Datos obtenidos el lunes 11 de febrero de 2002
Registro 1 de 10 en INSPEC 2001/01-2001/08
TI: Solitons in nonlinear waveguides with sinusoidal Kerr-index
AU: Villatoro-FR; Ramos-JI
SO: ISRAMT'99. 1999 7th International Symposium on Recent
Advances in Microwave
Technology Proceedings. ISRAMT, Spain; 1999; iii+801 pp.
p.41-4.
PY: 1999
LA: English
AB: The effect of a nonlinear optical medium with a sinusoidal
variation of the Kerr refraction
index on the propagation of solitons is studied numerically
by means of a linearized theta -method.
Both the width and wavelength of the sinusoidal variation
and the width of the soliton determine
whether the soliton will be trapped in or pass through
the region where the sinusoidal variation
occurs. In both cases, the soliton radiates energy upstream
and downstream. The effect of linear
losses is small and does not alter the main characteristics
of the interaction of the soliton with the
periodically nonlinear medium.
AN: 6957075
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Registro 2 de 10 en INSPEC 1999/01-1999/10
TI: On the method of modified equations. VI. Asymptotic
analysis of and asymptotic
successive-corrections techniques for two-point, boundary-value
problems in ODE's
AU: Villatoro-FR; Ramos-JI
SO: Applied-Mathematics-and-Computation. vol.105, no.2-3;
Nov. 1999; p.137-71.
PY: 1999
LA: English
AB: The modified equation technique is extended to two-point,
boundary-value problems, and a
second-order accurate, implicit, centered, finite difference
scheme for nonhomogeneous,
second-order, ordinary differential equations with linear
boundary conditions is analyzed. The
first, second and third modified equations, or equivalent,
second equivalent and (simply) modified
equations, respectively, for this scheme and its boundary
conditions are presented. It is shown that
the three kinds of modified equations are asymptotically
equivalent when the equivalent equation
is used for the boundary conditions, since an asymptotic
analysis of these equations with the grid
size as small parameter yields exactly the same results.
For a linear problem, multiple scales and
summed-up asymptotic techniques are used and the resulting
uniform asymptotic expansions are
shown to be equivalent to the solution of the original
finite difference scheme. Asymptotic
successive-corrections techniques are also applied to
the three kinds of modified equations to
obtain higher-order schemes. Higher-order boundary conditions
are easily treated in the
asymptotic successive-corrections technique, although
these boundary conditions must be
obtained by using the equivalent equation in order to
obtain a correct estimate of the global error
near the domain boundaries. The methods introduced in
this paper are applied to homogeneous
and non-homogeneous, second-order, linear and non-linear,
ordinary differential equations, and
yield very accurate results.
AN: 6392069
FTXT:
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Registro 3 de 10 en INSPEC 1999/01-1999/10
TI: On the method of modified equations. V. Asymptotic
analysis of and direct-correction and
asymptotic successive-correction techniques for the implicit
midpoint method
AU: Villatoro-FR; Ramos-JI
SO: Applied-Mathematics-and-Computation. vol.103, no.2-3;
15 Aug. 1999; p.241-85.
PY: 1999
LA: English
AB: For pt.IV. see ibid., p. 213-40. The equivalent, second
equivalent and (simply) modified
equations for the implicit midpoint rule are shown to
be asymptotically equivalent in the sense that
an asymptotic analysis of these equations with the time
step size as small parameter yields exactly
the same results; for linear problems with constant coefficients,
they are also equivalent to the
original finite difference scheme. Straight forward (regular),
multiple scales and summed-up
asymptotic techniques are used for the analysis of the
implicit midpoint rule difference method,
and the accuracy of the resulting asymptotic expansion
is assessed for several first-order,
non-linear, autonomous ordinary differential equations.
It is shown that, when the resulting
asymptotic expansion is uniformly valid, the asymptotic
method yields very accurate results if the
solution of the leading order equation is smooth and does
not blow up. The modified equation is
also studied as a method for the development of new numerical
schemes based on both
direct-correction and asymptotic successive-correction
techniques applied to the three kinds of
modified equations, the linear stability of these techniques
is analyzed, and their results are
compared with those of Runge-Kutta schemes for several
autonomous and non-autonomous,
first-order, ordinary differential equations.
AN: 6296085
FTXT:
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Registro 4 de 10 en INSPEC 1999/01-1999/10
TI: On the method of modified equations. IV. Numerical
techniques based on the modified
equation for the Euler forward difference method
AU: Villatoro-FR; Ramos-JI
SO: Applied-Mathematics-and-Computation. vol.103, no.2-3;
15 Aug. 1999; p.213-40.
PY: 1999
LA: English
AB: The modified equation method is studied as a technique
for the development of new
numerical techniques for ordinary differential schemes
based on the third modified or (simply)
modified equation of the explicit Euler forward method.
Both direct-correction and
successive-correction techniques based on the modified
equation are used to obtain higher-order
schemes. The resulting numerical techniques are completely
explicit, of order of accuracy as high
as desired, and self-starting since the truncation error
terms in the modified equation have no
derivatives. The methods introduced in this paper are
applied to autonomous and
non-autonomous, scalar and systems of ordinary differential
equations and compared with
second- and fourth-order accurate Runge-Kutta schemes.
It is shown that, for sufficiently small
step sizes, the fourth-order direct-correction and successive-correction
methods are as accurate as
the fourth-order Runge-Kutta scheme.
AN: 6296084
FTXT:
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Registro 5 de 10 en INSPEC 1999/01-1999/10
TI: On the method of modified equations. III. Numerical
techniques based on the second
equivalent equation for the Euler forward difference method
AU: Villatoro-FR; Ramos-JI
SO: Applied-Mathematics-and-Computation. vol.103, no.2-3;
15 Aug. 1999; p.179-212.
PY: 1999
LA: English
AB: For pt.II. see ibid., p. 141-178. Direct-correction
and asymptotic successive-correction
methods based on the second equivalent equation are applied
to the Euler forward explicit
scheme. In direct-correction, the truncation error terms
of the second equivalent equation which
contain higher-order derivatives together with a starting
procedure, are discretized by means of
finite differences. Both explicit and implicit direct-correction
schemes are presented and their
stability regions are studied. The asymptotic successive-correction
numerical technique developed
in Part II of this series with a consistent starting procedure
is applied to the second equivalent
equation. Both all-backward and all-centered asymptotic
successive-correction methods are
presented. The numerical methods introduced in this paper
are applied to autonomous and
non-autonomous, scalar and systems of ordinary differential
equations and compared with the
results of second- and fourth-order accurate Runge-Kutta
methods. It is shown that the
fourth-order Runge-Kutta method is more accurate than
the successive-correction techniques for
large time steps due to the need for higher-order derivatives
of the Euler solution; however, for
sufficiently small time steps, but larger enough so that
round-off errors are negligible, both
methods have nearly the same accuracy.
AN: 6296083
FTXT:
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Registro 6 de 10 en INSPEC 1999/01-1999/10
TI: On the method of modified equations. II: Numerical
techniques based on the equivalent
equation for the Euler forward difference method
AU: Villatoro-FR; Ramos-JI
SO: Applied-Mathematics-and-Computation. vol.103, no.2-3;
15 Aug. 1999; p.141-77.
PY: 1999
LA: English
AB: For pt.I. see ibid., p. 111-39. New numerical successive-correction
techniques for ordinary
differential equations based on the Euler forward explicit
method and the first modified or
equivalent equation are presented. These techniques are
similar to iterative updating deferred
methods and are based on the application of asymptotic
methods to modified equations which do
not require initial conditions for the high order derivatives
in the truncation terms and which yield
stable numerical methods. It is shown that, depending
on the discretization of the high order
derivatives in the high order correction equations, different
methods of as high order of
consistency as required can be developed. In this paper,
backward and centered formulas are
used, but the resulting numerical methods are not self-starting.
It is shown that, if the starting
procedure is not adequate, the numerical order of the
method can be smaller than the theoretical
one. In order to avoid this loss of numerical order, a
method for consistently starting the
asymptotic successive-correction technique based on the
use of fictitious times is presented and
applied to autonomous and nonautonomous, ordinary differential
equations, and compared with
the results of second and fourth-order Runge-Kutta methods.
It is shown that the fourth-order
Runge-Kutta method is more accurate than the successive-correction
techniques for large time
steps due to the higher order derivatives in the successive-correction,
but, for sufficiently small
time steps, these techniques have almost the same accuracy
as the fourth-order Runge-Kutta
method.
AN: 6296082
FTXT:
Mostrar Registro Completo
Registro 7 de 10 en INSPEC 1999/01-1999/10
TI: On the method of modified equations. I. Asymptotic
analysis of the Euler forward difference
method
AU: Villatoro-FR; Ramos-JI
SO: Applied-Mathematics-and-Computation. vol.103, no.2-3;
15 Aug. 1999; p.111-39.
PY: 1999
LA: English
AB: The method of modified equations is studied as a technique
for the analysis of finite
difference equations. The non-uniqueness of the modified
equation of a difference method is
stressed and three kinds of modified equations are introduced.
The first modified or equivalent
equation is the natural pseudo-differential operator associated
to the original numerical method.
Linear and nonlinear combinations of the equivalent equation
and their derivatives yield the
second modified or second equivalent equation and the
third modified or (simply) modified
equation, respectively. For linear problems with constant
coefficients, the three kinds of modified
equations are equivalent among them and to the original
difference scheme. For nonlinear
problems, the three kinds of modified equations are asymptotically
equivalent in the sense that an
asymptotic analysis of these equations with the time step
as small parameter yields exactly the
same results. In this paper, both regular and multiple
scales asymptotic techniques are used for the
analysis of the Euler forward difference method, and the
resulting asymptotic expansions are
verified for several nonlinear, autonomous, ordinary differential
equations. It is shown that, when
the resulting asymptotic expansion is uniformly valid,
the asymptotic method yields very accurate
results if the solution of the leading order equation
is smooth and does not blow up, even for large
step sizes.
AN: 6296081
FTXT:
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Registro 8 de 10 en INSPEC 1993-1994
TI: Classical forces on solitons in finite and infinite
nonlinear planar waveguides
AU: Ramos-JI; Villatoro-FR
SO: Microwave-and-Optical-Technology-Letters. vol.7, no.13;
Sept. 1994; p.620-5.
PY: 1994
LA: English
AB: Conservation equations for the mass, linear momentum,
and energy densities of solitons
propagating in finite, infinite, and periodic nonlinear
planar waveguides and governed by the
nonlinear Schrodinger equation are derived. These conservation
equations are used to determine
classical force densities that are compared with those
derived by drawing a quantum mechanics
analogy between the propagation of solitons and the motion
of a quantum particle in a nonlinear
potential well.
AN: 4821659
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Registro 9 de 10 en INSPEC 1993-1994
TI: A quantum mechanics analogy for the nonlinear Schrodinger
equation in the finite line
AU: Ramos-JI; Villatoro-FR
SO: Computers-&-Mathematics-with-Applications. vol.28,
no.4; Aug. 1994; p.3-17.
PY: 1994
LA: English
AB: A quantum mechanics analogy is used to determine the
forces acting on and the energies of
solitons governed by the nonlinear Schrodinger equation
in finite intervals with periodic and with
homogeneous Dirichlet, Neumann and Robin boundary conditions.
It is shown that the energy
densities remain nearly constant for periodic, while they
undergo large variations for
homogeneous boundary conditions. The largest variations
in the force and energy densities occur
for the Neumann boundary conditions, but, for all the
boundary conditions considered, the
magnitudes of these forces and energies recover their
values prior to the interaction of the soliton
with the boundary, after the soliton rebound process is
completed. It is also shown that the
quantum momentum changes sign but recovers its original
value after the collision of the soliton
with the boundaries. The asymmetry of the Robin boundary
conditions shows different dynamic
behaviour at the left and right boundaries of the finite
interval.
AN: 4736811
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Registro 10 de 10 en INSPEC 1993-1994
TI: Forces on solitons in finite, nonlinear, planar waveguides
AU: Ramos-JI; Villatoro-FR
SO: Microwave-and-Optical-Technology-Letters. vol.7, no.8;
5 June 1994; p.378-81.
PY: 1994
LA: English
AB: The forces acting on and the energies of solitons
governed by the nonlinear Schrodinger
equation in finite planar waveguides with periodic and
with homogeneous Dirichlet, Neumann,
and Robin boundary conditions are determined by means
of a quantum analogy. It is shown that
these densities have S-shaped profiles and increase as
the hardness of the boundary conditions
increases.
AN: 4693674
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