banner USF Home College of Arts & Sciences OASIS myUSF USF A-Z Index

USF Home > College of Arts and Sciences > Department of Mathematics & Statistics

Mathematics & Statistics

Differential Equations
(Leader: )

Thursday, November 29, 2012

Title
Speaker
Time
Place

Solving linear differential equations with variable coefficients
Wen-Xiu Ma
4:00pm-5:00pm
NES 108

Abstract

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.

Thursday, November 8, 2012

Title
Speaker
Time
Place

Symmetries and conserved quantities by hereditary operators of bi-Hamiltonian systems
Jinghan Meng
4:00pm-5:00pm
NES 108

Abstract

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.

Thursday, October 25, 2012

Title
Speaker
Time
Place

Soliton equations and matrix Lie algebras, Part II
Wen-Xiu Ma
4:00pm-5:00pm
NES 108

Thursday, October 18, 2012

Title
Speaker
Time
Place

Soliton equations and matrix Lie algebras, Part I
Wen-Xiu Ma
4:00pm-5:00pm
NES 108

Abstract

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.

Thursday, October 4, 2012

Title
Speaker

Time
Place

Recursion operators of soliton equations
Roy Choudhury
University of Central Florida
11:00am-12:00pm
CMC 117

Abstract

We will discuss the construction problem of recursion operators of soliton equations, starting with \(2\times 2\) and \(3\times 3\) matrix spectral problems.

Tuesday, September 25, 2012

Title
Speaker
Time
Place

Bi-Hamiltonian structure of the Korteweg-de Vries equation, Part II
Junyi Tu
3:30pm-4:30pm
CHE 303

Tuesday, September 18, 2012

Title
Speaker
Time
Place

Bi-Hamiltonian structure of the Korteweg-de Vries equation
Junyi Tu
3:30pm-4:30pm
CHE 303

Abstract

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.

Tuesday, September 11, 2012

Title
Speaker
Time
Place

Matrix Lax pairs and Hamiltonian tri-integrable couplings
Jinghan Meng
3:00pm-4:00pm
CHE 303

Abstract

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.