arXiv subjects

J. de la Cruz

Publications and source records attributed to J. de la Cruz.

9 recordsLinked to original sources

arXiv2026

A family of non-autonomous hybrid Lienard oscillators based on a parametrically extended commutative factorization

We introduce a class of nonautonomous nonlinear oscillator equations of mixed Liénard type that arises from a parametric deformation of the commutative factorization procedure applied to second-order ordinary differential equations with periodic solutions. Their solutions, in particular the isochronous waveforms, are obtained in closed form through a Riccati reduction scheme for the power-law choice of the factorization function, $ϕ(x)=kx^{q}$, $k\in \mathbb{R}$, and $q\in\mathbb{N}$, corresponding to the so-called modified Emden oscillators, and do not depend on the arbitrary deformation parameter $A_1$. The variational structure of the equation is characterised by a Lagrangian supplemented with a generalised Rayleigh dissipation function that contains a non-standard cubic term in $\dot{x}$. We also show that multiplying the equation of motion by the Jacobi multiplier $M(x)=x^{-2A_1}$ a position-dependent-mass (PDM) form is obtained with related friction and restoring force.

nlin.SI↗

arXiv2026

Isochronous and underdamped waveforms of modified Emden oscillators

Bernoulli-type waveforms for modified Emden nonlinear oscillators of arbitrary natural power $q$ are obtained through a generalized commutative factorization approach. These oscillators display a well-defined odd-even dynamical dichotomy, which is discussed in detail: the odd-$q$ cases entail isochronous oscillators whose period $T = 2π/ω$ is independent of amplitude and initial conditions, while the even-$q$ cases display underdamped behavior. The Lagrangian formulation is presented in the Lurie's dissipative description. The isochronous regime and the period of the solutions in the odd case are also confirmed through a generalized polar-coordinate analysis in the spirit of Sabatini's work. The absence of periodic orbits for even $q$ is shown to be a consequence of the Bendixson-Dulac criterion applied to the radial velocity function. Explicit waveforms and their phase portraits are presented for $q = 1, 2, 3, 4$, along with the non exponential envelope formulas for the damped cases and singular-region bounds for the isochronous ones. A few possible applications are also mentioned.

nlin.SI↗

arXiv2026

Clothoid helices obtained via the Lie-Darboux method

The clothoid helices that have both curvature and torsion directly proportional to the arclength are obtained via the Lie-Darboux method and analyzed in some detail. Shifted counterparts are also introduced and studied within the same framework.

math-ph↗

arXiv2025

Isochronous waveforms of Liénard equations via commutative factorization

Isochronous waveform solutions of homogeneous Liénard equations are obtained by a modification of the nonlinear factorization method of Rosu and Cornejo-Pérez. The scheme is based on the assumption that the intermediate function $Φ$ that can be introduced in this factorization method depends on both the dependent and independent variables of the nonlinear equation. The method is applied to three cases, a noted cubic anharmonic oscillator, a Liénard-reduced form of the Sharma-Tasso-Olver evolution equation, and the cubic-quintic Wilson's Liénard equation. All these cases are written in a commutative factored form that allows to obtain the general solutions as solutions of a certain type of Bernoulli differential equation. A theorem is also given asserting the general form of the Liénard equation, i.e., for given polynomial degree n of its coefficients, which can be solved by this method. The conditions under which these equations can be also approached by non-local transformations are established.

math.CA↗

arXiv2024

Normalized eigenfunctions of parametrically factored Schroedinger equations

The factorizations using the general Riccati solution constructed from a given particular solution by means of the Bernoulli ansatz initiated in 1984 by Mielnik and Fernandez C. for the cases of the quantum harmonic oscillator and the radial Hydrogen equation, respectively, are briefy reviewed. The issue of the eigenfunction normalization of the obtained one-parameter Darboux-deformed Hamiltonians is addressed here.

math-ph↗

arXiv2024

Singular parametric oscillators from the one-parameter Darboux transformation of the classical harmonic oscillator

The singular parametric oscillators obtained from the one-parameter Darboux deformation/transformation effected upon the classical harmonic oscillator are introduced and discussed in some detail using sin(omega_0 t) and cos(omega_0 t) as seed solutions. The corresponding Ermakov-Lewis integrability problem of these parametric oscillators is also studied. It is shown that the Ermakov-Lewis invariants do not depend on the deformation parameter and are singularity-free.

physics.class-ph↗

arXiv2021

Multifractal analysis of the symmetry of a strictly isospectral energy landscape on a square lattice

We use the Holder regularity analysis to study the symmetry breaking and recovery due to a parametric potential generated via the strictly isospectral factorization method. The initial potential is two-dimensional and periodic in the two Cartesian directions, with the symmetry group $P_{4mm}$. The resulting parametric isospectral potential display a P_m symmetry for values of the parameter moderately close to the singular value gamma_s. However, at large values of the parameter, visually around gamma=gamma_s+110, the original symmetry is recovered. For a much higher precision value of the parameter for this symmetry recovery, we show that the multifractal spectrum of the parametric potential can be conveniently used. In the latter case, we obtain gamma=gamma_s+201.085 for three decimal digits precision.

cond-mat.other↗

arXiv2017

On $q$-analog Steiner systems of rank metric codes

In this paper we prove that rank metric codes with special properties imply the existence of $q$-analogs of suitable designs. More precisely, we show that the minimum weight vectors of a $[2d,d,d]$ dually almost MRD code $C\leq \mathbb{F}_{q^m}^n$ which has no code words of rank weight $d+1$ form a $q$-analog Steiner system $S_q(d-1,d,2d)$. In particular, $d+1$ must be a prime.

math.CO↗

arXiv2013

On extremal self-dual codes of length 120

We prove that the only primes which may divide the order of the automorphism group of a putative binary self-dual doubly-even [120, 60, 24] code are 2, 3, 5, 7, 19, 23 and 29. Furthermore we prove that automorphisms of prime order $p \geq 5$ have a unique cycle structure.

cs.IT↗