| Full text | |
| Author(s): |
Sales Filho, Nazime
;
Freire, Igor Leite
Total Authors: 2
|
| Document type: | Journal article |
| Source: | COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION; v. 114, p. 13-pg., 2022-07-04. |
| Abstract | |
Lie symmetries of a Novikov geometrically integrable equation are found and group-invariant solutions are obtained. Local conservation laws up to second order are established as well as their corresponding conserved quantities. Sufficient conditions for the L-1 norm of the solutions to be invariant are presented, as well as conditions for the existence of positive solutions. Two demonstrations for unique continuation of solutions are given: one of them is just based on the invariance of the L-1 norm of the solutions, whereas the other is based on well-posedness of Cauchy problems. Finally, pseudospherical surfaces determined by the solutions of the equation are studied: all invariant solutions that do not lead to pseudo-spherical surfaces are classified and the existence of an analytic metric for a pseudo-spherical surface is proved using conservation of solutions and well-posedness results. (C) 2022 Elsevier B.V. All rights reserved. (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 |