This paper investigates the phenomenon of ponderomotive cross-focusing of coaxial \(q\) -Gaussian laser beams propagating in a collisionless plasma. The \(q\) -parameter accounts for the non-ideality of the laser beam profile, deviating from the standard Gaussian case. We theoretically explore the interplay between self-focusing and cross-focusing mechanisms driven by the ponderomotive force induced by the laser beams on the plasma electrons. The analysis employs Variational theory to find the semi analytical solution of the nonlinear partial differential equations governing the evolution of beam envelopes. Our investigation focuses on the influence of the \(q\) -parameter on the laser beams on evolution of their beam widths.
