José R. Quintero | Searcharxiv

arXiv2026

Solitary waves for a higher order Boussinesq system: Stability and numerical experiments

In this work, we study the nonlinear orbital stability of solitary-wave solutions for a class of higher-order Boussinesq systems with Hamiltonian structure. Using variational methods and the asymptotic connection with generalized fifth-order KdV equations, we establish orbital stability results for a broad family of homogeneous and nonhomogeneous nonlinearities satisfying suitable scaling assumptions. We also perform numerical simulations to investigate the stability criterion associated with the solitary waves. The numerical results suggest that the range of wave velocities leading to orbital stability may be larger than that predicted by the theoretical analysis.

math.AP↗

arXiv2025

Traveling-wave solutions for a higher-order Boussinesq system: existence and numerical analysis

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 \textit{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.

math.AP↗