Abstract
In this paper, the (2 + 1)-dimensional variable coefficients equation which describes the thermophoric wave motion of wrinkles in graphene sheets (2D-vGS) is studied, where it has many applications in 2D optics, nanophotonic, and nanoelectronics. A direct simplified Hirota’s bilinear method is generalized to find the bilinear form of the 2D-vGS equation. Accordingly, one, two, and three soliton wave solutions indicate that our studied equation is fully integrable and has n-soliton solutions. Moreover, we have focused on the study of two and three solitons interactions, this leads to the identification of two distinct solution types, the Y-shape soliton and fork- shape soliton, which can be clearly distinguished from the 3D plots and density plots. These solutions are characterized by a rich spectrum of collision dynamics and encompassing phenomena such as fusion and fission. The nonlinear properties of the two and three soliton solutions could be useful for farther applications in 2D optics like metamaterials with exotic optical properties and ultra-compact and efficient photonic devices.
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The authors would like to thank the Deanship of Scientific Research, Majmaah University, Saudi Arabia, for funding this work under project Number R-2024-995
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Rehab M. Elshiekh wrote and applied different methodologies and Mahmoud Gaballah made physical applications and figures.
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El-Shiekh, R.M., Gaballah, M. Bilinear form and n-soliton thermophoric waves for the variable coefficients (2 + 1)-dimensional graphene sheets equation. Opt Quant Electron 56, 872 (2024). https://doi.org/10.1007/s11082-024-06789-7
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DOI: https://doi.org/10.1007/s11082-024-06789-7