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@article{33560, author = {Leite Freire, Igor and da Silva, Priscila Leal}, article_location = {San DIego}, article_number = {9}, doi = {http://dx.doi.org/10.1016/j.jde.2019.05.033}, keywords = {Camassa-Holm type equation; Well-posedness; Kato's approach; Conservation laws; Travelling wave solutions; Pseudo-spherical surfaces}, language = {eng}, issn = {0022-0396}, journal = {Journal of Differential Equations}, title = {Well-posedness, travelling waves and geometrical aspects of generalizations of the Camassa-Holm equation}, url = {https://www.sciencedirect.com/science/article/pii/S0022039619302505?via%3Dihub}, volume = {267}, year = {2019} }
TY - JOUR ID - 33560 AU - Leite Freire, Igor - da Silva, Priscila Leal PY - 2019 TI - Well-posedness, travelling waves and geometrical aspects of generalizations of the Camassa-Holm equation JF - Journal of Differential Equations VL - 267 IS - 9 SP - 5318-5369 EP - 5318-5369 PB - Academic Press Inc. Elsevier Science SN - 00220396 KW - Camassa-Holm type equation KW - Well-posedness KW - Kato's approach KW - Conservation laws KW - Travelling wave solutions KW - Pseudo-spherical surfaces UR - https://www.sciencedirect.com/science/article/pii/S0022039619302505?via%3Dihub L2 - https://www.sciencedirect.com/science/article/pii/S0022039619302505?via%3Dihub N2 - In this paper we consider a five-parameter equation including the Camassa-Holm and the Dullin-Gottwald-Holm equations, among others. We prove the existence and uniqueness of solutions of the Cauchy problem using Kato's approach. Conservation laws of the equation, up to second order, are also investigated. From these conservation laws we establish some properties for the solutions of the equation and we also find a quadrature for it. The quadrature obtained is of capital importance in a classification of bounded travelling wave solutions. We also find some explicit solutions, given in terms of elliptic integrals. Finally, we classify the members of the equation describing pseudo-spherical surfaces. ER -
LEITE FREIRE, Igor and Priscila Leal DA SILVA. Well-posedness, travelling waves and geometrical aspects of generalizations of the Camassa-Holm equation. \textit{Journal of Differential Equations}. San DIego: Academic Press Inc. Elsevier Science, 2019, vol.~267, No~9, p.~5318-5369. ISSN~0022-0396. Available from: https://dx.doi.org/10.1016/j.jde.2019.05.033.
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