Structural and qualitative properties of a geometrically integrable equation
Abstract
Lie symmetries of a Novikov geometrically integrable equation are found and groupinvariant 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 wellposedness of Cauchy problems. Finally, pseudospherical surfaces determined by the solutions of the equation are studied: all invariant solutions that do not lead to pseudospherical surfaces are classified and the existence of an analytic metric for a pseudospherical surface is proved using conservation of solutions and wellposedness results.
 Publication:

Communications in Nonlinear Science and Numerical Simulations
 Pub Date:
 November 2022
 DOI:
 10.1016/j.cnsns.2022.106668
 arXiv:
 arXiv:2201.03635
 Bibcode:
 2022CNSNS.11406668S
 Keywords:

 35A01;
 74G25;
 37K40;
 35Q51;
 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Mathematics  Differential Geometry;
 35A01;
 74G25;
 37K40;
 35Q51
 EPrint:
 doi:10.1016/j.cnsns.2022.106668