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 L1 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 L1 norm of the solutions, whereas the other is based on well-posedness of Cauchy problems. Finally, pseudo-spherical 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.
Communications in Nonlinear Science and Numerical Simulations
- Pub Date:
- November 2022
- Mathematics - Analysis of PDEs;
- Mathematical Physics;
- Mathematics - Differential Geometry;