University of South Florida
College of Arts and Sciences
Search
Menu
Give Now
Title: Solving linear differential equations with variable coefficients Speaker: Wen-Xiu Ma Time: 4:00pm‐5:00pm Place: NES 108
We will discuss solutions and their properties of linear differential equations with variable coefficients from a computational point of view. Instead of formulating general solutions, we will focus on ways to present closed-form solutions by reduction of order and infinite series.
Title: Symmetries and conserved quantities by hereditary operators of bi-Hamiltonian systems Speaker: Jinghan Meng Time: 4:00pm‐5:00pm Place: NES 108
We will discuss some characteristic features of completely integrable systems, such as infinitely many commuting symmetries and infinitely many conserved quantities. We will also talk about an approach for finding new completely integrable systems.
Title: Soliton equations and matrix Lie algebras, Part II Speaker: Wen-Xiu Ma Time: 4:00pm‐5:00pm Place: NES 108
Title: Soliton equations and matrix Lie algebras, Part I Speaker: Wen-Xiu Ma Time: 4:00pm‐5:00pm Place: NES 108
We will discuss a general framework for generating soliton equations as isospectral flows of eigenvalue problems. It is the key step to use the zero curvature equation on matrix Lie algebras.
Title: Recursion operators of soliton equations Speaker: Roy Choudhury, University of Central Florida Time: 11:00am‐12:00pm Place: CMC 117
We will discuss the construction problem of recursion operators of soliton equations, starting with \(2\times 2\) and \(3\times 3\) matrix spectral problems.
Title: Bi-Hamiltonian structure of the Korteweg-de Vries equation, Part II Speaker: Junyi Tu Time: 3:30pm‐4:30pm Place: CHE 303
Title Speaker Time Place
Title: Bi-Hamiltonian structure of the Korteweg-de Vries equation Speaker: Junyi Tu Time: 3:30pm‐4:30pm Place: CHE 303
We will review the bi-Hamiltonian structure of the Korteweg-de Vries equation, it's recursion operator and symmetry flows. These are the main characters of soliton equations.
Title: Matrix Lax pairs and Hamiltonian tri-integrable couplings Speaker: Jinghan Meng Time: 3:30pm‐4:30pm Place: CHE 303
Matrix Lax pairs and Hamiltonian tri-integrable couplings Jinghan Meng 3:00pm-4:00pm CHE 303
In this talk, we will present a method for generating matrix Lax pairs to construct tri-integrable couplings. We will talk about advantages of the approach, particularly how infinitely many symmetries and bi-Hamiltonian structures of enlarged soliton systems can be systematically determined. An application to the AKNS soliton hierarchy will be given as an illustration example.