Dear Hamideh,

No, your system's ''electromagnetic laws'' are not Maxwell's laws, because Maxwell''s equations are deeply tied to Poincaree symmetry (also Lorentz invariance). Your system, with G_{2} Lie algebra symmetry (that's an exceptional group!), breaks that connection.

In systems with Sutherland potential and G_{2} symmetry, interactions are not electromagnetic in the Maxwell sense --- they follow an integrable model structure strictly! (solvable via Lax pairs, Bethe ansatz, etc. etc.), potentially exhibiting soliton-like solutions or collective excitations rather than photons or classical EM fields.

Have a nice one ;-}

Kostadin Georgiev

could you please introduce me some references in this subject?

and another question is: solitons are particles or have wave like?

good luck

Absolutely:

Check these 4:

> M. A. Olshanetsky & A. M. Perelomov, Classical integrable finite‑dimensional systems related to Lie algebras, Physics Reports 71 (1981) 313–400. DOI: 10.1016/0370‑1573(81)90023‑5;

>> M. A. Olshanetsky & A. M. Perelomov, “Quantum integrable systems related to Lie algebras”, Physics Reports 94 (1983) 313–404. DOI: 10.1016/0370‑1573(83)90018‑2

>>> https://arxiv.org/abs/1405.7523

>>>> https://pubs.aip.org/aip/jmp/article-abstract/35/4/1738/461067/The-canonical-symmetry-for-integrable-systems?redirectedFrom=fulltext

Hamideh, solitons are nonlinear wave solutions to integrable systems (such as Korteweg-de Vries, sine-Gordon, or nonlinear Schroedinger equations) with particle-like properties.

:)

Njoy!

Kostadin Georgiev

Sure :)

Thanks a lot