ExactPolarobreathers

MATLAB code to compute and study spectral properties of numerically exact stationary and moving polarobreather solutions in a one-dimensional semi-classical crystal lattice model. Using the code and developed numerical algorithms, please cite Archilla, J.F.R., Bajārs, J.: Spectral Properties of Exact Polarobreathers in Semiclassical Systems. Axioms 12(5), 437 (2023), DOI: 10.3390/axioms12050437.

File ExactPolarobreathers_PureCode_WithoutData.zip contains pure code without precomputed data and images.

This research has been financially supported by the specific support objective activity 1.1.1.2. “Post-doctoral Research Aid” of the Republic of Latvia (Project No. 1.1.1.2/VIAA/4/20/617 “Data-Driven Nonlinear Wave Modelling”), funded by the European Regional Development Fund (project id. N. 1.1.1.2/16/I/001).

Instructions to run the code

• To perform a test numerical simulation, run the file main.m. Initial conditions are set in the same file main.m.
• All parameter values are defined in the file Parameter_Values.m, whereas all variables are initialized in the file Define_Variables.m.
• For convenience, all parameter values and variables are stored in structures: parm and vars, respectively.
• All functions can be found and are defined in the folder Functions.
• Simulation data and figures are saved in the following folders: SavedData and Figures, respectively.
• To obtain simulation data of approximate stationary polarobreather solution, run the following files: Parameter_Values_SimDataXTFT_approx_stat.m and main_SimDataXTFT_approx_stat.m.
• To obtain simulation data of approximate moving polarobreather solution, run the following files: Parameter_Values_SimDataXTFT_approx_mov.m and main_SimDataXTFT_approx_mov.m.
• The damped Gauss-Newton method is used to obtain numerically exact stationary and moving polarobreather solutions by running the files: main_exact_solution_muGaussNewton_E0_stat.m and main_exact_solution_muGaussNewton_E0_mov.m, respectively.
• To obtain numerical simulation data of exact stationary and moving polarobreather solutions, run the following files: main_SimDataXTFT_exact_stat.m and main_SimDataXTFT_exact_mov.m, respectively.
• Obtained simulation data is used to compute and study polarobreathers' spectral properties using the file plot_XTFT_spectra.m.