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Mathematics & Statistics

(Leader: Prof. Wen-Xiu Ma)

**Title**

**Speaker**

**Time**

**Place**

Wronskian solutions of the two-dimensional Toda molecule equation, Part II

Junyi Tu

9:30am-10:30am

NES 104

**Abstract**

Bi-directional Wronskian solutions and double Wronskian solutions are constructed for the two-dimensional Toda molecule equation. Two determinant identities including the Jacobi identity are the base of construction.

**Title**

**Speaker**

**Time**

**Place**

Wronskian solutions and Grammian solutions to the two-dimensional Toda lattice equation, Part II

Magdy Gamil Asaad

9:30am-10:30am

NES 104

**Abstract**

The Plücker relation and Pfaffian identities are applied to the two-dimensional Toda lattice equation. The resulting Wronskian and Pfaffian formulations generate two kinds of determinant solutions to the two-dimensional Toda lattice equation.

**Title**

**Speaker**

**Time**

**Place**

\(W\)-algebras in CKP and BKP hierarchies

Jingsong He

Ningbo University

Zhejiang, PR China

4:00pm-5:00pm

PHY 108

**Abstract**

This talk aims to construct additional symmetries associated with the constrained CKP and BKP hierarchies, and further to give the action of the symmetry flows on the eigenfunction and adjoint eigenfunction. We further show that their acting on the space of the wave operator, \(\partial_k^*\) forms two centerless algebras \(W^{cC}_{1+\infty}\) and \(W^{cB}_{1+\infty}\)-subalgebra of centerless \(W_{1+\infty}\), respectively.

**Title**

**Speaker**

**Time**

**Place**

Wronskian solutions and Grammian solutions to the two-dimensional Toda lattice equation

Magdy Gamil Asaad

9:30am-10:30am

NES 104

**Abstract**

The Plücker relation and Pfaffian identities are applied to the two-dimensional Toda lattice equation. The resulting Wronskian and Pfaffian formulations generate two kinds of determinant solutions to the two-dimensional Toda lattice equation.

**Title**

**Speaker**

**Time**

**Place**

Wronskian solutions of the two-dimensional Toda molecule equation

Junyi Tu

9:30am-10:30am

NES 104

**Abstract**

Bi-directional Wronskian solutions and double Wronskian solutions are constructed for the two-dimensional Toda molecule equation. Two determinant identities including the Jacobi identity are the base of construction.

**Title**

**Speaker**

**Time**

**Place**

Multi-wave solutions for nonlinear equations by the multiple exp-function method

Wen-Xiu Ma

9:30am-10:30am

NES 104

**Abstract**

A multiple exp-function method is proposed for constructing multi-wave solutions of nonlinear partial differential equations. The method is oriented towards ease of use and capability of computer algebra systems, and provides a direct and systematical solution procedure. Using Maple, an application of the approach is made to the \(3+1\) dimensional potential-Yu-Toda-Sasa-Fukuyama equation, and so, exact \(1\)-wave, \(2\)-wave and \(3\)-wave solutions are generated, along with \(1\)-soliton, \(2\)-soliton and \(3\)-soliton type solutions.

**Title**

**Speaker**

**Time**

**Place**

Wronski-type and Gramm-type Pfaffian solutions to the coupled KP equation, Part II

Alrazi Abdeljabbar

9:30am-10:30am

NES 104

**Abstract**

Pfaffian techniques are used to present Pfaffian structure of the coupled KP equation. The resulting Pfaffian formulation yields two kinds of Pfaffian solutions to the coupled KP equation. Such a solution process leads to Pfaffianization of the KP equation.

**Title**

**Speaker**

**Time**

**Place**

Wronski-type and Gramm-type Pfaffian solutions to the coupled KP equation

Alrazi Abdeljabbar

9:30am-10:30am

NES 104

**Abstract**

Pfaffian techniques are used to present Pfaffian structure of the coupled KP equation. The resulting Pfaffian formulation yields two kinds of Pfaffian solutions to the coupled KP equation. Such a solution process leads to Pfaffianization of the KP equation.

**Title**

**Speaker**

**Time**

**Place**

Pfaffian structure of the BKP equation

Yaning Tang

Northwest Polytechnic University

P.R. China

9:30am-10:30am

NES 104

**Abstract**

Pfaffian techniques are used to present Pfaffian structure of the BKP equation. The resulting Pfaffian formulation generates a class of Pfaffian solutions to the BKP equation.

**Title**

**Speaker**

**Time**

**Place**

Pfaffian structure of soliton equations, Part II

Magdy Gamil Asaad

9:30am-10:30am

NES 104

**Abstract**

Using Pfaffian techniques, we discuss the common structure of soliton equations and show how fundamental soliton equations, such as the KP, BKP, coupled KP, Toda lattice and Toda molecule equations, resolve themselves into Pfaffian identities.

**Title**

**Speaker**

**Time**

**Place**

Pfaffian structure of soliton equations

Alrazi Abdeljabbar

9:30am-10:30am

NES 104

**Abstract**

Using Pfaffian techniques, we discuss the common structure of soliton equations and show how fundamental soliton equations, such as the KP, BKP, coupled KP, Toda lattice and Toda molecule equations, resolve themselves into Pfaffian identities.

**Title**

**Speaker**

**Time**

**Place**

Pfaffian identities in soliton theory, Part II

Alrazi Abdeljabbar

9:30am-10:30am

NES 104

**Abstract**

We discuss a few fundamental Pfaffian identities in soliton theory. These include expansion formulae, addition formulae and derivative formulae for Pfaffians. The computation using Pfaffians is much simpler than using determinants in generating soliton solutions to Hirota bilinear equations.

**Title**

**Speaker**

**Time**

**Place**

Pfaffian identities in soliton theory

Magdy Gamil Asaad

9:30am-10:30am

NES 104

**Abstract**

We discuss a few fundamental Pfaffian identities in soliton theory. These include expansion formulae, addition formulae and derivative formulae for Pfaffians. The computation using Pfaffians is much simpler than using determinants in generating soliton solutions to Hirota bilinear equations.

**Title**

**Speaker**

**Time**

**Place**

Determinant and pfaffian solutions of Hirota bilinear equations, Part III

Junyi Tu

9:30am-10:30am

NES 104

**Abstract**

We discuss some facts about determinants and Pfaffians, and explore determinant and Pfaffian solutions to Hirota bilinear equations. Laplace expansions of determinants and Jacobi identities for determinants will be used to present PlÃ¼cker relations, perfect square formulae, addition formulae and derivative formulae for determinants and Pfaffians.

**Title**

**Speaker**

**Time**

**Place**

Determinant and pfaffian solutions of Hirota bilinear equations, Part II

Yaning Tang

Northwest Polytechnic University

P.R. China

9:30am-10:30am

NES 104

**Abstract**

We discuss some facts about determinants and Pfaffians, and explore determinant and Pfaffian solutions to Hirota bilinear equations. Laplace expansions of determinants and Jacobi identities for determinants will be used to present Plücker relations, perfect square formulae, addition formulae and derivative formulae for determinants and Pfaffians.

**Title**

**Speaker**

**Time**

**Place**

Determinant and pfaffian solutions of Hirota bilinear equations

Yaning Tang

Northwest Polytechnic University

P.R. China

9:30am-10:30am

NES 104

**Abstract**

We discuss some facts about determinants and Pfaffians, and explore determinant and Pfaffian solutions to Hirota bilinear equations. Laplace expansions of determinants and Jacobi identities for determinants will be used to present Plücker relations, perfect square formulae, addition formulae and derivative formulae for determinants and Pfaffians.