1
$\begingroup$

Could it happen than a solitary travelling wave (soliton) had a different propagation speed when seen from the usual wave equations from that in a non-linear equation. I mean, suppose a solution $F=f(x-vt)+g(x+vt)$ of the usual wave equation.

Could it happen than the "propagation speed" (if any) in a non-linear partial differential equation were different to $v$? I suppose the general response is "no", unless we speak of phase velocity and group velocity, but how to say then they are the "propagation speed". Also, I think that if we change the question into the dispersion relation, I suppose dispersion relationship from solitons into the general wave equation can differ from that of non-linear waves. Is that then possible?

Improve this question
$\endgroup$
2
  • $\begingroup$ I do not remember if solitons can do it, the KdV is unidirectional, though, but in an externally biased ferrite the phase velocity depends on the direction of propagation. All microwave non-reciprocal ferrite devices, isolators, switches, circulators, etc., take advantage of this linear phenomenon. $\endgroup$
    – hyportnex
    Commented Feb 16, 2023 at 19:31
  • $\begingroup$ I'm not sure if I understand the question. The velocity of KdV is not fixed and can be arbitrary, so the notion of dispersion relation is ill defined. Actually, it is is proportional to its amplitude which is a nonlinear effect. A multi-soliton solution can be constituted by different solitons going at different velocities as well. $\endgroup$
    – LPZ
    Commented Feb 16, 2023 at 20:09

0

Reset to default