91 research outputs found
Existence of periodic orbits in nonlinear oscillators of Emden-Fowler form
The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is
mapped to an Emden-Fowler (EF) equation that is written as an autonomous
two-dimensional ODE system for which we provide the phase-space analysis and
the parametric solution. Through an invariant transformation we find periodic
solutions to a certain class of EF equations that pass an integrability
condition. We show that this condition is necessary to have periodic solutions
and via the ODE analysis we also find the sufficient condition for periodic
orbits. EF equations that do not pass integrability conditions can be made
integrable via an invariant transformation which also allows us to construct
periodic solutions to them. Two other nonlinear equations, a zero-frequency
Ermakov equation and a positive power Emden-Fowler equation are discussed in
the same contextComment: 13 pages, 5 figures, title changed and content extended, version
accepted at Phys. Lett.
Pulses and Snakes in Ginzburg--Landau Equation
Using a variational formulation for partial differential equations (PDEs)
combined with numerical simulations on ordinary differential equations (ODEs),
we find two categories (pulses and snakes) of dissipative solitons, and analyze
the dependence of both their shape and stability on the physical parameters of
the cubic-quintic Ginzburg-Landau equation (CGLE). In contrast to the regular
solitary waves investigated in numerous integrable and non-integrable systems
over the last three decades, these dissipative solitons are not stationary in
time. Rather, they are spatially confined pulse-type structures whose envelopes
exhibit complicated temporal dynamics. Numerical simulations reveal very
interesting bifurcations sequences as the parameters of the CGLE are varied.
Our predictions on the variation of the soliton amplitude, width, position,
speed and phase of the solutions using the variational formulation agree with
simulation results.Comment: 30 pages, 14 figure
Shifted one-parameter supersymmetric family of quartic asymmetric double-well potentials
Extending our previous work (Rosu, Mancas, Chen, Ann.Phys. 343 (2014)
87-102), we define supersymmetric partner potentials through a particular
Riccati solution of the form F(x)=(x-c)^2-1, where c is a real shift parameter,
and work out the quartic double-well family of one-parameter isospectral
potentials obtained by using the corresponding general Riccati solution. For
these parametric double well potentials, we study how the localization
properties of the two wells depend on the parameter of the potentials for
various values of the shifting parameter. We also consider the supersymmetric
parametric family of the first double-well potential in the Razavy chain of
double well potentials corresponding to F(x)=(1/2)sinh 2x-2(1+sqrt 2)sinh
2x/[(1+sqrt 2) cosh 2x+1], both unshifted and shifted, to test and compare the
localization propertiesComment: 11 pages, 4 figures, published versio
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 equationsComment: 9 pages, 7 figures, 42 references, version matching the published
articl
Visco-elastic Cosmology for a Sparkling Universe?
We show the analogy between a generalization of the Rayleigh-Plesset equation of bubble dynamics including surface tension, elasticity and viscosity effects with a reformulation of the Friedmann-Lemaître set of equations describing the expansion of space in cosmology assuming a homogeneous and isotropic universe. By comparing both fluid and cosmic equations, we propose a bold generalization of the newly-derived cosmic equation mapping three continuum mechanics contributions. Conversely, the addition of a cosmological constant-like term in the fluid equation would lead also to a new phenomenology. Our work is purely speculative and does not rely on any observations or theoretical derivations from first principles
Nongauge bright soliton of the nonlinear Schrodinger (NLS) equation and a family of generalized NLS equations
We present an approach to the bright soliton solution of the NLS equation
from the standpoint of introducing a constant potential term in the equation.
We discuss a `nongauge' bright soliton for which both the envelope and the
phase depend only on the traveling variable. We also construct a family of
generalized NLS equations with solitonic sech^p solutions in the traveling
variable and find an exact equivalence with other nonlinear equations, such as
the Korteveg-de Vries and Benjamin-Bona-Mahony equations when p=2Comment: ~4 pages, 3 figures, 16 references, published versio
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