# Research

## Differential Equations

### Thursday, November 29, 2012

Title: Solving linear differential equations with variable coefficients
Speaker: Wen-Xiu Ma
Time: 4:00pm‐5:00pm
Place: 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: Symmetries and conserved quantities by hereditary operators of bi-Hamiltonian systems
Speaker: Jinghan Meng
Time: 4:00pm‐5:00pm
Place: 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: Soliton equations and matrix Lie algebras, Part II
Speaker: Wen-Xiu Ma
Time: 4:00pm‐5:00pm
Place: NES 108

### Thursday, October 18, 2012

Title: Soliton equations and matrix Lie algebras, Part I
Speaker: Wen-Xiu Ma
Time: 4:00pm‐5:00pm
Place: 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: Recursion operators of soliton equations
Speaker: Roy Choudhury, University of Central Florida
Time: 11:00am‐12:00pm
Place: 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: Bi-Hamiltonian structure of the Korteweg-de Vries equation, Part II
Speaker: Junyi Tu
Time: 3:30pm‐4:30pm
Place: CHE 303

### Tuesday, September 18, 2012

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

#### 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: 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

#### 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.