Abstract
In this paper, we investigate the Kraenkel-Manna-Merle (KMM) system, which explains the nonlinear propagation of ultra-short wave pulses in specific saturated ferromagnetic materials. Ferromagnetic materials play a crucial role in data storage, manipulation, and telecommunications applications. Lie symmetry invariance analysis was conducted to identify infinitesimal generators of symmetries, and the adjoint representation was utilized to formulate an optimal system based on the identified Lie vectors. We obtained the analytical solution using the powerful power series method. To assess the impact of damping on the nonlinear Kraenkel-Manna-Merle (KMM) system, we evaluated its stability based on modulation instability criteria. Furthermore, we visually depicted wave solutions obtained by applying damping with varying parameter values. Additionally, we computed conserved quantities for the nonlinear KMM equation using the multiplier technique.
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