共查询到19条相似文献,搜索用时 171 毫秒
1.
ZHANG Da-Jun 《中国物理快报》2007,24(11):3021-3023
2.
Two Darboux transformations of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawaka ( CDGKS) equation and (2+1)-dimensional modified Korteweg-de Vries (mKdV) equation are constructed through the Darboux matrix method, respectively. N-soliton solutions of these two equations are presented by applying the Darboux trans- formations N times. The right-going bright single-soliton solution and interactions of two and three-soliton overtaking collisions of the (2+1)-dimensional CDGKS equation are studied. By choosing different seed solutions, the right-going bright and left-going dark single-soliton solutions, the interactions of two and three-soliton overtaking collisions, and kink soliton solutions of the (2+1)-dimensional mKdV equation are investigated. The results can be used to illustrate the interactions of water waves in shallow water. 相似文献
3.
A simple algebraic transformation relation of a special type of solution between the (3 1)-dimensional Kadomtsev-petviashvili(KP) equation and the cubic nonlinear Klein-Gordon equation (NKG) is established.Using known solutions of the NKG equation,we can obtain many soliton solutions and periodic solution of the (3 1)-dimensional KP equation. 相似文献
4.
Introducing an explicit expression of gauge transformation turning the spin in linear order of spectral parameter in the first Lax pair into the third axis in spin space, we derive the required Hamiltonian densities for the spin chain with the easy axis, easy plane, and full anisotropy, respectively. 相似文献
5.
In this paper,the variable separation approach is used to obtain localized coherent structures of the (2 1)-dimensional generalized Davey-Stewarson equations:iqt 1/2(qxx=qyy) (R S)q=0,Rx=-σ/2|q|y^2,Sy=-σ/2|q|2/x.Applying a special Baecklund transformation and introducing arbitrary functions of the seed solutions.and abundance of the localized structures of this model is derived,By selceting the arbitrary functions appropriately,some special types of localized excitations such as dromions,dromion lattice,breathers,and instantons are constructed. 相似文献
6.
YANZhen-Ya 《理论物理通讯》2002,37(3):269-276
We have found two types of important exact solutions,compacton solutions,which are solitary waves with the property that after colliding with their own kind,they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction,in the (1 1)D,(1 2)D and even (1 3)D models,and dromion solutions (exponentially decaying solutions in all direction) in many (1 2)D and (1 3)D models.In this paper,symmetry reductions in (1 2)D are considered for the break soliton-type equation with fully nonlinear dispersion (called BS(m,n) equation)ut b(u^m)xxy 4b(u^n δx^-1uy)x=0,which is a generalized model of (1 2)D break soliton equation ut buxxy 4buuy 4buxδx^-1uy=0,by using the extended direct reduction method.As a result,six types of symmetry reductions are obtained.Starting from the reduction equations and some simple transformations,we obtain the solitary wavke solutions of BS(1,n) equations,compacton solutions of BS(m,m-1) equations and the compacton-like solution of the potential form (called PBS(3,2)) ωxt b(ux^m)xxy 4b(ωx^nωy)x=0.In addition,we show that the variable ∫^x uy dx admits dromion solutions rather than the field u itself in BS(1,n) equation. 相似文献
7.
DONG Zhong-Zhou LIU Xi-Qiang BAI Cheng-Lin 《理论物理通讯》2006,46(1):15-20
Using the classical Lie method of infinitesimals, we first obtain the symmetry of the (2+1)-dimensional Burgers-Korteweg-de-Vries (3D-BKdV) equation. Then we reduce the 3D-BKdV equation using the symmetry and give some exact solutions of the 3D-BKdV equation. When using the direct method, we restrict a condition and get a relationship between the new solutions and the old ones. Given a solution of the 3D-BKdV equation, we can get a new one from the relationship. The relationship between the symmetry obtained by using the classical Lie method and that obtained by using the direct method is also mentioned. At last, we give the conservation laws of the 3D-BKdV equation. 相似文献
8.
9.
Exact solution and exotic coherent solition structures of the (2+1)—dimensional generalized nonlinear Schroedinger equation 下载免费PDF全文
In this paper,a variable separation approach is used to obtain localized coherent structures of the (2 1)-dimensional generalized nonlinear Schroedinger equation:Iφt-(α-β)φxx (α β)φyy-2λφ[(α β)(∫-∞^x|φ|y^2ydx u1(y,t))-(α-β)(∫-∞^y|φ|x^2dy u2(x,t))]=0,By applying a special Baecklund transformation and introducing arbitrary functions of the seed solutions,the abundance of the localized structures of this model are derived.By selecting the arbitrary function appropriately,some special types of localized excitations such as dromions,dromion lattice,breathers and istantons are constructed. 相似文献
10.
CHENYong WANGQi LIBiao 《理论物理通讯》2004,42(5):655-660
We generalize the algebraic method presented by Fan [J.Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). As an application of the method, we choose a (2 1)-dimensional asymmetric Nizhnik Novikov Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions‘soliton-like solutions, double-like periodic and trigonometric-like function solutions. 相似文献
11.
XIE Fu-Ding Xiao-Shan LIU Feng 《理论物理通讯》2004,42(11)
Based on the rank analysis method, algorithmization idea, and symbolic computation, in this paper we have presented a method to construct the conservation laws for nonlinear evolution equations. The polynomial conservation laws for K (n 2, n) equations and mnK(m, n) equations are found by using of this approach and some new results have been obtained. 相似文献
12.
13.
14.
Mustafa Inc 《理论物理通讯》2006,45(3):389-394
In this paper, we establish exact
solutions for the R(m,n) equations by using an sn-cn method. As a result,
abundant new compactons, i.e. solitons with the absence of infinite wings, new
type of Jacobi elliptic function, solitary wave and periodic wave solutions, of
this equation are obtained with minimal calculations. The properties of the
R(m,n) equations are shown in figures. 相似文献
15.
Under investigation in this paper are two coupled integrable dispersionless (CID) equations modeling the dynamics of the current-fed string within an external magnetic field. Through a set of the dependent variable transformations, the bilinear forms for the CID equations are derived. Based on the Hirota method and symbolic computation, the analytic N-soliton solutions are presented. Infinitely many conservation laws for the CID equations are given through the known spectral problem. Propagation characteristics and interaction behaviors of the solitons are analyzed graphically. 相似文献
16.
Under investigation in this paper are two coupled integrable dispersionless (CID) equations modeling the dynamics of the current-fed string within an external magnetic field. Through a set of the dependent variable transformations, the bilinear forms for the CID equations are derived. Based on the Hirota method and symbolic computation, the analytic N-soliton solutions are presented. Infinitely many conservation laws for the CID equations are given through the known spectral problem. Propagationcharacteristics and interaction behaviors of the solitons are analyzed graphically. 相似文献
17.
With the assistance of the symbolic
computation system Maple, rich higher order polynomial-type
conservation laws and a sixth order t/x-dependent conservation
law are constructed for a generalized seventh order nonlinear
evolution equation by using a direct algebraic method. From the
compatibility conditions that guaranteeing the existence of
conserved densities, an integrable unnamed seventh order KdV-type
equation is found. By introducing some nonlinear transformations,
the one-, two-, and three-solition solutions as well as the
solitary wave solutions are obtained. 相似文献
18.
QIN Mao-Chang MEI Feng-Xiang SHANG Mei 《理论物理通讯》2005,44(6):967-968
Conservation laws of some differential equations in fiance are studied in this paper. This method does not involve the use or existence of a variational principle. As an alternative, linearize the given equation and find adjoint equation of the linearized equation, the conservation laws can be constructed directly from the symmetries and adjoint symmetries of the associated linearized equation and its adjoint equation. 相似文献
19.
ZHANG Zhi-Yong YONG Xue-Lin CHEN Yu-Fu 《理论物理通讯》2009,51(1):35-38
In this paper, we investigate conservation laws of a class of partial differential equations, which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations. Moreover, some special conservation laws of the combined equations are obtained by means of symmetry classifications of wave equations uxx = H (x)utt. 相似文献