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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>');)

## Wednesday, April 18, 2012

Title
Speaker
Time
Place

Multi-integrable couplings with Hamiltonian structures
Wen-Xiu Ma
4:00pm-5:00pm
CHE 302

Abstract

We will discuss how to generate multi-integrable couplings, particularly bi-integrable or tri-integrable couplings. The starting point is non-semisimple Lie algebras consisting of block matrices. Variational identities will be tools for furnishing Hamiltonian structures.

## Wednesday, April 11, 2012

Title
Speaker

Time
Place

Reliable analysis for exact solutions of nonlinear Schrödinger equations
Ahmet Yildirim
Ege University
Turkey
4:00pm-5:00pm
CHE 302

Abstract

In this talk, we consider a few of nonlinear Schrödinger equations. A direct method will be presented to construct exact solutions to those nonlinear Schrödinger equations. Our examples will show that the approach is powerful in generating exact solutions to nonlinear partial differential equations, including non-integrable equations.

## Wednesday, April 4, 2012

Title
Speaker
Time
Place

Discussion on the multiple exp-function method and its application to the potential-YTSF equation
Arbin Rai
4:00pm-5:00pm
CHE 302

Abstract

In this talk, I will discuss the multiple exp-function method for exact multiple wave solutions of nonlinear partial differential equations. With the help of Maple, an application to the $$(3+1)$$-dimensional potential Yu-Toda-Sasa-Fukuyama equation yields exact explicit one-wave, two-wave, and three-wave solutions, including one-soliton, two-soliton and three-soliton type solutions.

## Wednesday, March 28, 2012

Title
Speaker

Time
Place

A brief introduction to the homogenous balance method
Hui-Qun Zhang
Qingdao University
PR China
4:00pm-5:00pm
CHE 302

Abstract

We would like to give a brief introduction to the homogenous balance method, including its solving process and abundant applications.

## Wednesday, March 21, 2012

Title
Speaker
Time
Place

Pfaffian and Wronskian solutions in $$3+1$$ dimensions
4:00pm-5:00pm
CHE 302

Abstract

In this talk, I will present our recent work on various classes of Pfaffian and Wronskian solutions to a class of generalized integrable nonlinear partial differential equations, including soliton equations, in three spatial and one temporal dimensions. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. As part of this talk, I will show how to obtain $$N$$-soliton solutions from the Pfaffian and Wronskian solutions.

## Wednesday, March 7, 2012

Title
Speaker

Time
Place

A study of Kawahara equation in weighted Sobolev spaces
Netra Khanal
University of Tampa
4:00pm-5:00pm
CHE 302

Abstract

The initial- and boundary-value problem for the Kawahara equation, a fifth-order KdV type equation, will be discussed in weighted Sobolev spaces. The theory presented includes the existence and uniqueness of a local mild solution and of a global strong solution in these weighted spaces. If the $$L^2$$-norm of the initial data is sufficiently small, these solutions decay exponentially in time.

## Wednesday, February 29, 2012

Title

Speaker

Time
Place

The variational iteration method: An efficient scheme for handling fractional partial differential equations in fluid mechanics
Ms. Canan Unlu
Istanbul University
Turkey
4:00pm-5:00pm
CHE 302

Abstract

We will discuss the variational iteration method and its applications. A general framework will be presented for analytical treatment of fractional partial differential equations in fluid mechanics. Numerical illustrations will be given to show the pertinent features of the technique.

## Wednesday, February 22, 2012

Title
Speaker

Time
Place

Polyvector fields and Lie derivatives
Hongchan Zheng
Northwestern Polytechnical University
China
4:00pm-5:00pm
CHE 302

Abstract

We will discuss $$k$$-vector fields and the Lie derivative operation, including properties of the Lie derivative and the relationship between the Lie derivative and the Lie bracket. We will show also how the Lie derivative can be extended to differential $$k$$-forms and how one can build its applications.

## Wednesday, February 15, 2012

Title
Speaker

Time
Place

Differential forms and polyvector fields on manifolds
Hongchan Zheng
Northwestern Polytechnical University
China
4:00pm-5:00pm
CHE 302

Abstract

We will discuss the differential $$k$$-forms and $$k$$-vector fields on differentiable manifolds and the operations on and between them, including the basic properties of the wedge product and the exterior derivative.

## Wednesday, February 8, 2012

Title
Speaker

Time
Place

A brief review of models in mosquito control
Prof. Nanhua Zhang
USF College of Public Health
4:00pm-5:00pm
CHE 302

Abstract

It is well known that mosquitoes transmit many infectious diseases (malaria, West Nile fever, Rift Valley fever, etc.) and there have been tremendous efforts to reduce their presence. Mathematical models are useful in guiding these mosquito control efforts. In this talk, I will review some models in mosquito control. I will introduce some unsolved problems that deserve attention from applied mathematicians.

## Wednesday, February 1, 2012

Title
Speaker
Time
Place

Integrable couplings of the Kaup-Newell hierarchy
Mengshu Zhang
4:00pm-5:00pm
CHE 302

Abstract

We will discuss integrable couplings of soliton equations. As an example, we will present a hierarchy of integrable couplings for the Kaup-Newell soliton equations by using zero curvature equations.

## Wednesday, January 25, 2012

Title
Speaker
Time
Place

Bi-integrable couplings and their Hamiltonian structures
Jinghan Meng
4:00pm-5:00pm
CHE 302

Abstract

We will present our recent research on bi-integrable couplings of soliton equations. Hamiltonian structures of the bi-integrable coupling hierarchies are established by means of the component trace identity, which generate infinitely many commuting symmetries and conservation laws. Illustrative examples will be given.

## Wednesday, January 18, 2012

Title
Speaker
Time
Place

Distributions and the Frobenius Theorem
Junyi Tu
4:00pm-5:00pm
CHE 302

Abstract

We would like to discuss some basic structures on real smooth manifolds, including the canonical form of vector fields near a regular point, and the generalization of this idea to higher-dimensional sub-manifolds, which is the content of the Frobenius Theorem.