(2+1)-dimensional three-wave resonant interaction systems: Lump pattern and slice physics-informed neural network algorithm - Yan, Xue-Wei; Gao, Guang-Yu; Zhu, Guang-Nan; Chen, Yong (Nonlinear dynamics, 2025)
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.