What is the physical meaning of this eqn

[MarkB]

I am doing a research about the wave function. I am planning on take ing teh way function and changing the power on the x.
m(d^(2)x/dt^(2)) + kx^n =0

What is the physical meaning when you do make the x rasied to some power?

Thanks

 

[arildno]

If n is not 1, but odd, you could call it a non-linear oscillator.

 

[nrqed]

I am doing a research about the wave function. I am planning on take ing teh way function and changing the power on the x.
m(d^(2)x/dt^(2)) + kx^n =0

What is the physical meaning when you do make the x rasied to some power?

Thanks

Arildno gave a good answer.
Note: you should not call x(t) a "wavefunction". A wavefunction would be, say y(x,t) for a transverse wave on a string (as one example).