Data Set for Research on Solving the One-Dimensional Nonlinear Schrödinger Equation for Single Soliton Solutions and Their Characteristics Based on Physics-Informed Neural Networks

This dataset supports the Bachelor's thesis titled “Research on Solving the One‑Dimensional Nonlinear Schrödinger Equation for Single Soliton Solutions and Their Characteristics Based on Physics‑Informed Neural Networks.” It contains the complete collection of figure data (CSV files) and publication‑ready images (PNG) for every figure presented in the thesis. All data were generated by the Python program listed in the reference section, which implements a physics‑informed neural network (PINN) solver and a split‑step Fourier method (SSFM) for the one‑dimensional nonlinear Schrödinger equation.

The naming convention directly maps each file to a specific figure in the thesis, and the corresponding CSV files store the raw numerical values needed to reproduce the plots. A detailed mapping between the program output files and the thesis figures, as well as the full source code, can be found in the referenced program listing.Figure 3.1 (Figure1_TrainingLoss) – Total loss curve during PINN training.Figure 3.2(a) (Figure2_PINN_Predicted_Amplitude) – Predicted amplitude |u|(x,t) from PINN.Figure 3.2(b) (Figure3_Analytical_Amplitude) – Analytical amplitude |u|(x,t).Figure 3.3 (Figure4_Amplitude_Error) – Absolute error of PINN predicted amplitude.Figure 3.4(a) (Figure5_Amplitude_t0) – Amplitude slice at t=0.Figure 3.4(b) (Figure6_Amplitude_tmid) – Amplitude slice at t=2.5.Figure 3.4(c) (Figure7_Amplitude_tend) – Amplitude slice at t=5.Figure 3.5(a) (Figure8_RealPart_tend) – Real part at t=5.Figure 3.5(b) (Figure9_ImagPart_tend) – Imaginary part at t=5.Figure 3.6 (Figure15_Phase_RMS_vs_Time) – Phase RMS error versus time.Figure 4.1(a) (Figure4_1a_N_vs_t) – Particle number N(t) conservation.Figure 4.1(b) (Figure4_1b_P_vs_t) – Momentum P(t) conservation.Figure 4.1(c) (Figure4_1c_E_vs_t) – Energy E(t) conservation.Figure 4.4 (Figure_SSFM_Dealias_E) – SSFM energy E(t) with and without dealiasing.Figure 4.5 (Figure4_3_GlobalRelL2Error_vs_t) – Global relative L² error versus time for PINN and SSFM.Figure 4.6 (Figure4_4_FinalTime_AbsAmpError_x) – Absolute amplitude error along x at final time for PINN and SSFM.