Stability? nonlinear mode? soliton?

[hanson]

Can someone explain to me what it means by nonlinear mode?
I heard people saying that soliton is a nonlinear mode of the nonlinear schrondinger equation and therefore perturbed pulses tend to reshape to the soliton shape. In the reshaping proces, the energy dispersed is known as continuous radiation.

I am confused about the energy dispersion process. I can accept that when there is energy disspation, a system can tend to a mode. But if the energy is just dispersed but not dissipated, can the system be really go to the nonlinear mode? Or it will tend to it anyway? I am kind of confused. I need to hear some more on this. Please say something on this. Thanks.

 

[jdg812]

Can someone explain to me what it means by nonlinear mode?
I heard people saying that soliton is a nonlinear mode of the nonlinear schrondinger equation and therefore perturbed pulses tend to reshape to the soliton shape. In the reshaping proces, the energy dispersed is known as continuous radiation.

I am confused about the energy dispersion process. I can accept that when there is energy disspation, a system can tend to a mode. But if the energy is just dispersed but not dissipated, can the system be really go to the nonlinear mode? Or it will tend to it anyway? I am kind of confused. I need to hear some more on this. Please say something on this. Thanks.

If a pulse already has soliton shape, everything is stable.
If the pulse is perturbed and does not correspond to soliton shape, then extra energy, or energy of perturbation, disperses and moves with different spped than basic soliton. Soon the dispersed wave and soliton become separated in space.