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# 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>');)

## Thursday, April 5, 2018

Title
Speaker

Time
Place

On some 2D orthogonal $$q$$-polynomials
Ruiming Zhang
Northwest A&F University
PR China
2:00pm-3:00pm
NES 104

Abstract

This talk is based on a joint work with Professor Mourad E. H. Ismail recently published on AMS Transactions, in which we have generalized several families of 2D orthogonal polynomials used in probability theory and physics (a.k.a. Zernike polynomials). In this talk, I introduce two $$q$$-analogues of the 2D-Hermite polynomials that are polynomials in two complex variables. For both families, I present explicit formulas, raising and lowering operator relations, generating functions, and Rodrigues formulas. These $$q$$-orthogonal polynomials also have unexpected connections to the theory of integer partitions.

## Thursday, February 15, 2018

Title
Speaker
Time
Place

A matrix spectral problem based on $$\mathrm{so}(3,R)$$ and its associated soliton hierarchy
Sumayah Batwa
2:00pm-3:00pm
NES 104

Abstract

In this talk, I will discuss a spectral problem associated with the real Lie algebra $$\mathrm{so}(3,R)$$ and generate a hierarchy of soliton equations from zero curvature equations linked with the spectral problem. Moreover, I will give an illustrative example of soliton equations with a bi-Hamiltonian structure.

## Thursday, February 8, 2018

Title
Speaker
Time
Place

Contour deformation in oscillatory Riemann-Hilbert problems associated with the mKdV equation III
Fudong Wang
2:00pm-3:00pm
NES 104

## Thursday, February 1, 2018

Title
Speaker

Time
Place

Nonlocal symmetries with pseudopotentials
Xiazhi Hao
East China Normal University
2:00pm-3:00pm
NES 104

Abstract

In this talk, I will discuss nonlocal symmetries by including pseudopotentials, which are equivalent to Lie point symmetries of a prolonged system. Moreover, I will show that through the transformations resulted from nonlocal symmetries, exact solutions to the original system can be generated.

## Thursday, January 25, 2018

Title
Speaker
Time
Place

Contour deformation in oscillatory Riemann-Hilbert problems associated with the mKdV equation II
Fudong Wang
2:00pm-3:00pm
NES 104

## Thursday, January 18, 2018

Title
Speaker
Time
Place

Contour deformation in oscillatory Riemann-Hilbert problems associated with the mKdV equation
Fudong Wang
2:00pm-3:00pm
NES 104

Abstract

I will discuss about how to extend oscillatory Riemann-Hilbert problems to an augmented contour. The focus will be on how to apply the steepest descent method introduced by Percy Deift and Xin Zhou to analyze long time asymptotics for the mKdV equation.