2020/03/13 by V. G. Dubrovsky, Dubrovsky, V. G., A. V. Topovsky +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2003.07225
openalex publication_date 2020/03/13 · openalex created_date 2020/03/23 · openalex updated_date 2026/07/28
We constructed new classes of exact multi-lump solutions of mKP-1,2 equations with integrable boundary condition u(x,y,t)|y=0=0 by the use of ∂-dressing method of Zakharov and Manakov. We exactly satisfied reality and boundary conditions for the field u(x,y,t) using general determinant formula for multi-lump solutions. We illustrated new calculated classes by simple examples of two-lump solutions and demonstrated how fulfilment of integrable boundary condition u|y=0=0 via special nonlinear superposition of several single lumps leads to formation of certain eigenmodes for the field u(x,y,t) in semiplane y≥0, the analogs of standing waves on the string arising from corresponding boundary conditions at endpoints of string.