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H. C. Rosu

Publications and source records attributed to H. C. Rosu.

At least 19 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↗
arXiv2023

Liouville soliton surfaces obtained using Darboux transformations

In this paper, Liouville soliton surfaces based on some soliton solutions of the Liouville equation are constructed and displayed graphically, including some of those corresponding to Darboux-transformed counterparts. We find that the Liouville soliton surfaces are centroaffine surfaces of Tzitzeica type and their centroaffine invariant can be expressed in terms of the Hamiltonian. The traveling wave solutions to Liouville equation from which these soliton surfaces stem are also obtained through a modified variation of parameters method which is shown to lead to elliptic functions solution method.

nlin.SI↗
arXiv2023

Factorization conditions for nonlinear second-order differential equations

For the case of nonlinear second-order differential equations with a constant coefficient of the first derivative term and polynomial nonlinearities, the factorization conditions of Rosu and Cornejo-Perez are approached in two ways: (i) by commuting the subindices of the factorization functions in the two factorization conditions and (ii) by leaving invariant only the first factorization condition achieved by using monomials or polynomial sequences. For the first case, the factorization brackets commute and the generated equations are only equations of Ermakov-Pinney type. The second modification is non commuting, leading to nonlinear equations with different nonlinear force terms, but the same first-order part as the initially factored equation. It is illustrated for monomials with the examples of the generalized Fisher and FitzHugh-Nagumo initial equations. A polynomial sequence example is also included.

nlin.SI↗
arXiv2022

One-parameter Darboux-deformed Fibonacci numbers

One-parameter Darboux deformations are effected for the simple ODE satisfied by the continuous generalizations of the Fibonacci sequence recently discussed by Faraoni and Atieh [Symmetry 13, 200 (2021)], who promoted a formal analogy with the Friedmann equation in the FLRW homogeneous cosmology. The method allows the introduction of deformations of the continuous Fibonacci sequences, hence of Darboux-deformed Fibonacci (non integer) numbers. Considering the same ODE as a parametric oscillator equation, the Ermakov-Lewis invariants for these sequences are also discussed.

math.GM↗
arXiv2022

Vanishing Poynting observers and electromagnetic field classification in Kerr and Kerr-Newman spacetimes

We consider electromagnetic fields having an angular momentum density in a locally non-rotating reference frame in Schwarzschild, Kerr, and Kerr-Newman spacetimes. The nature of such fields is assessed with two families of observers, the locally non-rotating ones and those of vanishing Poynting flux. The velocity fields of the vanishing-Poynting observers in the locally non-rotating reference frames are determined using the 3+1 decomposition formalism. From a methodological point of view, and considering a classification of the electromagnetic field based on its invariants, it is convenient to separate the consideration of the vanishing-Poynting observers into two cases corresponding to the pure and non-pure fields, additionally if there are regions where the field rotates with the speed of light (light surfaces) it becomes necessary to split these observers into two subfamilies. We present several examples of relevance in astrophysics and general relativity, such as pure rotating dipolar-like magnetic fields and the electromagnetic field of the Kerr-Newman solution. For the latter example, we see that vanishing-Poynting observers also measure a vanishing super-Poynting vector, confirming recent results in the literature. Finally, for all non-null electromagnetic fields, we present the 4-velocity fields of vanishing Poynting observers in an arbitrary spacetime.

gr-qc↗
arXiv2021

Quasi-exactly solvable hyperbolic potential and its anti-isospectral counterpart

We solve the eigenvalue spectra for two quasi exactly solvable (QES) Schrödinger problems defined by the potentials $V(x;γ,η) = 4γ^{2}\cosh^{4}(x) + V_{1}(γ,η) \cosh^{2}(x) + η\left( η-1 \right)\tanh^{2}(x)$ and $ U(x;γ,η) = -4γ^{2}\cos^{4}(x) - V_{1}(γ,η)\cos^{2}(x) + η\left( η-1 \right)\tan^{2}(x)$, found by the anti-isospectral transformation of the former. We use three methods: a direct polynomial expansion, which shows the relation between the expansion order and the shape of the potential function; direct comparison to the confluent Heun equation (CHE), which has been shown to provide only part of the spectrum in different quantum mechanics problems, and the use of Lie algebras, which has been proven to reveal hidden algebraic structures of this kind of spectral problems.

math-ph↗
arXiv2021

Radius evolution for bubbles with elastic shells

We present an analysis of an extended Rayleigh-Plesset (RP) equation for a three dimensional cell of microorganisms such as bacteria or viruses in some liquid, where the cell membrane in bacteria or the envelope (capsid) in viruses possess elastic properties. To account for rapid changes in the shape configuration of such microorganisms, the bubble membrane/envelope must be rigid to resist large pressures while being flexible to adapt to growth or decay. Such properties are embedded in the RP equation by including a pressure bending term that is proportional to the square of the curvature of the elastic wall. Analytical solutions to this extended equation are obtained in terms of elliptic functions.

cond-mat.soft↗
arXiv2021

Superfluid Rayleigh-Plesset extension of FLRW cosmology

Guided by the analogy with the Rayleigh-Plesset dynamics of multielectron bubbles in superfluid He-4, we consider the cosmological FLRW evolution equation with additional cubic and sixth powers of the inverse of the scale factor of the universe. For the barotropic parameter w=2/3 (coasting universe), along with zero cosmological constant in the absence of viscous terms, by using the Sundman time as evolution parameter, we present parametric solutions for the scale factor of the universe in terms of rational expressions of Weierstrass elliptic functions and their particular cases thereof. For other values of the equation of state parameter w, such as w=-1, but also the same coasting case, we present a more standard discussion in the conformal time variable using solutions obtained by numerical integration.

gr-qc↗
arXiv2021

Factorization method for some inhomogeneous Lienard equations

We obtain closed-form solutions of several inhomogeneous Lienard equations by the factorization method. The two factorization conditions involved in the method are turned into a system of first-order differential equations containing the forcing term. In this way, one can find the forcing terms that lead to integrable cases. Because of the reduction of order feature of factorization, the solutions are simultaneously solutions of first-order differential equations with polynomial nonlinearities. The illustrative examples of Lienard solutions obtained in this way generically have rational parts, and consequently display singularities.

nlin.SI↗
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↗
arXiv2020

Planar motion with Fresnel integrals as components of the velocity

We analyze the two-dimensional motion of a rigid body due to a constant torque generated by a force acting on the body parallel to the surface on which the body moves extending an old note of Ferris-Prabhu [Am. J. Phys. 38, 1356-1357 (1970)] and supplementing it with a short discussion of the jerking properties

physics.class-ph↗
arXiv2019

Traveling wave solutions for wave equations with two exponential nonlinearities

We use a simple method that leads to the integrals involved in obtaining the traveling wave solutions of wave equations with one and two exponential nonlinearities. When the constant term in the integrand is zero, implicit solutions in terms of hypergeometric functions are obtained while when that term is nonzero all the basic traveling wave solutions of Liouville, Tzitzeica and their variants, as well as sine/sinh-Gordon equations with important applications in the phenomenology of nonlinear physics and dynamical systems are found through a detailed study of the corresponding elliptic equations

math-ph↗