Introduction to Traveling Waves

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Anna R. Ghazaryan (Miami Univeristy, USA) Stéphane Lafortune (College of Charleston, USA)

Introduction to Traveling Waves

Anna R. Ghazaryan (Miami Univeristy, USA), Stéphane Lafortune (College of Charleston, USA), Vahagn Manukian (Miami University, USA)

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English

Chapman & Hall/CRC
14 November 2022

Algebra; Wave mechanics (vibration & acoustics); Mathematical physics; Mechanical engineering; Environmental science, engineering & technology

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.

By: Anna R. Ghazaryan (Miami Univeristy USA), Stéphane Lafortune (College of Charleston, USA), Vahagn Manukian (Miami University, USA)
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 380g
ISBN: 9780367707057
ISBN 10: 0367707055
Pages: 160
Publication Date: 14 November 2022
Audience: College/higher education , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

1. Nonlinear Traveling Waves. 1.1. Traveling Waves. 1.2. Reaction-Diffusion Equations. 1.3. Traveling Waves as Solutions of Reaction-Diffusion Equations. 1.4. Planar Waves. 1.5. Examples of Reaction-Diffusion Equations. 1.6. Other Partial Differential Equations that Support Waves. 2. Systems of Reaction-Diffusion Equations posed on Infinite Domains. 2.1. Systems of Reaction-Diffusion Equations. 2.2. Examples of Reaction-Diffusion Systems. 3. Existence of Fronts, Pulses, and Wavetrains. 3.1. Traveling Waves as Orbits in the Associated Dynamical Systems. 3.2. Dynamical Systems Approach: Equilibrium Points. 3.3. Existence of Fronts in Fisher-KPP Equation: Trapping Region Technique. 3.4. Existence of Fronts in Solid Fuel Combustion Model. 3.5. Wavetrains. 4. Stability of Fronts and Pulses. 4.1. Stability: Introduction. 4.2. A Heuristic Presentation of Spectral Stability for Front and Pulse Traveling Wave Solutions. 4.3. Location of the Point Spectrum. 4.4. Beyond Spectral Stability.

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.