2025/02/21 by Roberto de A. Capistrano–Filho, Capistrano-Filho, Roberto de A., Juan Carlos Muñoz +3
Medicine · Physics and Astronomy · #35A15 #37K40 #65M06 #65M70 #76B15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2502.15106
openalex publication_date 2025/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the existence and numerical computation of traveling wave solutions for a family of nonlinear higher-order Boussinesq evolution systems with a Hamiltonian structure. This general Boussinesq evolution system includes a broad class of homogeneous and non-homogeneous nonlinearities. We establish the existence of traveling wave solutions using the variational structure of the system and the concentration-compactness principle by P.-L. Lions, even though the nonlinearity could be non-homogeneous. For the homogeneous case, the traveling wave equations of the Boussinesq system are approximated using a spectral approach based on a Fourier basis, along with an iterative method that includes appropriate stabilizing factors to ensure convergence. In the non-homogeneous case, we apply a collocation Fourier method supplemented by Newton's iteration. Additionally, we present numerical experiments that explore cases in which the wave velocity falls outside the theoretical range of existence.