Management of rogue waves in variable shape optical lattice potential

Year 2025, Issue: 063, 24 - 37, 30.12.2025

Züleyha Öztaş

https://doi.org/10.59313/jsr-a.1687860

Abstract

We study the rational rogue wave solutions of the Gross-Pitaevskii equation with a variable shape optical lattice potential. The analytical solution is constructed via similarity transformation, which converts the Gross-Pitaevskii equation, including space and time varying coefficients, to the nonlinear Schrödinger equation. We explore how the rogue wave patterns change depending on the lattice parameters. It is shown that tuning the optical lattice parameters significantly influences the solution structures: small values of the modulational parameter and potential depth produce single-peak Peregrine solitons, while large values of these parameters lead to multi-peak, spatially periodic Akhmediev-like breather patterns. Therefore, we demonstrate that Akhmediev-like breathers can be obtained by adjusting the tunable parameters of the potential. The modulational instability is discussed, and the parameter region for modulational instability is determined. The results suggest potential applications in the control of nonlinear excitations in Bose–Einstein condensates, as well as in analogous optical systems where extreme waves play a crucial role.

Keywords

Rogue waves , Gross Pitaevskii equation , similarity transformation

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