| Full text | |
| Author(s): |
Freire, Igor Leite
[1]
Total Authors: 1
|
| Affiliation: | [1] Comput & Cognicao Univ Fed ABC, Ctr Matemat, Santo Andre, SP - Brazil
Total Affiliations: 1
|
| Document type: | Journal article |
| Source: | Journal of Mathematical Physics; v. 63, n. 1 JAN 1 2022. |
| Web of Science Citations: | 0 |
| Abstract | |
Lower order conservation laws and symmetries of a family of hyperbolic equations having the Camassa-Holm equation as a particular member are obtained. We show that the equation has two conservation laws with zeroth order characteristics and that its symmetries are generated by translations in the independent variables and a certain scaling, as well as some invariant solutions are studied. Next, we consider persistence and asymptotic properties for the solutions of the equation considered. In particular, we analyze the behavior of the solutions of the equation for large values of the spatial variable. We show that if the initial data has a certain asymptotic exponential decaying, then such a property persists for any time as long as the solution exists. Moreover, depending on the behavior of the initial data for large values of the spatial variable and if for some further time the solution shares the same behavior, then it necessarily vanishes identically. Finally, we prove unique continuation results for the solutions of the equation. (AU) | |
| FAPESP's process: | 20/02055-0 - Novikov equations with quadratic non-linearities: structural and qualitative properties |
| Grantee: | Igor Leite Freire |
| Support Opportunities: | Regular Research Grants |