LEITE FREIRE, Igor and Priscila Leal DA SILVA. Well-posedness, travelling waves and geometrical aspects of generalizations of the Camassa-Holm equation. 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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Basic information
Original name Well-posedness, travelling waves and geometrical aspects of generalizations of the Camassa-Holm equation
Authors LEITE FREIRE, Igor (76 Brazil, guarantor, belonging to the institution) and Priscila Leal DA SILVA (76 Brazil).
Edition Journal of Differential Equations, San DIego, Academic Press Inc. Elsevier Science, 2019, 0022-0396.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
WWW Journal of Differential Equations
RIV identification code RIV/47813059:19610/19:A0000061
Organization unit Mathematical Institute in Opava
Doi http://dx.doi.org/10.1016/j.jde.2019.05.033
UT WoS 000480416600011
Keywords in English Camassa-Holm type equation; Well-posedness; Kato's approach; Conservation laws; Travelling wave solutions; Pseudo-spherical surfaces
Tags MÚ
Tags International impact, Reviewed
Changed by Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 20/4/2020 16:03.
Abstract
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.
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