Nonlinear phenomena and dispersion

• Grant number: 23/06416-6
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2023
• End date: February 28, 2025
• 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

Abstract

In this project we are interested in considering some topics taht appear in the theory to describe some nonlinear phenomena. Generally this sort of phenomenoa are modeled my the evolution equations of dispersive type. Some of the main models that appear in this context are the nonlinear Schrodinger equation (NLS), Korteweg-de Vries equation (KdV), Benjamin-Ono equations, Intermediate long wave (ILW) equation and systems involving these equations. Our principal objective in this project is the study the initial value problems (IPV)associated to dispersie 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. (AU)

Scientific publications

(6)

(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)

BONA, J. L.; CHEN, H.; HONG, Y.; PANTHEE, M.; SCIALOM, M.. The long wavelength limit of periodic solutions of water wave models. STUDIES IN APPLIED MATHEMATICS, v. 153, n. 2, p. 15-pg., 2024-05-16. (23/06416-6, 22/05646-5)

FIGUEIRA, RENATA O.; NOGUEIRA, MARCELO; PANTHEE, MAHENDRA. Lower bounds on the radius of analyticity for a system of nonlinear quadratic interactions of the Schrödinger-type equations. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 75, n. 4, p. 14-pg., 2024-08-01. (23/06416-6, 21/04999-9)

FIGUEIRA, RENATA O.; PANTHEE, MAHENDRA. New lower bounds for the radius of analyticity for the mKdV equation and a system of mKdV-type equations. JOURNAL OF EVOLUTION EQUATIONS, v. 24, n. 2, p. 24-pg., 2024-06-01. (23/06416-6, 21/04999-9)

CORCHO, ADAN J.; PANTHEE, MAHENDRA. On the global and singular dynamics of the 2D cubic nonlinear Schrödinger equation on cylinders. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 243, p. 17-pg., 2024-02-28. (23/06416-6)

CARVAJAL, X.; PANTHEE, M.. Sharp Global Well-Posedness for the Cubic Nonlinear Schrödinger Equation with Third Order Dispersion. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, v. 30, n. 2, p. 23-pg., 2024-04-01. (23/06416-6)

FIGUEIRA, RENATA O.; PANTHEE, MAHENDRA. Decay of the radius of spatial analyticity for the modified KdV equation and the nonlinear Schrödinger equation with third order dispersion. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, v. 31, n. 4, p. 23-pg., 2024-07-01. (23/06416-6, 21/04999-9)