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961.
Dynamics of solitons in Bose-Einstein condensate with time-dependent atomic scattering length
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The evolution of solitons in Bose--Einstein condensates (BECs)
with time-dependent
atomic scattering length in an expulsive parabolic potential is studied. Based on
the extended hyperbolic function method, we successfully obtain the bright and dark
soliton solutions. In addition, some new soliton solutions in this model are found.
The results in this paper include some in the literature ({\em Phys. Rev. Lett.}
{\bf 94} (2005) 050402 and {\em Chin. Phys. Lett.} {\bf 22} (2005) 1855). 相似文献
962.
An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinear partial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraic mapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein-Gordon equation. This is applied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained, including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions. 相似文献
963.
LI Hua-Mei 《理论物理通讯》2003,39(4):395-400
In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained. 相似文献
964.
Starting from a special Bäcklund transform and a variable separation approach, a quite general variable separation solution of the
generalized (2+1)-dimensional perturbed nonlinear Schrödinger
system is obtained. In addition to the single-valued localized coherent soliton excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized
solution, a new type of multi-valued (folded) localized excitation is derived
by introducing some appropriate lower-dimensional multiple valued
functions. 相似文献
965.
In the previous Letter (Zheng C L and Zhang J F 2002 Chin. Phys. Lett. 19 1399), a localized excitation of the generalized Ablowitz-Kaup-Newell-Segur (GAKNS) system was obtained via the standard Painlevé truncated expansion and a special variable separation approach. In this work, starting from a new variable separation approach, a more general variable separation excitation of this system is derived. The abundance of the localized coherent soliton excitations like dromions, lumps, rings, peakons and oscillating soliton excitations can be constructed by introducing appropriate lower-dimensional soliton patterns. Meanwhile we discuss two kinds of interactions of solitons. One is the interaction between the travelling peakon type soliton excitations, which is not completely elastic. The other is the interaction between the travelling ring type soliton excitations, which is completely elastic. 相似文献
966.
LINJi QIANXian-Ming 《理论物理通讯》2003,40(3):259-261
Using the (2 1)-dimensional Schwartz dcrivative, the usual (2 1)-dimensional Schwartz Kadomtsev-Petviashvili (KP) equation is extended to (n 1)-dimensional conformal invariance equation. The extension possesses Painlcvc property. Some (3 1)-dimensional examples are given and some single three-dimensional camber soliton and two spatial-plane solitons solutions of a (3 1)-dimensional equation are obtained. 相似文献
967.
Some Special Types of Multisoliton Solutions of the Modified
Kadomtsev-Petviashvili Equation 总被引:3,自引:0,他引:3
Using the standard truncated Painlevé analysis approach, we
have obtained some new special types of multisoliton solutions of
a (2+1)-dimensional integrable model, the modified
Kadomtsev-Petviashvili (mKP) equation. 相似文献
968.
XUYou-Sheng LINJi LIHua-Mei WUPeng-Min 《理论物理通讯》2003,40(4):393-394
Making use of the full information obtained in our previous discussions, a new analytical solutions for the potential function of the digital microstructure image of porous media is reported in this paper. It is demonstrated that the distribution of potential function depends on the zeroth order Bessel function. All these will be helpful for analyzing the similar subjects in porous media. 相似文献
969.
ZHANGJie-Fang HUANGWen-Hua 《理论物理通讯》2003,40(5):533-536
Considering that the multi-valued (folded) localized excitations may appear in many (2 1)-dimensional soliton equations because some arbitrary functions can be included in the exact solutions, we use some special types of muliti-valued functions to construct folded solitrary waves and foldons in the (2 1)-dimensional Broer-Kaup equation.These folded excitations are invesigated both analytically and graphically in an alternative way. 相似文献
970.
Evolution property of soliton solutions for the Whitham-Broer-Kaup equation and variant Boussinesq equation
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Using the standard Painlevé analysis approach, the (1+1)-dimensional Whitham-Broer-Kaup (WBK) and variant Boussinesq equations are solved. Some significant and exact solutions are given. We investigate the behaviour of the interactions between the multi-soliton-kink-type solution for the WBK equation and the multi-solitonic solutions and find the interactions are not elastic. The fission of solutions for the WBK equation and the fusions of those for the variant Boussinesq equation may occur after their interactions. 相似文献