J
2019
Well-posedness, travelling waves and geometrical aspects of generalizations of the Camassa-Holm equation
LEITE FREIRE, Igor and Priscila Leal DA SILVA
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
Type of outcome
Článek v odborném periodiku
Field of Study
10101 Pure mathematics
Country of publisher
United States of America
Confidentiality degree
není předmětem státního či obchodního tajemství
RIV identification code
RIV/47813059:19610/19:A0000061
Organization unit
Mathematical Institute in Opava
Keywords in English
Camassa-Holm type equation; Well-posedness; Kato's approach; Conservation laws; Travelling wave solutions; Pseudo-spherical surfaces
Tags
International impact, Reviewed
V originále
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.
Displayed: 24/12/2024 04:15