MHB Is Wave Phenomena Related to PDE or Just Physics?

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Wave phenomena are intrinsically linked to both partial differential equations (PDE) and physics. A significant category of PDEs, known as dispersive wave equations, is often analyzed qualitatively to understand solution behavior, such as propagation in finite time or global existence. The Schrödinger wave equation, commonly encountered in quantum mechanics, exemplifies a dispersive equation. In educational contexts, wave phenomena are typically explored in both introductory and advanced physics courses, where they are described using PDEs, highlighting the dual relevance of these concepts in both mathematics and physics.
mathmari
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Hey! :o

Do you know if "Wave Phenomena" are related to PDE or only to physics?? (Wondering)
 
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mathmari said:
Hey! :o

Do you know if "Wave Phenomena" are related to PDE or only to physics?? (Wondering)

There is a large class of PDE known as dispersive wave equations. These equations are usually studied qualitatively. For example, one seeks to determine if solutions propagate in finite time or if they exist globally. If you've studied quantum mechanics, then you've seen a dispersive equation -- the Schrodinger wave equation.
 
Euge said:
There is a large class of PDE known as dispersive wave equations. These equations are usually studied qualitatively. For example, one seeks to determine if solutions propagate in finite time or if they exist globally. If you've studied quantum mechanics, then you've seen a dispersive equation -- the Schrodinger wave equation.

Ok! Thank you for the information! (Yes)
 
I would definitely say that wave phenomena are definitely related to both fields. Waves are described using PDE's, so they're related to that field; on the other hand, you usually study waves as a separate topic in most first-year physics courses, as well as more advanced physics courses where you actually solve the PDE.
 

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