  It is known that after a particular distance of evolution in fiber lasers,
two (input) asymmetric soliton like pulses emerge as two (output) symmetric
pulses having same and constant energy. We report such a compensation technique
in dispersion managed fiber lasers by means of a semi-analytical method known
as collective variable approach (CVA) with including third-order dispersion
(TOD). The minimum length of fiber laser, at which the output symmetric pulses
are obtained from the input asymmetric ones, is calculated for each and every
pulse parameters numerically by employing Runge-Kutta fourth order method. The
impacts of intercore linear coupling, asymmetric nature of initial parameters
and TOD on the evolution of pulse parameters and on the minimum length are also
investigated. It is found that strong intercore linear coupling and asymmetric
nature of input pulse parameters result in the reduction of fiber laser length.
Also, the role of TOD tends to increase the width of the pulses as well as
their energies. Besides, chaotic patterns and bifurcation points on the minimum
length of the fiber owing to the impact of TOD are also reported in a nutshell.
