I How do I name a generalisation of the wave equation?

[gnnmartin]

I am interested in discussing those phenomena which can be defined at a point. The wave equation is the simplest example. Is it acceptable to use the term 'wave' to indicate any phenomenon that is defined at a point, and to call the equation that results a wave equation?

To illustrate the difficulty I foresee, I wish to describe gravitational waves as waves, and to include the equations describing gravitational waves in the class of wave equations. Is there a better pair of terms to use than 'wave' and 'wave equation'?

 

[S.G. Janssens]

I am interested in discussing those phenomena which can be defined at a point. The wave equation is the simplest example. Is it acceptable to use the term 'wave' to indicate any phenomenon that is defined at a point, and to call the equation that results a wave equation?

This sounds a bit vague to me. A point mass sitting at the origin is a phenomenon defined at a point, but I suppose it does not have much to do with what you are interested in.

To illustrate the difficulty I foresee, I wish to describe gravitational waves as waves, and to include the equations describing gravitational waves in the class of wave equations. Is there a better pair of terms to use than 'wave' and 'wave equation'?

I think it is more important that you precisely state the physical and mathematical problem for the phenomenon in question, rather than ponder about a name. For now, you can just give it an equation number, or stick with the literature terminology.

Also, it is noteworthy that there are equations, such as certain classes of reaction-diffusion equations, that are well-known to admit solutions that are called "wave solutions" in the literature, although the name of the equation itself would not not suggest their existence.

 

[gnnmartin]

Thanks. You say 'This sounds a bit vague to me'. It is not vague, but it is a very general class of equations. As you say, it includes diffusion equations. It also includes static structures. The example you give of a point mass is not included, because the motion of the mass is not defined by the mass, though the gravitational field itself that the point mass illustrates is described by an equation in the class I wish to name.

 

[_PJ_]

I think you've answered your own question in describing the problem with "any phenomenon that is defined at a point" - If you're that concerned for the possibilities of ambiguity or confusion, why not just use "phenomenon"? Because after all, if you're not comfortable calling it a wave and "it" lacks adefinitive, accurate specific label, then it may be prescient to avoid using any specific labels - so long as you've identified that the "phenomenon" is a gravitational 'aberration' (?) defined at a point.
Another thought, if this is the properties of a given 'wave' AT A POINT within a larger whole, then is it not the curvature, potential or energy - the field strength or so on so forth etc. AT THAT POINT- or even the mathematical elements such as gradient or so on?

___If I understand your post correctly, I have similar concerns when writing about "particles", since this gives a misleading presumption of the phenomena in question being or being considered as point particles - As such, I tend to try to use the word "entity".

 

[gnnmartin]

Thanks. Food for thought.