123 research outputs found
Nonlinear second order ODE's: Factorizations and particular solutions
We present particular solutions for the following important nonlinear second
order differential equations: modified Emden, generalized Lienard, convective
Fisher, and generalized Burgers-Huxley. For the latter two equations these
solutions are obtained in the travelling frame. All these particular solutions
are the result of extending a simple and efficient factorization method that we
developed in Phys. Rev. E 71 (2005) 046607Comment: 6 pages, v3=published versio
Solutions of the Perturbed KDV Equation for Convecting Fluids by Factorizations
In this paper, we obtain some new explicit travelling wave solutions of the
perturbed KdV equation through recent factorization techniques that can be
performed when the coefficients of the equation fulfill a certain condition.
The solutions are obtained by using a two-step factorization procedure through
which the perturbed KdV equation is reduced to a nonlinear second order
differential equation, and to some Bernoulli and Abel type differential
equations whose solutions are expressed in terms of the exponential and
Weierstrass functionsComment: 4 pages, some changes in the text according to referees' suggestions,
added one reference, accepted at Central Europ. J. Phy
Mathematical methods of factorization and a feedback approach for biological systems
The first part of the thesis is devoted to factorizations of linear and
nonlinear differential equations leading to solutions of the kink type. The
second part contains a study of the synchronization of the chaotic dynamics of
two Hodgkin-Huxley neurons by means of the mathematical tools belonging to the
geometrical control theory.Comment: Ph. D. Thesis at IPICyT, San Luis Potosi, Mexico, 102 pp, 40 figs.
Supervisors: Dr. H.C. Rosu and Dr. R. Fema
Supersymmetric methods in the traveling variable: inside neurons and at the brain scale
We apply the mathematical technique of factorization of differential
operators to two different problems. First we review our results related to the
supersymmetry of the Montroll kinks moving onto the microtubule walls as well
as mentioning the sine-Gordon model for the microtubule nonlinear excitations.
Second, we find analytic expressions for a class of one-parameter solutions of
a sort of diffusion equation of Bessel type that is obtained by supersymmetry
from the homogeneous form of a simple damped wave equations derived in the
works of P.A. Robinson and collaborators for the corticothalamic system. We
also present a possible interpretation of the diffusion equation in the brain
contextComment: 14 pages, 1 figur
Riccati nonhermiticity with application to the Morse potential
A supersymmetric one-dimensional matrix procedure similar to relationships of
the same type between Dirac and Schrodinger equations in particle physics is
described at the general level. By this means we are able to introduce a
nonhermitic Hamiltonian having the imaginary part proportional to the solution
of a Riccati equation of the Witten type. The procedure is applied to the
exactly solvable Morse potential introducing in this way the corresponding
nonhermitic Morse problem. A possible application is to molecular diffraction
in evanescent waves over nanostructured surfacesComment: 8 pages, 4 figure
Classical harmonic oscillator with Dirac-like parameters and possible applications
We obtain a class of parametric oscillation modes that we call K-modes with
damping and absorption that are connected to the classical harmonic oscillator
modes through the "supersymmetric" one-dimensional matrix procedure similar to
relationships of the same type between Dirac and Schroedinger equations in
particle physics. When a single coupling parameter, denoted by K, is used, it
characterizes both the damping and the dissipative features of these modes.
Generalizations to several K parameters are also possible and lead to
analytical results. If the problem is passed to the physical optics (and/or
acoustics) context by switching from the oscillator equation to the
corresponding Helmholtz equation, one may hope to detect the K-modes as
waveguide modes of specially designed waveguides and/or cavitiesComment: 14 pages, 9 figures, revised, accepted at J. Phys.
Traveling kinks in cubic nonlinear Ginzburg-Landau equations
Nonlinear cubic Euler-Lagrange equations of motion in the traveling variable
are usually derived from Ginzburg-Landau free energy functionals frequently
encountered in several fields of physics. Many authors considered in the past
damped versions of such equations with the damping term added by hand
simulating the friction due to the environment. It is known that even in this
damped case kink solutions can exist. By means of a factorization method, we
provide analytic formulas for several possible kink solutions of such equations
of motion in the undriven and constant field driven cases, including the
recently introduced Riccati parameter kinks which were not considered
previously in such a context. The latter parameter controls the delay of the
switching stage of the kinksComment: 11 pages, 4 figures, final versio
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.Comment: 12 pages, 6 figures, 17 references, for NMMP-2022 proceeding
Potential of mathematical modeling in fruit quality
A review of mathematical modeling applied to fruit quality showed that these models ranged inresolution from simple yield equations to complex  representations of processes as respiration, photosynthesis and assimilation of nutrients. The latter models take into account complex  genotype environment interactions to estimate their effects on growth and yield. Recently, models are used to estimate seasonal changes in quality traits as fruit size, dry matter, water content and the concentration of sugars and acids, which are very important for flavor and aroma. These models have demonstrated their ability to generate relationships between physiological variables and quality attributes (allometric relations). This new kind of hybrid models has sufficient complexity to predict quality traits behavior
Factorization and Lie point symmetries of general Lienard-type equation in the complex plane
We present a variational approach to a general Lienard-type equation in order
to linearize it and, as an example, the Van der Pol oscillator is discussed.
The new equation which is almost linear is factorized. The point symmetries of
the deformed equation are also discussed and the two-dimensional Lie algebraic
generators are obtained
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