1
Department of Mathematics, ITER, SOA University, Bhubaneshwar, Odisha-751030, India.
2
Department of Mathematics, Comilla University, Cumilla, 3506, Bangladesh.
10.22034/cmde.2026.69195.3400
Abstract
In this work, we apply a novel analytical approach called bilinear neural network method to investigate the (2+1)-dimensional 4th-order nonlinear evolution equation. The single and double hidden-layers bilinear neural models are utilized to construct various analytical solutions for the considered equation. Specifically, four distinct exact solutions are derived for each single hidden-layer models (3-2-1 and 3-3-1), depicting periodic-lumps, kink-solitons, kink-types and breather wave structures. Similarly, three distinct exact solutions are obtained for each double hidden-layer models (3-2-2-1 and 3-2-3-1), depicting two-soliton interactions, rogue waves and periodic-lumps wave structures. All the obtained results reveal physically significant wave phenomena relevant to various nonlinear systems in fluid dynamics, optical fibers and plasma physics. To the best of our knowledge, the obtained solutions in this work are novel and not reported in existing literature. The bilinear neural network method offers a systematic and flexible approach for solving complex nonlinear models and can be extended to solve models with variable coefficients and fractional-order dynamics in the future.
Singh, S. , Panda, A. and Ullah, M. Safi (2026). Hybrid Wave Solutions of a (2+1)-Dimensional 4th-order Evolution Equation using Bilinear Neural Network Method. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2026.69195.3400
MLA
Singh, S. , , Panda, A. , and Ullah, M. Safi. "Hybrid Wave Solutions of a (2+1)-Dimensional 4th-order Evolution Equation using Bilinear Neural Network Method", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2026.69195.3400
HARVARD
Singh, S., Panda, A., Ullah, M. Safi (2026). 'Hybrid Wave Solutions of a (2+1)-Dimensional 4th-order Evolution Equation using Bilinear Neural Network Method', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2026.69195.3400
CHICAGO
S. Singh , A. Panda and M. Safi Ullah, "Hybrid Wave Solutions of a (2+1)-Dimensional 4th-order Evolution Equation using Bilinear Neural Network Method," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2026.69195.3400
VANCOUVER
Singh, S., Panda, A., Ullah, M. Safi Hybrid Wave Solutions of a (2+1)-Dimensional 4th-order Evolution Equation using Bilinear Neural Network Method. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2026.69195.3400
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