One of the fascinating aspects of nonlinear differential equations is the existence of solitary wave solutions, which are waveforms that maintain their shape while traveling at constant speed.

Conservation laws and propagation of shocks. Basic theory for three classical equations of mathematical physics (in all spatial dimensions): the wave equation, the heat/diffusion equation, the Laplace ...

Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green's functions, distribution theory, integral equations, transforms, potential theory, diffusion ...

8) Wave Equation: This is a differential equation, or an equation that describes how a property is changing through time in terms of that property's derivative, as above. The wave equation ...

The three main types of linear second order partial differential equations will be considered: parabolic (diffusion equation), elliptic (Laplace equation), and hyperbolic (wave equation). Techniques ...

These methods are particularly useful for problems involving wave propagation and the Poisson ... simpler parts called finite elements. Partial Differential Equation (PDE): An equation that ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...