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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>');)

## Monday, October 15, 2018

Title
Speaker
Time
Place

Essential Physics for Applied Mathematicians (I). — The principle of least action and the special relativity
Xiang Gu
2:00pm-3:00pm
NES 102

Abstract

This is a seminar talk for applied mathematicians to know some essential physics. In this talk, I will start from one of the most fundamental principles of our Nature, the principle of least action (and certainly the mathematics behind — the celebrated calculus of variations); then I will briefly review the theory of special relativity.

## Monday, October 1, 2018

Title

Speaker
Time
Place

The emergence of solitons of the Korteweg-de Vries Equation from sufficiently decaying initial conditions, Part II
Fudong Wang
2:00pm-3:00pm
NES 102

## Monday, September 24, 2018

Title
Speaker
Time
Place

The emergence of solitons of the Korteweg-de Vries Equation from sufficiently decaying initial conditions
Fudong Wang
2:00pm-3:00pm
NES 102

Abstract

We will discuss the solution of the KdV equation with the initial conditions $$u(x,0)=u_0(x)$$, where $$u_0(x)$$ decays sufficiently rapidly as $$|x|$$ goes to $$\infty$$. The analysis is based on the method of the inverse scattering transformation. And, we will prove that the solution of the KdV equation can be uniformly approximated by $$N$$-soliton solution, where $$N$$ is the number of bound states of Schrödinger scattering problem with potential $$u_0(x)$$.

## Monday, September 10, 2018

Topic
Speaker
Time
Place

Lump solutions to PDEs via symbolic computations
Wen-Xiu Ma
2:00pm-4:00pm
NES 102

Abstract

This talk introduces lump solutions to partial differential equations within the Hirota bilinear formulation. A characterization on the existence of lumps in general dimensions will be discussed, and via symbolic computations, a set of illustrative examples of linear and nonlinear equations that possess lumps will be presented in both $$(2+1)$$-dimensions and $$(3+1)$$-dimensions. A few open questions will be addressed at the end of the talk.