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# Differential Equations (Leader: Prof. Wen-Xiu Ma <mawx (at) usf.edu>document.write('<a href="mai' + 'lto:' + 'mawx' + '&#64;' + 'usf.edu' + '">Prof. Wen-Xiu Ma</a>');)

## Friday, June 17, 2011

Title
Speaker
Time
Place

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

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

2D Toda lattices and their bilinear Bäcklund transformations
10:00am-11:00am
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
Speaker
Time
Place

Bäcklund transformations for KP- and BKP-type bilinear equations
Alrazi Abdeljabbar
10:00am-11:00am
PHY 120

Abstract

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

## Friday, May 20, 2011

Title
Speaker

Time
Place

Bäcklund transformations for KdV-type bilinear equations
Yaning Tang
Northwest Polytechnic University
P.R. China
10:00am-11:00am
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.