共查询到18条相似文献,搜索用时 78 毫秒
1.
On the Conversion of High-Frequency Soliton Solutions to a (1+1)-Dimensional Nonlinear Partial Differential Evolution Equation 下载免费PDF全文
From the dynamical equation of barotropic relaxing media beneath pressure perturbations, and using the reductive perturbative analysis, we investigate the soliton structure of a (1+1)-dimensional nonlinear partial differential evolution (NLPDE) equation δy(δη + uδy + (u^2/2)δy)u + auy + u = 0, describing high-frequency regime of perturbations. Thus, by means of Hirota's bilinearization method, three typical solutions depending strongly upon a characteristic dissipation parameter are unearthed. 相似文献
2.
Soliton Structure of a Higher Order (2+1)-Dimensional Nonlinear Evolution Equation of Barothropic Relaxing Media beneath High-Frequency Perturbations 下载免费PDF全文
From the dynamical equation of barothopic relaxing media beneath pressure perturbations, followed with the reductive perturbative anadysis, we derive and investigate the soliton structure of a (2+1)-dimensional nonlineax evolution equation describing high-frequency regime of perturbations. Thus, by means of the Hirota's bilinearization method, we unearth three typical patterns of loop-, cusp- and hump-like shapes depending strongly upon a dissipation parameter. 相似文献
3.
BAICheng-Lin LIUXi-Qiang ZHAOHong 《理论物理通讯》2004,42(6):827-830
We study an approach to constructing multiple soliton solutions of the (3 1)-dimensional nonlinear evolution equation. We take the (3 1)-dimensional potential- YTSF equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3 1)-dimensional potential-YTSF equation into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3 1)-dimensional potential-YTSF equation are obtained by introducing a class of formal solutions. 相似文献
4.
In this paper, by means of double elliptic equation expansion approach, the novel double nonlinear wave solutions of the (2+1)-dimensional break soliton equation are obtained. These double nonlinear wave solutions contain the double Jacobi elliptic function-like solutions, the double solitary wave-like solutions, and so on. The method is also powerful to some other nonlinear wave equations in (2+1) dimensions. 相似文献
5.
PENG Yan-Ze E.V. Krishnan 《理论物理通讯》2005,44(5):807-809
The singular manifold method is used to obtain two general solutions to a (2+1)-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wave solutions in terms of the Jacobi elliptic functions are generated from the general solutions. The long wave limit yields the new types of dromion and solitary structures. 相似文献
6.
LIU Guan-Ting 《理论物理通讯》2008,49(2):287-290
Using the truncated Painleve expansion, symbolic computation, and direct integration technique, we study analytic solutions of (2+1)-dimensional Boussinesq equation. An auto-Backlund transformation and a number of exact solutions of this equation have been found. The set of solutions include solitary wave solutions, solitoff solutions, and periodic solutions in terms of elliptic Jacobi functions and Weierstrass & function. Some of them are novel. 相似文献
7.
ZHAOQiang LIUShi-Kuo FUZun-Tao 《理论物理通讯》2004,42(2):239-241
The (2 1)-dimensional Boussinesq equation and (3 1)-dimensional KP equation are studied by using the extended Jacobi elliptic-function method. The exact periodic-wave solutions for the two equations are obtained. 相似文献
8.
New Solitary Solutions of (2+1)-Dimensional Variable Coefficient Nonlinear Schrodinger Equation with an External Potential 下载免费PDF全文
By a series of transformations, the (2+1)-dimensional variable coefficient nonlinear Schr?dinger equation can turn to the Klein-Gordon equation. Many new double travelling wave solutions of the Klein-Gordon equation are obtained. Thus, the new solitary solutions of the variable coefficient nonlinear Schr?inger equation with an external potential can be found. 相似文献
9.
Solutions to Generalized mKdV Equation 总被引:13,自引:0,他引:13
FUZun-Tao DENGLian-Tang LIUShi-Kuo LIUShi-Da 《理论物理通讯》2003,40(6):641-644
A transformation is introduced for generalized mKdV (GmKdV for short) equation and Jacobi elliptic function expansion method is applied to solve it. It is shown that GmKdV equation with a real number parameter can be solved directly by using Jacobi elliptic function expansion method when this transformation is introduced, and periodic solution and solitary wave solution are obtained. Then the generalized solution to GmKdV equation deduces to some special solutions to some well~known nonlinear equations, such as KdV equation, mKdV equation, when the real parameter is set specific values. 相似文献
10.
《理论物理通讯》2011,(1):20-24
11.
A Bilinear Backlund Transformation and Explicit Solutions for a (3+1)-Dimensional Soliton Equation 下载免费PDF全文
Considering the bilinear form of a (3+1)-dimensional soliton equation, we obtain a bilinear Backlund transformation for the equation. As an application, soliton solution and stationary rational solution for the (3+1)- dimensional soliton equation are presented. 相似文献
12.
13.
We construct a two-soliton-like solution for the (2+1)-dimensionai breaking soliton equation. The obtained solution contains two arbitrary functions and hence can model various cross soliton-like waves including the two-solitary waves. We show the evolution of some special cross soliton-like waves diagrammatically. 相似文献
14.
Similarity Reductions and Similarity Solutions of the (3+1)-Dimensional Kadomtsev-Petviashvili Equation 总被引:2,自引:0,他引:2 下载免费PDF全文
Employing the compatibility method, we obtain the symmetries of the (3+1)-dimensional Kadomtsev Petviashvili (KP) equation. Four types of similarity reductions of the KP equation are obtained by solving the corresponding characteristic equations associated with symmetry equations. In addition, a lot of similarity solutions to the KP equation are obtadned. 相似文献
15.
The exact periodic homoclinic wave of (1+1)D long-short wave equation is obtained using an extended homoclinic test technique. This result shows complexity and variety of dynamical behaviour for a (1+1)-dimensional long-short wave equation. 相似文献
16.
New exact solutions of the (2 +1)-dimensional double sine-Gordon equation are studied by introducing the modified mapping relations between the cubic nonlinear Klein-Gordon system and double sine-Gordon equation. Two arbitrary functions are included into the Jacobi elliptic function solutions. New doubly periodic wave solutions are obtained and displayed graphically by proper selections of the arbitrary functions. 相似文献
17.
By introducing a new type of solutions, called the multiple-mode wave solutions which can be expressed in nonlinear superposition of single-mode waves with different speeds, we investigate the two-mode wave solutions in Degasperis-Procesi equation and two cases are derived. The explicit expressions for the two-mode waves as well as the existence conditions are presented. It is shown that the two-mode waves may be the nonlinear combinations of many types of single-mode waves, such as periodic waves, solJtons, compactons, etc., and more complicated multiple-mode waves can be obtained if higher order or more single-mode waves are taken into consideration. It is pointed out that the two-mode wave solutions can be employed to display the typical mechanism of the interactions between different single-mode waves. 相似文献