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**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.

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**Speaker**

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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

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**Speaker**

**Time**

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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 \(u_0(x)\).

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**Speaker**

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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.