2023/07/05 by G. T. Adamashvili, Adamashvili, G. T.
Physics and Astronomy · #Advanced Fiber Laser Technologies #FOS: Physical sciences #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS) #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.2307.02581
openalex publication_date 2023/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A nonlinear wave equation that describes different nonlinear effects in various fields of research was considered. In two particular cases, this equation was reduced to the Sine-Gordon equation and the Born-Infeld equation. Using the slowly varying envelope approximation and the generalized perturbative reduction method, the nonlinear wave equation was transformed to coupled nonlinear Schrodinger equations for auxiliary functions. An explicit analytical solution of a nonlinear wave equation in the form of a two-breather molecule was obtained. One breather oscillated with the sum, and the other with the difference of frequencies and wave numbers. The obtained solution coincides with the solutions of the two-breather molecule found in a number of well-known equations from different areas of physics. It is shown that in a particular case of the small amplitude waves, a solution in the form of a two-breather molecule for the nonlinear Klein-Gordon equation coincides with the vector 0πpulse of the self-induced transparency which is presented under less stringent conditions compared to the same solution of this equation obtained earlier.