  We study the finite size effect of rigidly rotating strings and closed folded
strings in $AdS_3\times S^3$ geometry with NS-NS B-field. We calculate the
classical exponential corrections to the dispersion relation of infinite size
giant magnon and single spike in terms of Lambert $\mathbf{W}-$function. We
also write the analytic expression for the dispersion relation of finite size
Gubser-Klebanov-Polyakov (GKP) string in the form of Lambert
$\mathbf{W}-$function.
