What is an on-site (off-site) soliton?

Question

Could you explain to me what a on-site resp. off-site soliton is?

And maybe what is a localized mode and internal mode of a soliton?

I cannot find explanations for these notions. Thank you in advance.

Answer 1

The "on" and "off" refer to the intensity of the soliton being focused at a grid point or inbetween adjacent grid points when you are examining discretized solitons.

See the paper Onsite and offsite bound states of the discretenonlinear Schrödinger equation and thePeierls–Nabarro barrier by Drs. Jenksinson and Weinstein.