Well-posedness, travelling waves and geometrical aspects of
generalizations of the Camassa-Holm equation

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

Language

English

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

References:

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

Abstract

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.

Citovat

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.

@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.

Detailed Information on Publication Record