Existence and stability properties of travelling wave solutions for some nonlinear partial differential equations of second order: deterministic and stochastic models

• Grant number: 22/14833-3
• Support Opportunities: Scholarships abroad - Research
• Start date: September 01, 2023
• End date: August 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Lynnyngs Kelly Arruda Saraiva de Paiva
• Grantee: Lynnyngs Kelly Arruda Saraiva de Paiva
• Host Investigator: Dmitry Pelinovsky
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: McMaster University, Canada

Abstract

This project is concerned with the existence and stability of travelling waves of some deterministic (zero noise) nonlinear Partial Differential Equations (PDEs) of second order classified by A. Hone, V. Novikov and J. Wang, in 2018 (Reference [36] in the Research Project). This family of nonlinear partial differential equations of second order contains the important integrable equations of Ostrovsky-Hunter and Hunter-Saxton. We also intend to prove the existence of travelling wave solutions for some stochastic (additive and multiplicative) perturbations of this same family of nonlinear PDEs of second order and study the properties of these solutions. (AU)