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# Differential Equations (Leader: Prof. Wen-Xiu Ma <wma3 (at) usf.edu>document.write('<a href="mai' + 'lto:' + 'wma3' + '&#64;' + 'usf.edu' + '">Prof. Wen-Xiu Ma</a>');)

## Tuesday, December 3, 2013

Title
Speaker
Time
Place

Tri-linear equations and their resonant solutions by Bell polynomials
Yuan Zhou
1:00pm-2:00pm
EDU 257

Abstract

We shall talk about a class of tri-linear differential operators described by triple Bell polynomials. The superposition principle will be applied to the construction of resonant solutions of exponential waves for the tri-linear equations. A few illustrative examples will be presented.

## Tuesday, November 26, 2013

Title
Speaker

Time
Place

Bi-integrable couplings of Dirac equations
Dr. Wenying Zhang
Shanghai University
Shanghai, PR China
1:00pm-2:00pm
EDU 257

Abstract

A non-semisimple matrix loop algebra is presented, and a class of zero curvature equations over this loop algebra is used to generate bi-integrable couplings. An illustrative example is made for the Dirac soliton hierarchy.

## Tuesday, November 19, 2013

Title
Speaker

Time
Place

Solitary waves and solitons to nonlinear evolutionary equations
Dr. Shuimeng Yu
Jiangnan University
Wuxi, PR China
1:00pm-2:00pm
EDU 257

Abstract

First, definitions and characteristics of solitary waves and solitons will be introduced. Second, some analytical solution methods will be discussed. Finally, an application example of the solution methods will be given.

## Tuesday, November 12, 2013

Title
Speaker

Time
Place

Lie symmetry method and its application to PDEs
Dr. Shoufeng Shen
Zhejiang University of Technology
Hangzhou, PR China
1:00pm-2:00pm
EDU 257

Abstract

We will talk about the Lie symmetry method and its application to PDEs, and pay particular attention to Kac-Moody-Virasoro symmetries for high dimensional integrable systems.

## Tuesday, November 5, 2013

Title
Speaker
Time
Place

A spectral problem from $$\mathrm{so}(3,R)$$ and its associated soliton hierarchy
Morgan Mcanally
1:00pm-2:00pm
EDU 257

Abstract

I will talk about a hierarchy of soliton equations from the zero curvature equations associated with the real Lie algebra $$\mathrm{so}(3,R)$$. In particular, I will show you using Maple how to generate the hierarchy of soliton equations and that the resulting infinitely many vector fields commute.

## Tuesday, October 29, 2013

Title

Speaker

Time
Place

Darboux transformations for a twisted derivation and its applications to several classical integrable systems, Part II
Dr. Chunxia Li
Capital Normal University
Beijing, PR China
1:00pm-2:00pm
EDU 257

## Tuesday, October 22, 2013

Title
Speaker

Time
Place

Image restoration based on PDEs
Dr. Hongyi Liu
Nanjing University of Science and Technology
Nanjing, PR China
1:00pm-2:00pm
EDU 257

Abstract

We would like to discuss image restoration based on PDE models. The topics of the talk include digital image processing, mathematics model of image restoration, and recent developments of image restoration based on PDEs.

## Tuesday, October 15, 2013

Title

Speaker

Time
Place

Darboux transformations for a twisted derivation and its applications to several classical integrable systems
Dr. Chunxia Li
Capital Normal University
Beijing, PR China
1:00pm-2:00pm
EDU 257

Abstract

In my talk, I will first introduce a twisted derivation and then construct its general Darboux transformations. Based on the general Darboux transformation, we're able to derive Darboux transformations for the KP equation, $$(2+1)$$-dimensional Toda lattice equation, fully discrete KP equation, super KdV equation and $$q$$-deformed Toda lattice equation. By iteration of their Darboux transformations, we are able to recover determinant solutions to the above-mentioned soliton equations and obtain quasideterminant solutions to their noncommutative analogues.

## Tuesday, October 8, 2013

Title

Speaker
Time
Place

Applications of Bell polynomials and the linear superposition principle to generalized bilinear equations, Part II
Xiang Gu
1:00pm-2:00pm
EDU 257

## Tuesday, October 1, 2013

Title
Speaker
Time
Place

Applications of Bell polynomials and the linear superposition principle to generalized bilinear equations
Xiang Gu
1:00pm-2:00pm
EDU 257

Abstract

Following Emmanuel A. Appiah's talk on Ma's generalized bilinear equations, I would like to discuss applications of Bell polynomials and the linear superposition principle to solution subspaces of the generalized bilinear equations. Illustrative examples will also be presented for group discussion.

## Tuesday, September 24, 2013

Title
Speaker
Time
Place

Generalized Bilinear Differential Equations, Part II
Emmanuel Appiah
1:00pm-2:00pm
EDU 257

## Tuesday, September 17, 2013

Title
Speaker
Time
Place

Generalized Bilinear Differential Equations
Emmanuel Appiah
1:00pm-2:00pm
EDU 257

Abstract

We will introduce a kind of generalized bilinear differential operator and explore instances where the linear superposition principle applies to the corresponding bilinear differential equations.

## Tuesday, September 10, 2013

Title
Speaker
Time
Place

A soliton hierarchy associated with $$\mathrm{so}(3,R)$$, Part II
Solomon Manukure
1:00pm-2:00pm
EDU 257

We will continue to talk about zero curvature equations and construct a hierarchy of integrable equations from the Lie algebra $$\mathrm{so}(3,R)$$.

## Tuesday, September 3, 2013

Title
Speaker
Time
Place

A soliton hierarchy associated with $$\mathrm{so}(3,R)$$
Solomon Manukure
1:00pm-2:00pm
CMC 116

Abstract

We will talk about zero curvature equations and construct a hierarchy of integrable equations from the Lie algebra $$\mathrm{so}(3,R)$$.