The bound states of pure-quartic solitons

In this paper, we quantitatively study the equilibrium bound state and the oscillating bound state of pure-quartic solitons (PQSs). Based on the Lagrangian of the system, we obtain the analytic expression of the effective interaction potential, which makes it convenient to predict the critical separation between the interacting PQSs in the equilibrium bound state. Furthermore, we study the oscillation period of PQSs in the oscillating bound state by making an analogy between the evolution of PQS pair and the motion of the Newtonian particle in a potential well. The effective mass and the effective force are derived, and thereby the semianalytic expression of the oscillation period is obtained. The results are useful for gaining a physical insight into the evolution of the interacting PQSs in the two types of bound states.

Automated summary

This paper quantitatively studies the equilibrium bound state and the oscillating bound state of pure-quartic solitons (PQSs). By analyzing the Lagrangian of the system, the analytic expression of the effective interaction potential is obtained, which facilitates the prediction of the critical separation between interacting PQSs in the equilibrium bound state. Furthermore, the oscillation period of PQSs in the oscillating bound state is studied by drawing an analogy between the evolution of PQS pairs and the motion of a Newtonian particle in a potential well. The derived effective mass and force lead to a semi-analytic expression for the oscillation period. These results provide valuable insights into the evolution of interacting PQSs in the two types of bound states.