Research

Differential Equations

(Leader: )

Wednesday, April 17, 2013

Title: The matrix exponential approach for exact solutions to linear differential equations
Speaker: Xiang Gu
Time: 4:15pm‐5:00pm
Place: 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: The factors influencing on international grain prices
Speaker: Wang Rui, Wuhan Polytechnic University
PR China
Time: 4:00pm‐5:00pm
Place: 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: Finite-dimensional super integrable systems generated from the super NLS-mKdV hierarchy
Speaker: Qiulan Zhao, Shandong University of Science and Technology
P.R. China
Time: 4:00pm‐5:00pm
Place: 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: Hirota’s bilinear method and its generalizations
Speaker: Wen-Xiu Ma
Time: 4:00pm‐5:00pm
Place: 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: Exact solutions and integrable properties of nonlinear evolution equations
Speaker: Yi Zhang, Zhejiang Normal University
Time: 4:00pm‐5:00pm
Place: 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: A generalization of the Korteweg–de Vries equation
Speaker: Lin Luo, Shanghai Second Polytechnic University
Time: 4:00pm‐5:00pm
Place: 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: A \(3\times 3\) matrix problem for the AKNS hierarchy
Speaker: Emmanuel Appiah
Time: 4:00pm‐5:00pm
Place: 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: Applications of irreducible representations of the Lie algebra \(\mathrm{sl}(2,R)\) to integrable couplings
Speaker: Wen-Xiu Ma
Time: 4:00pm‐5:00pm
Place: 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: Enlarged AKNS Equations
Speaker: Solomon Manukure
Time: 4:00pm‐5:00pm
Place: 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: Generating the AKNS hierarchy of soliton equations
Speaker: Emmanuel Appiah
Time: 4:00pm‐5:00pm
Place: 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: Grain trade mechanism and food security in China, Part II
Speaker: Rui Wang, Wuhan Polytechnic University
Time: 4:00pm‐5:00pm
Place: NES 103

Wednesday, January 23, 2013

Title: Grain trade mechanism and food security in China
Speaker: Rui Wang, Wuhan Polytechnic University
Time: 4:00pm‐5:00pm
Place: 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: Loop algebras and variational identities
Speaker: Wen-Xiu Ma
Time: 4:00pm‐5:00pm
Place: 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.