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Abstract This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions. These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers. By analyzing the Lax pair and the Riemann-Hilbert problem, we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system. Furthermore, we study the impacts of group velocity dispersion or fourth-order dispersion on soliton behaviors. Through appropriate parameter selection, we observe various nonlinear phenomena, including the disappearance of solitons after interaction and their transformation into breather-like solitons, as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.
Zhao et al. (Mon,) studied this question.