This article aims to study the time fractional coupled nonlinear Schrödinger equation, which explains the interaction between modes in nonlinear optics and Bose-Einstein condensation. The proposed generalized projective Riccati equation method and modified auxiliary equation method extract a more efficient and broad range of soliton solutions. These include novel solutions like a combined dark-lump wave soliton, multiple dark-lump wave soliton, two dark-kink solitons, flat kink-lump wave, multiple U-shaped with lump wave, combined bright-dark with high amplitude lump wave, bright-dark with lump wave and kink dark-periodic solitons are derived. The travelling wave patterns of the model are graphically presented with suitable parameters in 3D, density, contour and 2D surfaces, enhancing understanding of parameter impact. The proposed model's dynamics were observed and presented as quasi-periodic chaotic, periodic systems and quasi-periodic. This analysis confirms the effectiveness and reliability of the method employed, demonstrating its applicability in discovering travelling wave solitons for a wide range of nonlinear evolution equations.

Department of Computer Science and Mathematics Lebanese American University Byblos Lebanon

Department of Mathematics College of Science King Khalid University Abha Saudi Arabia

Department of Mathematics University of Management and Technology Lahore Pakistan

It4innovations VSB Technical University of Ostrava Ostrava Czech Republic

PLoS One. 2024 Oct 31;19(10):e0313333. doi: 10.1371/journal.pone.0313333. PubMed

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