2022/05/03 by Gabriel E. Bittencourt Moraes, Moraes, Gabriel E. Bittencourt, Guilherme de Loreno +3
Mathematics · Physics and Astronomy · #35B35 #35G35 #35Q35 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2205.01439
openalex publication_date 2022/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
New results concerning the orbital stability of periodic traveling wave solutions for the "abcd" Boussinesq model will be shown in this manuscript. For the existence of solutions, we use basic tools of ordinary differential equations to show that the corresponding periodic wave depends on the Jacobi elliptic function of cnoidal type. The spectral analysis for the associated linearized operator is determined by using some tools concerning the Floquet theory. The orbital stability is then established by applying the abstract results [2] and [14] which give us sufficient conditions to the orbital stability for a general class of evolution equations.