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Asymptotic behavior of rapidly oscillating solutions of the modified Camassa—Holm equation

Theoretical and Mathematical Physics, 2020
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С. А. Кащенко
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Oscillation and Asymptotic Behavior of Forced Nonlinear Equations

SIAM Journal on Mathematical Analysis, 1979
The oscillation and the asymptotic behavior of the solutions of the equation \[x^{(n)} + H(t,x(q(t))) = Q(t)\] are studied under assumptions of smallness or periodicity for $Q(t)$. Recent results of Mahfoud concerning the case $Q(t) \equiv 0$ are extended via a transformation introduced recently by the first author.
Kartsatos, A. G., Toro, J.
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Asymptotic behaviours in stochastic pumped Duffing oscillators

Physics Letters A, 1987
Abstract Both static and dynamic properties of the Duffing oscillator with fluctuating elastic constant are simulated by means of an analogue circuit. A regime of large intensity and long correlation time of the applied fluctuation is determined where the experimental data are not reproduced by previous theoretical predictions.
MARCHESONI, Fabio, M. POCHINI, S. SANTUCCI   +2 more
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Asymptotic Behavior and Oscillation of Classes of Integrodifferential Equations

Proceedings of the American Mathematical Society, 1992
Consider the integrodifferential equation \[ \begin{multlined} y''(t) + \int^ t_ 0 k(t-s)y(s)ds+ \varphi(t) \int^ t_ 0 K(t-s)y'(s)ds =\\=f(t,y(t),y'(t),\int^ t_ 0 g(t,s,y(s),y'(s))ds), t \geq 0,\end{multlined}\tag{1} \] and \[ \begin{multlined} y''(t) + \int^ t_ 1 k({t\over s})y(s){1\over s}ds + \varphi(t) \int^ t_ 1 K({t\over s})y'(s)ds =\\= f(t,y(t ...
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ASYMPTOTIC BEHAVIOR OF THE EIGENVALUES OF AN ANHARMONIC OSCILLATOR

Mathematics of the USSR-Sbornik, 1970
In this paper we study the properties of the spectrum of the boundary-value problem Let be the points of the spectrum of this problem, arranged in order of increasing absolute value.Our main result is Theorem. Let satisfy the conditions L.$ SRC=http://ej.iop.org/images/0025-5734/10/2/A01/tex_sm_2153_img4.gif/>Then for any 0$ SRC=http://ej.iop.org ...
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On asymptotic behavior in cascades chaotically excited non-linear oscillators

Journal of Sound and Vibration, 1989
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Burton, T. D., Anderson, M.
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ASYMPTOTIC BEHAVIOR OF NONLINEAR OSCILLATIONS IN A CHEMICAL SYSTEM

Transactions of the New York Academy of Sciences, 1974
AbstractA chemical system beyond a nonequilibrum unstable transition is known to exhibit a limit‐cycle type of oscillation. The shape and period of this cycle are analyzed in the asymptotic limit when there is a large separation between the time scales characterizing the various chemical steps.
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Asymptotic Behavior of Solutions of SDE for Relaxation Oscillations

SIAM Journal on Mathematical Analysis, 1993
The paper deals with a stochastic Liénard equation of the form \(\varepsilon x''+kx'+g(x)=\delta w'\), where \(\varepsilon\), \(k\), \(\delta\) are positive constants, \(w'\) is white noise, \(g\) is a real-valued function. Here \(\varepsilon\) is a small parameter. Setting \(y=\varepsilon x'+kx\), as \(\varepsilon\) goes to 0, we have a fast variable \
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Nonlinear time-dependent anharmonic oscillator: Asymptotic behavior and connected invariants

Journal of Mathematical Physics, 1983
The motion of a particle in a potential decreasing with time as ‖X‖n is considered. Different time and space rescaling are considered in order to obtain the asymptotic solutions. The validity of adiabatic invariants is discussed. The classical critical case corresponds to the obtainment of self-similar solutions for the quantum problem.
Besnard, D., Burgan, J. R., Munier, A., Feix, M. R., Fijalkow, E.   +4 more
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