Non-autonomous positon and breather molecule for the variable-coefficient Kundu-nonlinear Schrödinger equation

Abstract

We construct novel non-autonomous positons, breather-positons, and breather molecules for the variable-coefficient Kundu-nonlinear Schrödinger equation —a key model for pulse propagation in optical fibers. Through degenerate Darboux transformation, we reveal intricate dynamics previously unattainable. For non-autonomous positon solution, generalized asymptotic analysis method yields exact expressions of asymptotic solitons with logarithmic trajectories. Arising from the different non-autonomous breather-positon, we give the non-autonomous rogue wave generation process and other results. For the non-autonomous breather molecule, the related dynamic behaviors under the periodic, exponential and hyperbolic function parameters are explored by the characteristic line analysis. This work provides a unified framework for investigating degenerate complex waves in inhomogeneous optical media.