Nonlinear dispersive wave models

• Grant number: 20/14833-8
• Support Opportunities: Regular Research Grants
• Duration: April 01, 2021 - March 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Mahendra Prasad Panthee
• Grantee: Mahendra Prasad Panthee
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated researchers: Xavier Carvajal Paredes

Abstract

In this project we consider nonlinear evolution equations of dispersive type. Our principal objective is the study of the Acauchy problems associated to dispersive models. More precisely, we study the local and global existence, controllability, stabilization, stability of solitary wave solutions, analyticity of solutions and unique continuation property (UCP) of solutions and their generalization. The main models considered in this project are the nonlinear Schrödinger equation (NLS), Korteweg-de Vries equation (KdV), Benjamin-Ono equations, Intermediate long wave (ILW) equation and systems involving these equations. We will consider these models posed in euclidean domains as well as in Riemannian manifolds. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FIGUEIRA, RENATA O.; PANTHEE, MAHENDRA. EVOLUTION OF THE RADIUS OF ANALYTICITY FOR THE GENERALIZED BENJAMIN EQUATION. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. N/A, p. 17-pg., 2023-04-23. (21/04999-9, 20/14833-8)

NOGUEIRA, MARCELO; PANTHEE, MAHENDRA. Local well-posedness for the quadratic Schrodinger equation in two-dimensional compact manifolds with boundary. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, JUL 2021. (20/14833-8)

CARVAJAL, X.; PANTHEE, M.. On propagation of regularities and evolution of radius of analyticity in the solution of the fifth-order KdV-BBM model. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 73, n. 2, p. 15-pg., 2022-04-01. (20/14833-8)