(2+1)-dimensional three-wave resonant interaction systems: Lump pattern and slice physics-informed neural network algorithm

• Published in: Nonlinear dynamics Vol. 113; no. 21; pp. 29861 - 29884
• Main Authors: Yan, Xue-Wei, Gao, Guang-Yu, Zhu, Guang-Nan, Chen, Yong
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.11.2025; Springer Nature B.V
• Subjects: Algorithms; Applications of Nonlinear Dynamics and Chaos Theory; Boundary conditions; Classical Mechanics; Control; Coordinate transformations; Dynamical Systems; Neural networks; Nonlinear systems; Optics; Parameters; Partial differential equations; Physics; Physics and Astronomy; Polynomials; Resonant interactions; Statistical Physics and Dynamical Systems; Vibration; Water waves; Prediction lump solution; Slice physics-informed neural network algorithm; (2+1)-dimensional three-wave resonant interaction; Kadomtsev-Petviashvili hierarchy reduction
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-025-11664-5

In this work, we study the high-order true lump solutions of the (2+1)-dimensional three-wave resonant interaction systems using the Hirota’s bilinear method and Kadomtsev-Petviashvili hierarchy reduction method. Then we also derive the prediction lump solutions associated with the root structures of the Yablonskii-Vorob’ev polynomial hierarchy and Adler-Moser polynomials under the conditions of large time t and large internal parameters a 2 m + 1 . We find that the high-order lumps with large internal parameters only generate a displacement without changing their shapes, as time evolves. We further numerically calculate the data-driven lump solutions of the target nonlinear system with the Dirichlet boundary conditions using the slice physics-informed neural network algorithm. Finally, we compare the true lump solutions with analytical prediction solutions as well as data-driven solutions, and show excellent agreement.