# Research

## Differential Equations

### Friday, June 17, 2011

Title: Soliton equations and eigenvalue problems
Speaker: Wen-Xiu Ma
Time: 10:00am‐11:00am
Place: PHY 120

#### Abstract

We will discuss how to generate soliton equations as isospectral flows of eigenvalue problems on the Kac-Moody algebras. The zero curvature equation is the key tool in the general formulation.

### Friday, June 10, 2011

Title: Hirota bilinear equations, Bell polynomials and linear superposition principles
Speaker: Wen-Xiu Ma
Time: 10:00am‐11:00am
Place: PHY 120

#### Abstract

We will discuss the linear superposition principle applying to Hirota bilinear equations, and show basic relations among Hirota bilinear equations, Bell polynomials and linear subspaces of solutions. The starting point to generate linear subspaces of solutions is resonance between different traveling waves.

### Friday, June 3, 2011

Title: 2D Toda lattices and their bilinear Bäcklund transformations
Speaker: Magdy Gamil Assad
Time: 10:00am‐11:00am
Place: PHY 120

#### Abstract

We will discuss the Bäcklund transformation for (i) the Toda lattice equation and (ii) the Toda molecule equation. We will also check how we can use the $$\{L1,L2\}$$ to present the 2D Toda equation. We will take a look at the modified Toda equation and Miura transformation as well.

### Friday, May 27, 2011

Title: Bäcklund transformations for KP- and BKP-type bilinear equations
Speaker: Alrazi Abdeljabbar
Time: 10:00am‐11:00am
Place: PHY 120

#### Abstract

Using bi-linear techniques, Bäcklund transformations for the KP, BKP, modified BKP equations are generated.

### Friday, May 20, 2011

Title: Bäcklund transformations for KdV-type bilinear equations
Speaker: Yaning Tang, Northwest Polytechnic University
P.R. China
Time: 10:00am‐11:00am
Place: PHY 120

#### Abstract

Following a rule that a Bäcklund transformation in bilinear form corresponds to an exchange formula for the $$D$$-operator, we look for a Bäcklund transformation for the KdV equation and demonstrate that such Bäcklund transformations generate: (i) Lax pairs used in the inverse scattering method, (ii) new soliton equations, and (iii) Miura transformations. Some applications are illustrated.