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Mathematics & Statistics

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 17, 2013

Title
Speaker
Time
Place

The matrix exponential approach for exact solutions to linear differential equations
Xiang Gu
4:15pm-5:00pm
NES 103

Abstract

The Cauchy problem of linear differential equations is among the most important ones in the theory of ordinary differential equations. I will talk about the matrix exponential approach for representing solutions to the Cauchy problem. The approach needs a commutativity condition on the coefficient matrix. An interesting question is whether the commutativity condition is necessary. To answer this question, we will discuss a related problem and present two illustrative examples to show the condition may not be necessary.

Wednesday, April 10, 2013

Title
Speaker

Time
Place

The factors influencing on international grain prices
Wang Rui
Wuhan Polytechnic University
PR China
4:00pm-5:00pm
NES 103

Abstract

We will discuss the factors which influence on international grain prices. The factors can be divided to two categories, one concludes Global Macroeconomic Factors and the other concludes Developments in Agricultural Markets.

Wednesday, April 3, 2013

Title
Speaker

Time
Place

Finite-dimensional super integrable systems generated from the super NLS-mKdV hierarchy
Qiulan Zhao
Shandong University of Science and Technology
P.R. China
4:00pm-5:00pm
NES 103

Abstract

We will focus on binary nonlinearization of Lax pairs. First, based on a constructed Lie superalgebra, a super bi-Hamiltonian structure of the super NLS-mKdV hierarchy is obtained by making use of the super-trace identity. Second, an explicit super Bargmann symmetry constraint and its binary nonlinearization of the associated Lax pairs are carried out for the super NLS-mKdV hierarchy.

Wednesday, March 27, 2013

Title
Speaker
Time
Place

Hirota’s bilinear method and its generalizations
Wen-Xiu Ma
4:00pm-5:00pm
NES 103

Abstract

We will discuss Hirota’s bilinear method and its generalizations. Bell polynomials are the primary tool to characterize linear subspaces of exact solutions.

Wednesday, March 20, 2013

Title
Speaker

Time
Place

Exact solutions and integrable properties of nonlinear evolution equations
Yi Zhang
Zhejiang Normal Univesrity
4:00pm-5:00pm
NES 108

Abstract

It is significantly important to search for exact solutions to nonlinear differential equations in mathematical physics. We will focus on exact solutions and integrable properties, based on the Hirota structure, and meanwhile present some interesting problems.

Wednesday, March 6, 2013

Title
Speaker

Time
Place

A generalization of the Korteweg–de Vries equation
Lin Luo
Shanghai Second Polytechnic University
4:00pm-5:00pm
NES 103

Abstract

In this talk, we talk about a generalization of the Korteweg–de Vries equation. The resulting equation is shown to be completely integrable in the sense of existence of Lax pair and Hamiltonian structure. Bilinear Baecklund transformations and conservation laws are presented. A Darboux transformation is derived with the help of a gauge transformation between two Lax pairs, and soliton and periodic wave solutions are given through the Darboux transformation.

Wednesday, February 27, 2013

Title
Speaker
Time
Place

A $$3\times 3$$ matrix problem for the AKNS hierarchy
Emmanuel Appiah
4:00pm-5:00pm
NES 103

Abstract

We shall discuss a $$3\times 3$$ matrix spectral problem associated with the Lie algebra $$\mathrm{sl}(3,R)$$ for the AKNS soliton hierarchy.

Wednesday, February 20, 2013

Title
Speaker
Time
Place

Applications of irreducible representations of the Lie algebra $$\mathrm{sl}(2,R)$$ to integrable couplings
Wen-Xiu Ma
4:00pm-5:00pm
NES 103

Abstract

We shall discuss applications of irreducible representations of $$\mathrm{sl}(2,R)$$ to soliton equations, and as an Illustrative example, present commuting integrable couplings of the AKNS soliton hierarchy by a three dimensional representation.

Wednesday, February 13, 2013

Title
Speaker
Time
Place

Enlarged AKNS Equations
Solomon Manukure
4:00pm-5:00pm
NES 103

Abstract

We will solve the enlarged zero curvature equation and subsequently derive a hierarchy of commuting coupling systems for the AKNS hierarchy, based on a non-semisimple loop algebra.

Wednesday, February 6, 2013

Title
Speaker
Time
Place

Generating the AKNS hierarchy of soliton equations
Emmanuel Appiah
4:00pm-5:00pm
NES 103

Abstract

We shall discus a $$2 \times 2$$ matrix spectral problem associated with the Lie algebra $$\mathrm{sl}(2,R)$$ and generate the AKNS soliton hierarchy using zero curvature equations.

Wednesday, January 30, 2013

Title
Speaker

Time
Place

Grain trade mechanism and food security in China, Part II
Rui Wang
Wuhan Polytechnic University
4:00pm-5:00pm
NES 103

Wednesday, January 23, 2013

Title
Speaker

Time
Place

Grain trade mechanism and food security in China
Rui Wang
Wuhan Polytechnic University
4:00pm-5:00pm
NES 103

Abstract

Grain import and export mechanism in China’s food security under volatile fluctuations of food prices will be discussed, together with a few problems within grain trade and food security in China.

Wednesday, January 16, 2013

Title
Speaker
Time
Place

Loop algebras and variational identities
Wen-Xiu Ma
4:00pm-5:00pm
NES 103

Abstract

We will discuss structures of loop algebras which generate integrable couplings. Variational identities associated with loop algebras are used to construct Hamiltonian formulations of integrable couplings.