Stochastic dynamics of symmetry reductions to the parabolic nonlinear model in metamaterials - Muhammad Idrees Afridi (Results in Engineering)
The Schrödinger model is investigated in this work using electromagnetic pulse waves in metamaterials with parabolic nonlinearity law. The model is first analysed using Lie symmetry analysis to obtain a better grasp of the system's symmetries and invariants. This leads to symmetry reduction, simplifying the problem and facilitating the derivation of soliton solutions. We investigate localised wave packets with stable soliton solutions that maintain their amplitude and form throughout waves. Dark, bright, hyperbolic, and periodic solitons are some of these solutions. Understanding these soliton dynamics is necessary to comprehend the complex behaviour of electromagnetic pulses in metamaterials. Because of their artificial electromagnetic properties, which are not present in nature, metamaterials hold considerable promise for advancements in optics and telecommunications. Finally, to enhance visual comprehension, include density plots and 3-D graphs. This comprehensive approach aids in the elucidation of soliton dynamics in metamaterials and makes it easier to apply these findings in cutting-edge technological fields.