November 5, 2024

Novel explicit solutions for a Novikov equation

In this presentation, we investigate a symmetry-integrable equation proposed by V. Novikov (J. Phys. A, 2009) with quadratic nonlinearities, and we present explicit solutions to it. The first solution is derived from invariant solutions combined with a collage process designed to preserve continuity. Subsequently, we derive a second solution that corresponds to the 2-peakon solution of the Degasperis-Procesi equation. Furthermore, we explore more general forms of solutions and exhibit a shock wave associated with the shock-peakon solution for the Degasperis-Procesi equation, as established by Lundmark (J. Nonlinear Sci., 2007).

About the speaker

Priscila Leal da Silva is a Lecturer in Mathematics at Universidade Federal de São Carlos, Brazil. She earned dual BS degrees from Universidade Federal do ABC, one in Science and Technology (2011) and the other in Mathematics (2013). Priscila completed her PhD in Mathematics at the same university in 2016, making history as the first to defend a Mathematics thesis there. Her doctoral research focused on finding explicit solutions for integrable systems. Before her current role, she was a research associate at Universidade Federal de São Carlos and served as a Newton International Fellow at Loughborough University, UK, where she expanded her research to explore the qualitative properties of solutions across various spaces.