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黄思训 《数学物理学报(A辑)》1992,(2)
本文讨论了静力平衡下的绝热自由大气非线性重力惯性波的孤立渡解存在性,设运动在y方向是均匀的,又采用了β平面近似,同时忽略了动量方程中垂直平流项,我们导出了孤立波解的解析解表达式,通过对波速c的讨论,我们指出:在中纬地区,很难形成孤立波;在低纬地区(热带地区),由于科氏力很小,层结稳定度较弱有可能产生孤立波。最后我们讨论了孤立波的波速c与科氏力f,β和稳定参数σ_8之间关系。 相似文献
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以小振幅波理论为基础,利用摄动方法研究了两层密度成层状态下的毛细重力波,求得了两层密度成层状态下各层流体速度势的三阶解及毛细重力波波面位移的三阶Stokes波解.结果表明:三阶方程的解均受到表面张力的影响.三阶Stokes波解描述了毛细重力波的三阶非线性修正,波速不仅取决于波数和各层流体的厚度,而且还与波幅及表面张力有关. 相似文献
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本文研究有限水深连续分层流中二阶孤立波理论,得到了一阶、二阶发展方程,详细计算了当Brunt-Visl频率N为常数的情形。所得波速公式和发展方程显示了Boussinesq参数对波速和波形的影响。在某些情况下,一阶发展方程的非线性项系数将变为零值而使其失效。本文对此给出了新的尺度分析,建立了含有立方项的发展方程。在N为常数时,找到了一阶方程的孤立波表达式。也对二阶方程进行了数值计算。 相似文献
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本文运用摄动法和WKB方法(多尺度方法), 从位涡守恒方程出发,
分析旋转层结大气中基本流有垂直切变以及层结效应对$\beta$效应、地形效应和强迫耗散共同作用下的Rossby波的影响,
得到一个非标准形式的非线性Schr\"{o}dinger方程,而在水平波数小于3时该方程有包络孤立波解;
又进一步说明基本流的垂直切变对包络Rossby孤立波的波速的影响;强迫耗散对包络Rossby孤立波稳定度的影响.另外, 本
文还应用常数变异法求解了非齐次的Bessel方程, 得到包络Rossby孤立波的经向结构. 相似文献
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本文采用作者提出的修正的完全近似法,分析几个强非线性振动和波动问题。首先研究一类虽非线性振动问题,并对修正的van der Pol振子,较为简捷地给出了它的极限环解的二阶近似表达式,与文献[3]中用推广的平均法得出的结果一致。接着分析修正的KdV方程,得到了孤立波的正确的二阶渐近解。最后,对于有五阶色散项的推广的KdV方程,在三阶近似下,导得了孤立波的渐近解,解析地给出了振荡型孤立波解的形式。这些结果表明,修正的完全近似法可以有效地应用于一些强非线性数学问题的研究。 相似文献
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本文研究了在流动方向有缓慢变化的任意截面渠道中的非线性周期波、孤立波以及孤立波在这种渠道中的分裂;导出了适用于这种渠道的变系数KdV方程,并求出了该方程的首项近似解;得出了波速、周期、波高和渠道几何尺寸之间的关系,得到了分裂后孤立波个数的判别式及分裂后孤立波波幅的表示式,并应用于矩形渠道和左右对称的三角形渠道。对于矩形渠道的情况,本文的结果和Madsen和Mei,Johnson,Svendsen和Buhr Hansen等人的结果一致。 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2007,12(7):1195-1201
The Hirota method is applied to construct exact analytical solitary wave solutions of the system of multi-dimensional nonlinear wave equation for n-component vector with modified background. The nonlinear part is the third-order polynomial, determined by three distinct constant vectors. These solutions have not previously been obtained by any analytic technique. The bilinear representation is derived by extracting one of the vector roots (unstable in general). This allows to reduce the cubic nonlinearity to a quadratic one. The transition between other two stable roots gives us a vector shock solitary wave solution. In our approach, the velocity of solitary wave is fixed by truncating the Hirota perturbation expansion and it is found in terms of all three roots. Simulations of solutions for the one component and one-dimensional case are also illustrated. 相似文献
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Kamruzzaman Khan Md. Abdus Salam Manik Mondal M. Ali Akbar 《Mathematical Methods in the Applied Sciences》2023,46(2):2042-2054
Traveling wave solutions have played a vital role in demonstrating the wave character of nonlinear problems emerging in the field of mathematical sciences and engineering. To depict the nature of propagation of the nonlinear waves in nature, a range of nonlinear evolution equations has been proposed and investigated in the existing literature. In this article, solitary and traveling periodic wave solutions for the (2 + 1)-dimensional modified KdV-KP equation are derived by employing an ansatz method, named the enhanced (G′/G)-expansion method. For this continued equation, abundant solitary wave solutions and nonlinear periodic wave solutions, along with some free parameters, are obtained. We have derived the exact expressions for the solitary waves that arise in the continuum-modified KdV-KP model. We study the significance of parameters numerically that arise in the obtained solutions. These parameters play an important role in the physical structure and propagation directions of the wave that characterizes the wave pattern. We discuss the relation between velocity and parameters and illustrate them graphically. Our numerical analysis suggests that the taller solitons are narrower than shorter waves and can travel faster. In addition, graphical representations of some obtained solutions along with their contour plot and wave train profiles are presented. The speed, as well as the profile of these solitary waves, is highly sensitive to the free parameters. Our results establish that the continuum-modified KdV-KP system supports solitary waves having different shapes and speeds for different values of the parameters. 相似文献
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The defocusing Hirota equation has dark and gray soliton solutions which are stable on a background of periodic waves of constant amplitude. In this paper, gray solitary wave evolution for a higher-order defocusing Hirota equation is examined. A direct analysis is used to identify families of higher-order gray Hirota solitary waves, which are embedded for certain parameter values. Soliton perturbation theory is used to determine the detailed behavior of an evolving higher-order gray Hirota solitary wave. An integral expression for the first-order correction to the wave is found and analytical expressions for the steady-state and transient components of the solitary wave tail are derived. A subtle and complex picture of the development of solitary wave tails emerges. It is found that solitary wave tails develop for two reasons, one is decay of the solitary wave caused by resonance, the second is corrections at first-order to the background wave. Strong agreement is found between the theoretical predictions of the perturbation theory and numerical solutions of the governing equations. 相似文献
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By using the extended hyperbolic auxiliary equation method, we present explicit exact solutions of the high-order nonlinear Schrödinger equation with the third-order and fourth-order dispersion and the cubic-quintic nonlinear terms, describing the propagation of extremely short pulses. These solutions include trigonometric function type and exact solitary wave solutions of hyperbolic function type. Among these solutions, some are found for the first time. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2008,13(3):567-574
The exact analytical solution of the optical soliton equation with higher-order dispersion and nonlinear effects has been obtained by the method of separating variables. The new type of optical solitary wave solution, which is quite different from the bright and dark soliton solutions, has been found under two special cases. The stability of the solitary wave solutions for the optical soliton equation is discussed. Some new conclusion of the stability are obtained, for the solitary wave solutions of the nonlinear wave equations, by using the Liapunov direct method. 相似文献
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在推广的β平面近似下,从包含耗散和外源的准地转位涡方程出发,利用Gardner-Morikawa变换和弱非线性摄动展开法,推导出带有外源和耗散强迫的非线性Boussinesq方程去刻画非线性Rossby波振幅的演变和发展.利用修正的Jacobi椭圆函数展开法,得到Boussinesq方程的周期波解和孤立波解,从解的结构分析了推广的β效应、切变基本流、外源和耗散是影响非线性Rossby波的重要因素. 相似文献
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José Raúl Quintero Juan Carlos Muñoz Grajales 《Nonlinear Analysis: Theory, Methods & Applications》2008
We study linear instability of solitary wave solutions of a one-dimensional generalized Benney–Luke equation, which is a formally valid approximation for describing two-way water wave propagation in the presence of surface tension. Further, we implement a finite difference numerical scheme which combines an explicit predictor and an implicit corrector step to compute solutions of the model equation which is used to validate the theory presented. 相似文献
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In this paper, an analytical method is proposed to construct explicitly exact and approximate solutions for nonlinear evolution
equations. By using this method, some new traveling wave solutions of the Kuramoto-Sivashinsky equation and the Benny equation
are obtained explicitly. These solutions include solitary wave solutions, singular traveling wave solutions and periodical
wave solutions. These results indicate that in some cases our analytical approach is an effective method to obtain traveling
solitary wave solutions of various nonlinear evolution equations. It can also be applied to some related nonlinear dynamical
systems. 相似文献
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Md. Shafiqul Islam Kamruzzaman Khan M. Ali Akbar 《Journal of the Egyptian Mathematical Society》2017,25(1):13-18
In this article, we pay attention to the analytical method named, the improved F-expansion method combined with Riccati equation for finding the exact traveling wave solutions of the Benney–Luke equation and the Phi-4 equation. By means of this method we have explored three classes of explicit solutions-hyperbolic, trigonometric and rational solutions with some free parameters. When the parameters are taken as special values, the solitary wave solutions are originated from the traveling wave solutions. Our outcomes disclose that this method is very active and forthright way of formulating the exact solutions of nonlinear evolution equations arising in mathematical physics and engineering. 相似文献