共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper studies the propagation of three‐dimensional surface waves in water with an ambient current over a varying bathymetry. When the ambient flow is near the critical speed, under the shallow water assumptions, a forced Benney–Luke (fBL) equation is derived from the Euler equations. An asymptotic approximation of the water's reaction force over the varying bathymetry is derived in terms of topographic stress. Numerical simulations of the fBL equation over a trough are compared to those using a forced Kadomtsev–Petviashvilli equation. For larger variations in the bathymetry that upstream‐radiating three‐dimensional solitons are observed, which are different from the upstream‐radiating solitons simulated by the forced Kadomtsev–Petviashvilli equation. In this case, we show the fBL equation is a singular perturbation of the forced Kadomtsev–Petviashvilli equation which explains the significant differences between the two flows. 相似文献
2.
Transverse Orbital Stability of Periodic Traveling Waves for Nonlinear Klein–Gordon Equations 下载免费PDF全文
In this paper, we establish the orbital stability of a class of spatially periodic wave train solutions to multidimensional nonlinear Klein–Gordon equations with periodic potential. We show that the orbit generated by the one‐dimensional wave train is stable under the flow of the multidimensional equation under perturbations which are, on one hand, coperiodic with respect to the translation or Galilean variable of propagation, and, on the other hand, periodic (but not necessarily coperiodic) with respect to the transverse directions. That is, we show their transverse orbital stability. The class of periodic wave trains under consideration is the family of subluminal rotational waves, which are periodic in the momentum but unbounded in their position. 相似文献
3.
Boussinesq was the first to explain the existence of Scott Russell's solitary wave mathematically. He employed a variety of asymptotically equivalent equations to describe water waves in the small-amplitude, long-wave regime. We study the linearized stability of solitary waves for three linearly well-posed Boussinesq models. These are problems for which well-developed Lyapunov methods of stability analysis appear to fail. However, we are able to analyze the eigenvalue problem for small-amplitude solitary waves, by comparison to the equation that Boussinesq himself used to describe the solitary wave, which is now called the Korteweg–de Vries equation. With respect to a weighted norm designed to diminish as perturbations convect away from the wave profile, we prove that nonzero eigenvalues are absent in a half-plane of the form R λ>− b for some b >0, for all three Boussinesq models. This result is used to prove the decay of solutions of the evolution equations linearized about the solitary wave, in two of the models. This "convective linear stability" property has played a central role in the proof of nonlinear asymptotic stability of solitary-wave-like solutions in other systems. 相似文献
4.
Markus Daub Guido Schneider Katharina Schratz 《Mathematical Methods in the Applied Sciences》2016,39(18):5371-5380
In a singular limit, the Klein–Gordon (KG) equation can be derived from the Klein–Gordon–Zakharov (KGZ) system. We point out that for the original system posed on a d‐dimensional torus, the solutions of the KG equation do not approximate the solutions of the KGZ system. The KG system has to be modified to make correct predictions about the dynamics of the KGZ system. We explain that this modification is not necessary for the approximation result for the whole space with d≥3. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
5.
Hasib Khan Aziz Khan Wen Chen Kamal Shah 《Mathematical Methods in the Applied Sciences》2019,42(2):723-732
Fractional order nonlinear Klein‐Gordon equations (KGEs) have been widely studied in the fields like; nonlinear optics, solid state physics, and quantum field theory. In this article, with help of the Sumudu decomposition method (SDM), a numerical scheme is developed for the solution of fractional order nonlinear KGEs involving the Caputo's fractional derivative. The coupled method provides us very efficient numerical scheme in terms of convergent series. The iterative scheme is applied to illustrative examples for the demonstration and applications. 相似文献
6.
Alessandra Aimi Stefano Panizzi 《Numerical Methods for Partial Differential Equations》2014,30(6):2042-2082
A transmission (bidomain) problem for the one‐dimensional Klein–Gordon equation on an unbounded interval is numerically solved by a boundary element method‐finite element method (BEM‐FEM) coupling procedure. We prove stability and convergence of the proposed method by means of energy arguments. Several numerical results are presented, confirming theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 2042–2082, 2014 相似文献
7.
Fbio M. Amorin Natali Ademir Pastor Ferreira 《Journal of Mathematical Analysis and Applications》2008,347(2):428-441
In the present paper we show some results concerning the orbital stability of dnoidal standing wave solutions and orbital instability of cnoidal standing wave solutions to the following Klein–Gordon equation:
utt−uxx+u−|u|2u=0.