Evolution of pure-quartic solitons studied by the variational approach

Evolution of pure-quartic solitons (PQSs) is theoretically studied by the variational approach based on the Lagrangian of the system. The evolution equations resulting from the standard Gaussian trial solution yield an analytic solution of the stationary PQSs, which approximates well to the numerical result. However, they cannot reflect the damping of the oscillation for the breathing PQSs. To compensate this problem, the trial solution is modified to take into account the dispersion radiation. The modified evolution equations resulting from the modified trial solution can well reflect the radiation-induced oscillation damping of the breathing PQSs as expected.

Automated summary

The evolution of pure-quartic solitons (PQSs) is studied using the variational approach based on the Lagrangian of the system. The standard Gaussian trial solution provides an analytic solution for the stationary PQSs, but fails to capture the damping of the oscillation for breathing PQSs. To address this issue, a modified trial solution is introduced to account for dispersion radiation. The resulting modified evolution equations accurately reflect the radiation-induced oscillation damping of breathing PQSs.