Research by New Projects

Below is a list of our new research projects. For more information click on the title of the project. 

Multi-Soliton Solutions and their Properties

Advisor(s): Alicia Machuca

Abstract:  The study of integrable nonlinear partial differential equations is interesting to mathematicians, engineers, and physicists because such equations have physically important solutions that can be expressed in terms of elementary functions.  This research project will focus on studying a certain solution formula for multi-soliton solutions of the Kadomtsev-Petviashvili (KP) equation.  The solution formula that will be studied is dependent on a matrix quadruplet, (A, M, B, C), and can be expressed in terms of matrix exponentials.  The student researchers will make use of this solution formula to examine the physical properties of these multi-soliton solutions analytically.  

Number of students needed: 2

Name of students you have identified to work on the project: Rey Andrade-Flores and Angel Paucar

Research Description: In addition to the analytical study of certain solutions the student researchers will be expected to use Mathematica to animate certain solutions and to present their final results in a written report.  Students will be expected to attend a conference to present their results.

Student qualifications: Completion of Math 200 and programming experience is required.

Hours per week:  10

Start/Stop dates: October 6 - December 12