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Mathematics & Statistics

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**Speaker**

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Tri-linear equations and their resonant solutions by Bell polynomials

Yuan Zhou

1:00pm-2:00pm

EDU 257

**Abstract**

We shall talk about a class of tri-linear differential operators described by triple Bell polynomials. The superposition principle will be applied to the construction of resonant solutions of exponential waves for the tri-linear equations. A few illustrative examples will be presented.

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Bi-integrable couplings of Dirac equations

Dr. Wenying Zhang

Shanghai University

Shanghai, PR China

1:00pm-2:00pm

EDU 257

**Abstract**

A non-semisimple matrix loop algebra is presented, and a class of zero curvature equations over this loop algebra is used to generate bi-integrable couplings. An illustrative example is made for the Dirac soliton hierarchy.

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Solitary waves and solitons to nonlinear evolutionary equations

Dr. Shuimeng Yu

Jiangnan University

Wuxi, PR China

1:00pm-2:00pm

EDU 257

**Abstract**

First, definitions and characteristics of solitary waves and solitons will be introduced. Second, some analytical solution methods will be discussed. Finally, an application example of the solution methods will be given.

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Lie symmetry method and its application to PDEs

Dr. Shoufeng Shen

Zhejiang University of Technology

Hangzhou, PR China

1:00pm-2:00pm

EDU 257

**Abstract**

We will talk about the Lie symmetry method and its application to PDEs, and pay particular attention to Kac-Moody-Virasoro symmetries for high dimensional integrable systems.

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A spectral problem from \(\mathrm{so}(3,R)\) and its associated soliton hierarchy

Morgan Mcanally

1:00pm-2:00pm

EDU 257

**Abstract**

I will talk about a hierarchy of soliton equations from the zero curvature equations associated with the real Lie algebra \(\mathrm{so}(3,R)\). In particular, I will show you using Maple how to generate the hierarchy of soliton equations and that the resulting infinitely many vector fields commute.

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Darboux transformations for a twisted derivation and its applications to several classical integrable systems, Part II

Dr. Chunxia Li

Capital Normal University

Beijing, PR China

1:00pm-2:00pm

EDU 257

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**Speaker**

**Time**

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Image restoration based on PDEs

Dr. Hongyi Liu

Nanjing University of Science and Technology

Nanjing, PR China

1:00pm-2:00pm

EDU 257

**Abstract**

We would like to discuss image restoration based on PDE models. The topics of the talk include digital image processing, mathematics model of image restoration, and recent developments of image restoration based on PDEs.

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Darboux transformations for a twisted derivation and its applications to several classical integrable systems

Dr. Chunxia Li

Capital Normal University

Beijing, PR China

1:00pm-2:00pm

EDU 257

**Abstract**

In my talk, I will first introduce a twisted derivation and then construct its general Darboux transformations. Based on the general Darboux transformation, we're able to derive Darboux transformations for the KP equation, \((2+1)\)-dimensional Toda lattice equation, fully discrete KP equation, super KdV equation and \(q\)-deformed Toda lattice equation. By iteration of their Darboux transformations, we are able to recover determinant solutions to the above-mentioned soliton equations and obtain quasideterminant solutions to their noncommutative analogues.

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Applications of Bell polynomials and the linear superposition principle to generalized bilinear equations, Part II

Xiang Gu

1:00pm-2:00pm

EDU 257

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Applications of Bell polynomials and the linear superposition principle to generalized bilinear equations

Xiang Gu

1:00pm-2:00pm

EDU 257

**Abstract**

Following Emmanuel A. Appiah's talk on Ma's generalized bilinear equations, I would like to discuss applications of Bell polynomials and the linear superposition principle to solution subspaces of the generalized bilinear equations. Illustrative examples will also be presented for group discussion.

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Generalized Bilinear Differential Equations, Part II

Emmanuel Appiah

1:00pm-2:00pm

EDU 257

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Generalized Bilinear Differential Equations

Emmanuel Appiah

1:00pm-2:00pm

EDU 257

**Abstract**

We will introduce a kind of generalized bilinear differential operator and explore instances where the linear superposition principle applies to the corresponding bilinear differential equations.

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A soliton hierarchy associated with \(\mathrm{so}(3,R)\), Part II

Solomon Manukure

1:00pm-2:00pm

EDU 257

We will continue to talk about zero curvature equations and construct a hierarchy of integrable equations from the Lie algebra \(\mathrm{so}(3,R)\).

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A soliton hierarchy associated with \(\mathrm{so}(3,R)\)

Solomon Manukure

1:00pm-2:00pm

CMC 116

**Abstract**

We will talk about zero curvature equations and construct a hierarchy of integrable equations from the Lie algebra \(\mathrm{so}(3,R)\).