Is f_{\mu} a Soliton Equation?

[panchan]

[tex]
f_{\mu}=\frac{\beta_{\mu}\psi\xi_{_{g}}}{\cosh^{2}\psi\xi}
,\hspace{2em}
\xi=\xi_{_{T}}x^{0}+\xi_{_{S}}\sqrt{(x^{1})^{2}+(x^{2})^{2}+(x^{3})^{2}}
,\hspace{2em}
\beta_{\mu},\:\xi_{_{g}}},\:\xi_{_{T}},\:\xi_{_{S}}\rightarrow constant
[/tex]

Is this f_{\mu} soliton ?

 

[marlon]

I don't think many people will be able to help if you are not going to try to be a bit more clear. Elaborate on the context surrounding your question, please. Whithin what course are you seeing this ?

As far as i remember, you acquire a soliton solution (in 2+1 dimensional QFT) if your solution gives you a constant value at infinity (both + and - infinities) and if in between, there is a continuous evolution from the "minus-infinity constant" towards the "+ infinity constant". Both constants are equal in magnitude but have opposite signs and they correspond to the socalled "vacuum value" (degenerate lowest energy value).

Here's more

marlon

 

[Kalimaa23]

Thanks Marlon! Good link.