43 citations · 142 across the 17 of their papers we have counts for
18 papers
Edge-cusped compactons from gradient-power nonlinear dispersion: exact transitions and singular spectral structure
Francisco R. Villatoro
We introduce a conservative two-exponent dispersive family, with the nonlinear-flux exponent and the gradient-dispersion exponent, that separates the mechanisms governi…
Basin-Preserving Discretizations of Modern Hopfield Retrieval Dynamics: Energy Cells, Dissipation, and the Attention Limit
Francisco R. Villatoro
The retrieval dynamics of a modern Hopfield network is the gradient flow of a log-sum-exp energy, while the attention update is its exact difference-of-convex minimization step. We…
Annular liquid jets: exact constraint absorption and finite-time loss of global admissibility
Francisco R. Villatoro
An annular liquid jet may enclose a volume of gas and, when surface tension dominates over inertia, close on the symmetry axis at a finite distance. In the one-dimensional membrane…
Discrete Breathers in Klein-Gordon Lattices: a Deflation-Based Approach
F. Martin-Vergara, J. Cuevas-Maraver, P. E. Farrell +2
Deflation is an efficient numerical technique for identifying new branches of steady state solutions to nonlinear partial differential equations. Here, we demonstrate how to extend…
Fractal structure of the soliton scattering for the graphene superlattice equation
Francisca Martin-Vergara, Francisco Rus, Francisco R. Villatoro
The graphene superlattice equation, a modified sine-Gordon equation, governs the propagation of solitary electromagnetic waves in a graphene superlattice. This equation has kink so…
The Nonlinear Schrödinger Equation in the Finite Line
Juan I. Ramos, Francisco R. Villatoro
A numerical study of the nonlinear Schrödinger (NLS) equation subject to homogeneous Dirichlet, Neumann and Robin boundary conditions in the finite line is presented. The results a…