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采用分步确定拟解的原则, 对齐次平衡法求非线性发展方程孤子解的关键步骤作了进一步改 进. 以广义Boussinesq方程和bidirectional Kaup-Kupershmidt方程为应用实例, 说明使用 该方法可有效避免“中间表达式膨胀”的问题, 除获得标准Hirota形式的孤子解外, 还能获 得其他形式的孤子解.
关键词:
齐次平衡法
孤子解
孤波解
广义Boussinesq方程
bidirectional Kaup-Kupershmi dt方程 相似文献
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非线性振动、非线性波与Jacobi椭圆函数 总被引:13,自引:4,他引:9
介绍用较易懂且简捷的Jacobi椭圆函数解法求非线性振动与非线性波的解析解,并以单摆,达芬(Duffing)振子,KdV方程,正弦戈登(Gordon)方程(SG方程),非线性薛定谔方程(NLS方程)的椭圆函数解,钟形孤立波解,扭结与反扭结波解,呼吸子解,扭结波与反扭结波迎头碰撞及包络型孤立子波解等重要实例,给出了说明. 相似文献
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变系数(2+1)维Broer-Kaup方程新的类孤子解 总被引:1,自引:0,他引:1
基于齐次平衡原则和分离变量法的思想,通过两个推广的Riccati方程组和Mathematica软件,求出了变系数(2+1)维Broer-kaup方程的一些精确解,包括各种类孤立波解、类周期解,其中许多解是新的. 相似文献
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Some new exact solutions of the generalized Lienard equation are obtained, and the solutions of the equation are applied to
solve nonlinear wave equations with nonlinear terms of any order directly. The generalized one-dimensional Klein-Gordon equation,
the generalized Ablowitz (A) equation and the generalized Gerdjikov-Ivanov (GI) equation are investigated and abundant new
exact travelling wave solutions are obtained that include solitary wave solutions and triangular periodic wave solutions.
相似文献
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The nonlocal nonlinear Gerdjikov-Ivanov (GI) equation is one of the most important integrable equations, which can be reduced from the third generic deformation of the derivative nonlinear Schrödinger equation. The Darboux transformation is a successful method in solving many nonlocal equations with the help of symbolic computation. As applications, we obtain the bright-dark soliton, breather, rogue wave, kink, W-shaped soliton and periodic solutions of the nonlocal GI equation by constructing its 2n-fold Darboux transformation. These solutions show rich wave structures for selections of different parameters. In all these instances we practically show that these solutions have different properties than the ones for local case. 相似文献
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FAN En-Gui 《理论物理通讯》2001,35(6):651-656
An explicit N-fold Darboux transformation for a coupled of derivative nonlinear Schrödinger equations is constructed with the help of a gauge transformation of spectral problems. As a reduction, the Darboux transformation for well-known Gerdjikov-Ivanov equation is further obtained, from which a general form of N-soliton solutions for
Gerdjikov-Ivanov equation is given. 相似文献
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A new fractional mapping method based on a generalized fractional auxiliary equation is proposed and applied to solve the space-time fractional perturbed Gerdjikov-Ivanov equation. The main feature of this approach is to obtain more accurate solutions by means of an auxiliary equation. Some exact fractional nonlinear wave solutions, including bright soliton, periodical wave and singularity soliton solutions are constructed by Mittag–Leffler function. Some deformations appear in those fractional nonlinear wave solutions, and those deformations become more obvious with the increase of the fractional order parameter. In addition, the coefficient of group velocity dispersion and the self-steepening for short pulses also affect the intensity of the soliton when the fractional order parameter remains unchanged. The effect of fractional order is explained by the graphical representation of a series of solutions and their physical meanings. 相似文献
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LIU Cheng-Shi 《理论物理通讯》2005,44(5):799-801
Using trial equation method, abundant exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schr6dinger equation, which include envelope soliton solutions, triangular function envelope solutions, and Jacobian elliptic function envelope solutions, are obtained. To our knowledge, all of these results are new. In particular, our proposed method is very simple and can be applied to a lot of similar equations. 相似文献
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Houria Triki 《Waves in Random and Complex Media》2017,27(1):153-162
In this work, we propose an efficient generalization of the trial equation method introduced recently by Liu [Appl. Math. Comput. 217 (2011) 5866] to construct exact chirped traveling wave solutions of complex differential equations with variable coefficients. The effectiveness of the proposed method has been tested by applying it successfully to the quintic derivative nonlinear Schrödinger equation with variable coefficients. As a result, a class of chirped soliton-like solutions including bright and kink solitons is derived for the first time. Compared with previous work of Liu in which unchirped solutions were given, we obtain exact chirped solutions which have nontrivial phase that varies as a function of the wave intensity. These localized structures characteristically exist due to a balance among the group-velocity dispersion, self-steepening and competing cubic-quintic nonlinearity. Parametric conditions for the existence of envelope solutions with nonlinear chirp are also presented. It is shown that the chirping can be effectively controlled through the variable parameters of group-velocity dispersion and self-steepening. 相似文献
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A class of nonlinear Schrödinger-type equations, including the Rangwala-Rao equation, the Gerdjikov-Ivanov equation, the Chen-Lee-Lin equation and the Ablowitz-Ramani-Segur equation are investigated, and the exact solutions are derived with the aid of the homogeneous balance principle, and a set of subsidiary higher order ordinary differential equations (sub-ODEs for short). 相似文献
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《中国物理快报》2017,(9)
Bilinear forms of the coupled Gerdjikov-Ivanov equation are derived. The N-soliton solutions to the equation are obtained by Hirota's method. It is interesting that the two-soliton solutions can generate the rogue-wave-like phenomena by selecting special parameters. The equation can be reduced to the Gerdjikov-Ivanov equation as well as its bilinear forms and its solutions. 相似文献
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SHI Yun-Long YANG Hong-Wei YIN Bao-Shu YANG De-Zhou XU Zhen-Hua FENG Xing-Ru 《理论物理通讯》2015,64(4):464-472
The dissipative nonlinear Schrödinger equation with a forcing item is derived by using of multiple scales analysis and perturbation method as a mathematical model of describing envelope solitary Rossby waves with dissipation effect and external forcing in rotational stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency and β effect are important factors in forming the envelope solitary Rossby waves. By employing Jacobi elliptic function expansion method and Hirota's direct method, the analytic solutions of dissipative nonlinear Schrödinger equation and forced nonlinear Schrödinger equation are derived, respectively. With the help of these solutions, the effects of dissipation and external forcing on the evolution of envelope solitary Rossby wave are also discussed in detail. The results show that dissipation causes slowly decrease of amplitude of envelope solitary Rossby waves and slowly increase of width, while it has no effect on the propagation speed and different types of external forcing can excite the same envelope solitary Rossby waves. It is notable that dissipation and different types of external forcing have certain influence on the carrier frequency of envelope solitary Rossby waves. 相似文献
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E. Tala-Tebue Z.I. Djoufack A. Djimeli-Tsajio A. Kenfack-Jiotsa 《Chinese Journal of Physics (Taipei)》2018,56(3):1232-1246
In order to investigate the nonlinear fractional Zoomeron equation, we propose three methods, namely the Jacobi elliptic function rational expansion method, the exponential rational function method and the new Jacobi elliptic function expansion method. Many kinds of solutions are obtained and the existence of these solutions is determined. For some parameters, these solutions can degenerate to the envelope shock wave solutions and the envelope solitary wave solutions. A comparison of our new results with the well-known results is made. The methods used here can also be applicable to other nonlinear partial differential equations. The fractional derivatives in this work are described in the modified Riemann–Liouville sense. 相似文献