Overview

Introduction to Traveling Waves is an invitation to research focused on traveling waves for undergraduate and masters level students. Traveling waves are not typically covered in the undergraduate curriculum, and topics related to traveling waves are usually only covered in research papers, except for a few texts designed for students. This book includes techniques that are not covered in those texts. Through their experience involving undergraduate and graduate students in a research topic related to traveling waves, the authors found that the main difficulty is to provide reading materials that contain the background information sufficient to start a research project without an expectation of an extensive list of prerequisites beyond regular undergraduate coursework. This book meets that need and serves as an entry point into research topics about the existence and stability of traveling waves. Features Self-contained, step-by-step introduction to nonlinear waves written assuming minimal prerequisites, such as an undergraduate course on linear algebra and differential equations. Suitable as a textbook for a special topics course, or as supplementary reading for courses on modeling. Contains numerous examples to support the theoretical material. Supplementary MATLAB codes available via GitHub.

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Anna R. Ghazaryan is a Professor of Mathematics at Miami University, Oxford, OH. She received her Ph.D. in 2005 from the Ohio State University. She is an applied analyst with research interests in applied dynamical systems, more precisely, traveling waves and their stability. Stéphane Lafortune is Professor of Mathematics at the College of Charleston in South Carolina. He earned his Ph.D. in Physics from the Université de Montréal and Université Paris VII in 2000. He is an applied mathematician who works on nonlinear waves phenomena. More precisely, he is interested in the theory of integrable systems and in the problems of existence and stability of solutions to nonlinear partial differential equations. Vahagn Manukian is an Associate Professor of Mathematics at Miami University. He obtained a M.A. Degree Mathematics from SUNY at Buffalo and a Ph.D. in mathematics from the Ohio State University in 2005. Vahagn Manukian uses dynamical systems methods such as local and global bifurcation theory to analyze singularly perturbed nonlinear reaction diffusions systems that model natural phenomena.

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