2018/04/04 by Ying Shi, Shi, Ying, Jun‐Xiao Zhao +1
Mathematics · Physics and Astronomy · #35Q58 #39A10 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1804.01470
openalex publication_date 2018/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain the well-known discrete modified Boussinesq equation in two-component form as well as its Lax pair in 3×3 matrix form through a 3-periodic reduction technique on the Hirota-Miwa equation and its Lax pair. We describe how Darboux transformations and binary Darboux transformations can be constructed for this two-component discrete integrable equation. These transformations are then used to obtain classes of explicit solutions in the form of Casorati- and Gramm-type determinants. N-soliton solutions of the discrete modified Boussinesq equation are discussed as well when taking the vacuum potentials as constants.