.0905, Bibcode:2009ArRMA.192..165C, doi:10.1007/s00205-008-0128-2, S2CID 17294466 Ivanov, Rossen (2007), "Water waves and integrability", Phil. Trans. R. Soc. A, vol. 365, no. 1858, pp. 2267–2280, arXiv:0707.1839, Bibcode:2007RSPTA.365.2267I, doi:10.1098/rsta.2007.2007, PMID 17360266, S2CID 11248237
Degasperis, Holm & Hone 2002. Degasperis, Antonio; Holm, Darryl D.; Hone, Andrew N. W. (2002), "A new integrable equation with peakon solutions", Theoret. And Math. Phys., vol. 133, no. 2, pp. 1463–1474, arXiv:nlin.SI/0205023, doi:10.1023/A:1021186408422, S2CID 121862973
Lundmark & Szmigielski 2003; Lundmark & Szmigielski 2005. Lundmark, Hans; Szmigielski, Jacek (2003), "Multi-peakon solutions of the Degasperis–Procesi equation", Inverse Problems, vol. 19, no. 6, pp. 1241–1245, arXiv:nlin.SI/0503033, Bibcode:2003InvPr..19.1241L, doi:10.1088/0266-5611/19/6/001, S2CID 250887009 Lundmark, Hans; Szmigielski, Jacek (2005), "Degasperis–Procesi peakons and the discrete cubic string", Internat. Math. Res. Papers, vol. 2005, no. 2, pp. 53–116, arXiv:nlin.SI/0503036, doi:10.1155/IMRP.2005.53
Matsuno 2005a; Matsuno 2005b. Matsuno, Yoshimasa (2005a), "Multisoliton solutions of the Degasperis–Procesi equation and their peakon limit", Inverse Problems, vol. 21, no. 5, pp. 1553–1570, arXiv:nlin/0511029, Bibcode:2005InvPr..21.1553M, doi:10.1088/0266-5611/21/5/004, S2CID 122820100 Matsuno, Yoshimasa (2005b), "The N-soliton solution of the Degasperis–Procesi equation", Inverse Problems, vol. 21, no. 6, pp. 2085–2101, arXiv:nlin.SI/0511029, Bibcode:2005InvPr..21.2085M, doi:10.1088/0266-5611/21/6/018
Coclite & Karlsen 2006; Coclite & Karlsen 2007; Lundmark 2007; Escher, Liu & Yin 2007. Coclite, Giuseppe Maria; Karlsen, Kenneth Hvistendahl (2007), "On the uniqueness of discontinuous solutions to the Degasperis–Procesi equation" (PDF), J. Differential Equations, vol. 234, no. 1, pp. 142–160, Bibcode:2007JDE...234..142C, doi:10.1016/j.jde.2006.11.008 Lundmark, Hans (2007), "Formation and dynamics of shock waves in the Degasperis–Procesi equation", J. Nonlinear Sci., vol. 17, no. 3, pp. 169–198, Bibcode:2007JNS....17..169L, doi:10.1007/s00332-006-0803-3, S2CID 28451735 Escher, Joachim; Liu, Yue; Yin, Zhaoyang (2007), "Shock waves and blow-up phenomena for the periodic Degasperis–Procesi equation", Indiana Univ. Math. J., vol. 56, no. 1, pp. 87–117, doi:10.1512/iumj.2007.56.3040

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