2020/03/13 by V. G. Dubrovsky, Dubrovsky, V. G., A. V. Topovsky +1
Physics and Astronomy · #Advanced Fiber Laser Technologies #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2003.07227
openalex publication_date 2020/03/13 · openalex created_date 2020/03/23 · openalex updated_date 2026/07/28
We proposed general scheme for construction of exact real periodical solutions of mKP-1 equation via Zakharov-Manakov ∂-dressing method, derived convenient determinant formula for calculation of such solutions and demonstrated how reality and boundary conditions for the field u(x,y,t) can be satisfied. We calculated the new classes of exact periodical solutions of mKP-1 equation: 1. the class of nonsingular one-periodic solutions or nonlinear plane monochromatic waves; 2. the class of two-periodic solutions without imposition of any boundary condition; 3. the class of two-periodic solutions with integrable boundary condition u(x,y,t)|y=0=0. We interpreted the third class of two-periodic solutions with integrable boundary condition obtained by the use of special nonlinear superpositions of two simple one-periodical waves as eigenmodes of oscillations of the field u(x,y,t) in semi-plane y≥ 0, the analogs of standing waves on the string with fixed endpoints.