3,114 research outputs found
The Fourier method for the linearized Davey-Stewartson I equation
The linearized Davey-Stewartson equation with varing coefficients is solved
by Fourier method. The approach uses the inverse scattering transform for the
Davey-Stewartson equation.Comment: 4 pages, LaTe
Emission of autoresonant trajectories and thresholds of resonant pumping
We study an autoresonant asymptotic behaviour for nonlinear oscillators under
slowly changing frequency and amplitude of external driver. As a result we
obtain formulas for threshold values of amplitude and frequency of the driver
when autoresonant behaviour for the nonlinear oscillator is observed. Also we
study a capture into resonance and emission out of the resonance for
trajectories of the oscillator. A measure of autoresonant asymptotic behaviours
for nonlinear oscillator is obtained.Comment: 15 pages, 6 figure
Asymptotics of soliton solution for the perturbed Davey-Stewartson-1 equations
The dromion of the Davey-Stewartson-1 equation is studied under perturbation
on the large time.Comment: Mistake and misprints are corrected. Latex, 14 page
Asymptotic approach for the rigid condition of appearance of the oscillations in the solution of the Painleve-2 equation
The asymptotic solution for the Painleve-2 equation with small parameter is
considered. The solution has algebraic behavior before point and fast
oscillating behavior after the point . In the transition layer the
behavior of the asymptotic solution is more complicated. The leading term of
the asymptotics satisfies the Painleve-1 equation and some elliptic equation
with constant coefficients, where the solution of the Painleve-1 equation has
poles. The uniform smooth asymptotics are constructed in the interval,
containing the critical point .Comment: Latex, 18 page
The slowly passage through the resonances and wave packets with the different carriers
Solution of the nonlinear Klein-Gordon equation perturbed by small external
force is investigated. The perturbation is represented by finite collections of
harmonics. The frequencies of the perturbation vary slowly and pass through the
resonant values consecutively. The resonances lead to the sequence of the wave
packets with the different fast oscillated carriers. Full asymptotic
description of this process is presented.Comment: 24 pages, LaTe
Scattering of solitons on resonance
We investigate a propagation of solitons for nonlinear Schrodinger equation
under small driving force. The driving force passes the resonance. The process
of scattering on the resonance leads to changing of number of solitons. After
the resonance the number of solitons depends on the amplitude of the driving
force.Comment: LaTeX, 10 page
The solution of the Painleve equations as special functions of catastrophes, defined by a rejection in these equations of terms with derivative
The relation between the Painleve equations and the algebraic equations with
the catastrophe theory point of view are considered. The asymptotic solutions
with respect to the small parameter of the Painleve equations different types
are discussed. The qualitative analysis of the relation between algebraic and
fast oscillating solutions is done for Painleve-2 as an example.Comment: Latex, 15 page
The capture into parametric autoresonance
In this work we show that the capture into parametric resonance may be
explained as the pitchfork bifurcation in the primary parametric resonance
equation. We prove that the solution close to the moment of the capture is
described by the Painleve-2 equation. We obtain the connection formulas for the
asymptotic solution of the primary parametric resonance equation before and
after the capture using the matching of the asymptotic expansions.Comment: LaTeX, 21 pages, 3 figure
Asymptotic description of nonlinear resonance
We study a hard regime of stimulation of two-frequency oscillations in the
main resonance equation with a fast oscillating external force: \ve i \psi' +
|\psi|^2\psi = \exp\big(it^2/ (2\ve)\big), 0<\ve\ll1. This phenomenon is
caused by resonance between an eigenmode and the external force. The asymptotic
solution before, inside and after the resonance layer is studied in detail and
matched.Comment: LaTeX, 48 pages, two figure
Asymptotics of perturbed soliton for Davey--Stewartson II equation
It is shown that, under a small perturbation of lump (soliton) for
Davey--Stewartson (DS-II) equation, the scattering data gain the nonsoliton
structure. As a result, the solution has the form of Fourier type integral.
Asymptotic analysis shows that, in spite of dispertion, the principal term of
the asymptotic expansion for the solution has the solitary wave form up to
large time.Comment: In this replaced version the formula for the perturbed parameter of
the soliton is corrected. Amstex, 13 page
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