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1.
We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations
(of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the KdV line solitary wave or the Zaitsev solitary waves
which are localized in x and y periodic or conversely). 相似文献
2.
S. V. Petrovskii 《Technical Physics》1999,44(8):878-881
Two new methods for obtaining exact solutions of the initial-value problem on an unbounded straight line (the Cauchy problem)
for the inhomogeneous Burgers equation are considered. They are applied to the cases of a stationary and a transient external
force. A self-similar solution and a solution which describes the localization (blocking) of solitary traveling waves are
obtained as examples.
Zh. Tekh. Fiz. 69, 10–14 (August 1999) 相似文献
3.
《Waves in Random and Complex Media》2013,23(1):56-76
Abstract In this paper, we introduce and study rigorously a Hamiltonian structure and soliton solutions for a weakly dissipative and weakly nonlinear medium that governs two Korteweg–de vries (KdV) wave modes. The bounded solution and traveling wave solution such as cnoidal wave and solitary wave are obtained. Subsequently, the equation is numerically solved by Fourier spectral method for its two-soliton solution. These solutions may be useful to explain the nonlinear dynamics of waves for an equation supporting multi-mode weakly dispersive and nonlinear wave medium. In addition, we give an explicit explanation of the mathematics behind the soliton phenomenon for a better understanding of the equation. 相似文献
4.
Anders Szepessy 《Communications in Mathematical Physics》1999,202(3):547-569
One dimensional weak detonation waves of a basic reactive shock wave model are proved to be nonlinearly stable, i.e. initially
perturbed waves tend asymptotically to translated weak detonation waves. This model system was derived as the low Mach number
limit of the one component reactive Navier-Stokes equations by Majda and Roytburd [SIAM J. Sci. Stat. Comput. 43, 1086–1118 (1983)], and its weak detonation waves have been numerically observed as stable. The analysis shows in particular
the key role of the new nonlinear dynamics of the position of the shock wave, The shock translation solves a nonlinear integral
equation, obtained by Green's function techniques, and its solution is estimated by observing that the kernel can be split
into a dominating convolution operator and a remainder. The inverse operator of the convolution and detailed properties of
the traveling wave reduce, by monotonicity, the remainder to a small L
1 perturbation.
Received: 17 August 1998 / Accepted: 13 November 1998 相似文献
5.
The phenomenon of energy transfer, both monotonic and oscillating, between the fundamental and higher harmonics of standing
acoustic waves is observed during the laser generation of sound in YFeO3 crystals. An analogous phenomenon for traveling light waves is well known in nonlinear optics.
Pis’ma Zh. éksp. Teor. Fiz. 70, No. 12, 789–792 (25 December 1999) 相似文献
6.
《Journal of Nonlinear Mathematical Physics》2013,20(4):461-471
Abstract It is shown that in water of finite depth, there are no periodic traveling waves with the property that the pressure in the underlying fluid flow is constant along streamlines. In the case of infinite depth, there is only one such solution, which is due to Gerstner. 相似文献
7.
The one-dimensional reaction-diffusion equations for the process (D) $$A + B \to 2A,B + C \to 2B,C + A \to 2C$$ are extended to include the counteracting reactions (R) $$A + 2B \to 3B,B + 2C \to 3C,C + 2A \to 3A$$ which have a reaction rate α relative to the direct process (D). This process can be seen as a three-component version of the reaction which is described by the Fisher-Kolmogorov equation. The fixed points of the equations are studied as a function of α. It is shown that the equations admit solutions which consist of a series of traveling fronts. Other solutions exist which are traveling periodic waves. A very remarkable fact is that for these waves exact expressions can be constructed. 相似文献
8.
Osamu Yamashita 《Optik》2011,122(23):2119-2123
The spin angular momentum S of light has never been linked to the Faraday rotation of light traveling in an optically active medium possessing a rotational invariance of a crystal, because there was no helicity term associated with the phase shift in the previous torque equation for S. In order to relate the change in S with time to the Faraday rotation, therefore, we derived an exact torque equation for S. As a result, a magnetic helicity term appeared in a new torque equation for S, so that one-half of the phase shift derived from the helicity term was equivalent to the Faraday rotation angle. However, the orbital angular momentum L had no relation to the Faraday rotation. It was thus clarified that the change in S with time is related to the Faraday rotation angle of light traveling in an optically active medium, owing to the appearance of the helicity term without a rotational invariance around the optical axis. It was also demonstrated theoretically that the Faraday rotation is accompanied by a torque acting on the crystal so that the total angular momentum of light and matter is conserved. 相似文献
9.
F. N. Si Q. X. Liu J. Z. Zhang L. Q. Zhou 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(4):507-513
It has been reported that traveling waves propagate
periodically and stably in sub-excitable systems driven by noise
[Phys. Rev. Lett. 88, 138301 (2002)]. As a further
investigation, here we observe different types of traveling waves
under different noises and periodic forces, using a simplified
Oregonator model. Depending on different noises and periodic forces,
we have observed different types of wave propagation (or their
disappearance). Moreover, reversal phenomena are observed in this
system based on the numerical experiments in the one-dimensional
space. We explain this as an effect of periodic forces. Thus, we
give qualitative explanations for how stable reversal phenomena
appear, which seem to arise from the mixing function of the periodic
force and the noise. The output period and three velocities (normal,
positive and negative) of the travelling waves are defined and their
relationship with the periodic forces, along with the types of
waves, are also studied in sub-excitable system under a fixed noise
intensity.
Electronic supplementary material Supplementary Online Material 相似文献
10.
Previous work has shown that Benjamin-Feir unstable traveling waves of the complex Ginzburg-Landau equation (CGLE) in two spatial dimensions cannot be stabilized using a particular time-delayed feedback control mechanism known as ‘time-delay autosynchronization’. In this paper, we show that the addition of similar spatial feedback terms can be used to stabilize such waves. This type of feedback is a generalization of the time-delay method of Pyragas [K. Pyragas, Continuous control of chaos by self-controlling feedback, Phys. Lett. A 170 (1992) 421-428] and has been previously used to stabilize waves in the one-dimensional CGLE by Montgomery and Silber [K. Montgomery, M. Silber, Feedback control of traveling wave solutions of the complex Ginzburg Landau equation, Nonlinearity 17 (6) (2004) 2225-2248]. We consider two cases in which the feedback contains either one or two spatial terms. We focus on how the spatial terms may be chosen to select the direction of travel of the plane waves. Numerical linear stability calculations demonstrate the results of our analysis. 相似文献
11.
Considered here is a generalized μ-type integrable equation, which can be regarded as a generalization to both the μ-Camassa–Holm and modified μ-Camassa–Holm equations. It is shown that the proposed equation is formally integrable with the Lax-pair and the bi-Hamiltonian structure and its scale limit is an integrable model of hydrodynamical systems describing short capillary-gravity waves. Local well-posedness of the Cauchy problem in the suitable Sobolev space is established by the viscosity method. Existence of peaked traveling wave solutions and formation of singularities of solutions for the equation are investigated. It is found that the equation admits single and multi-peaked traveling wave solutions. The effects of varying μ-Camassa–Holm and modified μ-Camassa–Holm nonlocal nonlinearities on blow-up criteria and wave breaking are illustrated in detail. Our analysis relies on the method of characteristics and conserved quantities and is proceeded with a priori differential estimates. 相似文献
12.
13.
14.
It is shown that a waveguide in the form of a channel of infinite length filled by a two-layer heavy fluid with a free surface
can have nonpropagating waves (trapped vibrational modes) along with traveling waves. These waves are localized in the region
of a dynamic inclusion, i.e., a solid block (massive die) on the bottom of the channel. The appearance of such waves is due
to the presence of a real discrete frequency spectrum of eigenmodes, which is located on the axis of the continuous spectrum
corresponding to the divergent waves in the fluid. A relation between the geometric parameters of the channel and the characteristics
of the fluid and the solid block for which such a spectrum exists is found for cases with fluids of similar density in the
waveguide.
Zh. Tekh. Fiz. 68, 15–19 (March 1998) 相似文献
15.
Anna Geyer 《Journal of Nonlinear Mathematical Physics》2015,22(4):545-551
Following a general principle introduced by Ehrnström, Holden and Raynaud in 2009, we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves. 相似文献
16.
In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves. 相似文献
17.
Electric dipole radiation consists of traveling and evanescent plane waves. When radiation is detected in the far field, only the traveling waves will contribute to the intensity distribution, as the evanescent waves decay exponentially. We propose a method to spatially separate the traveling and evanescent waves before detection. It is shown that when the radiation passes through an interface, evanescent waves can be converted into traveling waves and can subsequently be observed in the far field. Let the radiation be observed under angle theta(t) with the normal. Then there exists an angle theta(ac) such that for 0 < or = theta(t) < theta(ac) all intensity originates in traveling waves, whereas for theta(ac) < theta(t) < pi/2 only evanescent waves contribute. It is shown that with this technique and under the appropriate conditions almost all far-field power can be provided by evanescent waves. 相似文献
18.
We derive the threshold conditions for the instability of counterpropagating waves in a nonlinear medium with local photorefractive
response against the excitation of transverse small-angle structures. These conditions allow for all the important types of
diffraction from refractive-index reflection gratings and are not limited to the case of strict frequency degeneracy of the
waves. We study the dependence of the crystal-thickness threshold and the secondary wave emission angle on the crystal parameters
and the pump conditions. We show that when the pump wave intensities differ considerably, excitation of standing light structures
is replaced by excitation of traveling structures. Finally, we discuss the applications of the theory to experiments with
the photorefractive crystals LiNbO3 and LiTaO3.
Zh. éksp. Teor. Fiz. 111, 1611–1623 (May 1977) 相似文献
19.
V. P. Ruban 《Journal of Experimental and Theoretical Physics》2010,110(3):529-536
The formation of rogue waves in sea states with two close spectral maxima near the wave vectors k
0 ± Δk/2 in the Fourier plane is studied through numerical simulations using a completely nonlinear model for long-crested surface
waves [24]. Depending on the angle θ between the vectors k
0 and Δk, which specifies a typical orientation of the interference stripes in the physical plane, the emerging extreme waves have
a different spatial structure. If θ ≲ arctan(1/√2), then typical giant waves are relatively long fragments of essentially
two-dimensional ridges separated by wide valleys and composed of alternating oblique crests and troughs. For nearly perpendicular
vectors k
0 and Δk, the interference minima develop into coherent structures similar to the dark solitons of the defocusing nonlinear Schroedinger
equation and a two-dimensional killer wave looks much like a one-dimensional giant wave bounded in the transverse direction
by two such dark solitons. 相似文献
20.
The hydrostatic pressure and temperature effects on a hydrogenic impurity in a spherical quantum dot
S. J. Liang W. F. Xie 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,79(1):79-84
Exact analytical solutions of the reaction-diffusion equations with spatial inhomogeneous
reaction and diffusion coefficients are found. It is shown that the space-oscillating approximate
solution of a traveling wave type [P.K. Brazhnik, J.J. Tyson, SIAM J. Appl. Math. 60, 371
(1999)] is the exact one for the inhomogeneous Fisher-Kolmogorov equation in two dimensions. 相似文献