Introduction to Traveling Waves

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.

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• Ciência ambiental, engenharia e tecnologia
• Cálculo diferencial e equações
• Mecânica ondulatória (vibração e acústica)
• Física Matemática
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• Modelação matemática
• Álgebra

Traveling Waves;nonlinear waves;linear algebra;differential equations;modeling;Ordinary Differential Equations;Traveling Wave Solutions;Fisher KPP Equation;Reaction Diffusion Equations;Homoclinic Orbit;Heteroclinic Orbit;Equilibrium Points;Unstable Manifold;High Lewis Number;Reaction Diffusion Systems;Inviscid Burgers Equation;Traveling Wave Equation;Traveling Wave;Partial Differential Equations;Phase Portrait;Stable Manifold;Quasilinear Partial Differential Equations;FitzHugh Nagumo Model;Hopf Bifurcation Theorem;Burgers Equation;Nonlinear Convection Term;Periodic Orbits;Vector Field;Solid Fuel Combustion;Constant Solutions