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Mathematics & Statistics

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**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.

**Title**

**Speaker**

**Time**

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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.

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**Speaker**

**Time**

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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.

**Title**

**Speaker**

**Time**

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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.

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**Speaker**

**Time**

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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.

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**Speaker**

**Time**

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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.

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**Speaker**

**Time**

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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.

**Title**

**Speaker**

**Time**

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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.

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**Speaker**

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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.

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**Speaker**

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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.

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Grain trade mechanism and food security in China, Part II

Rui Wang

Wuhan Polytechnic University

4:00pm-5:00pm

NES 103

**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.

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**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.