arXiv subjects

O. Pavón-Torres

Publications and source records attributed to O. Pavón-Torres.

7 recordsLinked to original sources

arXiv2026

Supersymmetric pairing of Lambert W-kink nerve impulses

Nerve impulses can be modelled as electromechanical density waves within the improved Heimburg-Jackson model. The inclusion of higher-order polynomial nonlinearities leads to a generalized Boussinesq equation with third and fourth order nonlinearities that, under a traveling-wave reduction, reduces to a Liénard-type equation. Applying a factorization method yields exact Lambert W-kink soliton solutions that represent localized nonlinear density waves near the membrane melting transition. Beyond providing exact solutions, the factorization uncovers an underlying supersymmetric structure. The associated operators satisfy algebraic relations analogous to those of supersymmetric quantum mechanics, thereby enabling the construction of a partner soliton. This supersymmetric pairing establishes a novel and previously unexplored connection between nonlinear electromechanical wave propagation in biological membranes and supersymmetric quantum-mechanical methods. The resulting framework offers a theoretical foundation for analysing mechanically induced perturbations and their nonlinear propagation in nerve membranes, with potential implications for understanding the biomechanical mechanisms underlying traumatic brain injury.

physics.bio-ph↗

arXiv2025

Exact solutions of the inhomogeneous nonlinear Schrödinger equation through supersymmetric potentials

By employing supersymmetric quantum mechanics, we present a general algorithm to construct supersymmetric partner potentials and hence derive exact stationary solutions of the inhomogeneous nonlinear Schrödinger equation (INLSE). This is possible due to the connection between the INLSE and the nonlinear Schrödinger equation (NLSE), which can be established from a treatment based on Lie point symmetries and is related with Schrödinger equation, under certain conditions. As an illustrative example, we construct exact solutions for the INLSE through a Pösch-Teller potential with a single bound state.

quant-ph↗

arXiv2025

Lambert W-kink Solitons Arising from Higher-Order Nonlinearities of Lipid Membranes

Accurate modelling of nerve impulse propagation requires accounting for strong higher-order nonlinearities in membrane dynamics, as incorporated in the extended Heimburg-Jackson model. By introducing third- and fourth-order polynomial terms into the membrane density equation, we derive a generalized Duffing-type equation that better captures the complex biophysical states involved in signal transmission. Applying the factorization method, we construct exact travelling wave solutions, including a novel class of Lambert W-Kink-type solitons. These findings provide new analytical insight into the nonlinear electromechanical behaviour of nerve membranes and contribute to the theoretical foundation for understanding pulse propagation in biomembranes.

physics.bio-ph↗

arXiv2025

Quasi-stationary evolution of cubic-quintic NLSE drop-like solitons in DNA-protein systems

Nonlinear molecular excitations in DNA have traditionally been modelled using the nonlinear Schrödinger equation (NLSE). An alternative approach is based on the plane-base rotator model and the SU(2)/U(1) generalized spin coherent states, which leads to a cubic quintic NLSE. Higher-order nonlinearities are particularly useful for modelling complex interactions, such as those in DNA-protein systems, where multiple competing forces play a significant role. Additionally, the surrounding viscous medium introduces dissipative forces that affect the propagation of molecular excitations, leading to energy dissipation and damping effects. These damping effects are modelled using the quasi-stationary method, which describes the system's near-equilibrium behaviour. In this work, we explore the evolution of nonlinear molecular excitations in DNA-protein systems, accounting for damping effects, and discuss potential applications to the transcription process.

physics.bio-ph↗

arXiv2024

Bilayer graphene in periodic and quasiperiodic magnetic superlattices

Starting from the effective Hamiltonian arising from the tight binding model, we study the behaviour of low-lying excitations for bilayer graphene placed in periodic external magnetic fields by using irreducible second order supersymmetry transformations. The coupled system of equations describing these excitations is reduced to a pair of periodic Schrödinger Hamiltonians intertwined by a second order differential operator. The direct implementation of more general second-order supersymmetry transformations allows to create nonsingular Schrödinger potentials with periodicity defects and bound states embedded in the forbidden bands, which turn out to be associated to quasiperiodic magnetic superlattices. Applications in quantum metamaterials stem from the ability to engineer and control such bound states which could lead to a fast development of the subject in the near future.

cond-mat.mes-hall↗

arXiv2024

Adiabatic evolution of solitons embedded on lipid membranes

The Heimburg-Jackson model, or thermodynamic soliton theory of nervous impulses, has a well-established record as an alternative model for studying the dynamics of nerve impulses and lipid bilayers. Within this framework, nerve impulses can be represented as nonlinear excitations of low amplitude depicted by the damped nonlinear Schrödinger equation and their adiabatic evolution can be analyzed using direct perturbative methods. Based on the foregoing, we carry out the current study using the quasi-stationary approach to obtain the adiabatic evolution of solitons embedded in lipid bilayers under the influence of a viscous elastic fluid. This analysis encompasses liquid-to-gel transition of the lipid bilayers, for whose dark and bright solitons arise, respectively.

nlin.PS↗

arXiv2024

Interaction and adiabatic evolution of orthodromic and antidromic impulses in the axoplasmic fluid

Unlike expected from the Hodgkin-Huxley model predictions, in which there is annihilation once orthodromic and antidromic impulses collide, the Heimburg-Jackson model demonstrates that both impulses penetrate each other as it has been shown experimentally. These impulses can be depicted as low amplitude nonlinear excitations in a weakly dissipative soliton model described by the damped NLSE. In view of the above, the Karpman-Solov'ev-Maslov perturbation theory turns out to be ideal to study the interaction and adiabatic evolution of orthodromic and antidromic impulses once axoplasmic fluid is present.

nlin.PS↗