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171.
Zhang Ping 《Applied mathematics and computation》2010,217(4):1688-1696
In this paper, by using the improved Riccati equations method, we obtain several types of exact traveling wave solutions of breaking soliton equations and Whitham-Broer-Kaup equations. These explicit exact solutions contain solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions. The method employed here can also be applied to solve more nonlinear evolution equations. 相似文献
172.
Desheng Shang 《Applied mathematics and computation》2010,217(4):1577-1583
In this paper, we employ the general integral method for traveling wave solutions of coupled nonlinear Klein-Gordon equations. Based on the idea of the exact Jacobi elliptic function, a simple and efficient method is proposed for obtaining exact solutions of nonlinear evolution equations. The solutions obtained include solitons, periodic solutions and Jacobi elliptic function solutions. 相似文献
173.
By using the bifurcation theory of dynamical systems to modified nonlinear dispersive phi-four equation, we analysis all bifurcations and phase portraits in the parametric space, the existence of solitary wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some explicit exact solution formulas are acquired for some special cases. 相似文献
174.
The traveling wave solutions of the magma equation are studied by using the approach of dynamical systems and the theory of bifurcations. With the aid of Maple, all bifurcations and phase portraits in the parametric space are obtained. Under different regions of parametric space, various sufficient conditions to guarantee the existence of solitary wave, periodic wave and breaking wave solutions are given. Moreover, the reason for appearance of breaking waves is explained. 相似文献
175.
By using the method of planar dynamical systems to an integrable nonlinear wave equation, the existence of periodic travelling wave, solitary wave and kink wave solutions is proved in the different parametric conditions. The phase portraits of the travelling wave system are given. It can be shown that the existence of singular curves in the travelling wave system is the reason why the travelling wave solutions lose their smoothness. Moreover, the so-called W/M-shaped solitary wave solutions are obtained. 相似文献
176.
In this paper, the Fornberg-Whitham equation with linear dispersion term is investigated by employing the bifurcation method of dynamical systems. As a result, the existence of smooth and non-smooth traveling wave solutions is obtained. And the analytic expressions of solitary wave solutions, periodic cusp wave solutions and peakons are given under some parameter conditions. 相似文献
177.
Emine Misirli 《Applied mathematics and computation》2010,216(9):2623-9197
The generalized solitary solutions of the classical Drinfel’d-Sokolov-Wilson equation (DSWE) are obtained using the Exp-function method. Then, some of these solutions are easily converted into kink-shaped solutions and blow-up solutions by a simple transformation. 相似文献
178.
We introduce a new family of hyperplane arrangements in dimension that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of a given subfamily have the same number of regions – the connected components of the complement of the union of the hyperplanes – which can be bijectively labeled with the Pak–Stanley labeling. In addition, we show that, in the cases of the Shi and the Ish arrangements, the number of labels with reverse centers of a given length is equal, and conjecture that the same happens with all of the members of the family. 相似文献
179.
Motivated by the relation , holding for the -generalized Catalan numbers of type and , the connection between dominant regions of the -Shi arrangement of type and is investigated. More precisely, it is explicitly shown how copies of the set of dominant regions of the -Shi arrangement of type , biject onto the set of type such regions. This is achieved by exploiting two different viewpoints of the representative alcove of each region: the Shi tableau and the abacus diagram. In the same line of thought, a bijection between copies of the set of -Dyck paths of height
and the set of lattice paths inside an rectangle is provided. 相似文献
180.
In this paper, we continue the study in [18]. We use the perturbation argument, modulational analysis and the energy argument in [15], [16] to show the stability of the sum of two solitary waves with weak interactions for the generalized derivative Schrödinger equation (gDNLS) in the energy space. Here (gDNLS) hasn't the Galilean transformation invariance, the pseudo-conformal invariance and the gauge transformation invariance, and the case we considered corresponds to the -supercritical case. 相似文献