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1.
A construction procedure is derived to obtain expressions for Hamiltonian densities which characterize the bi-Hamiltonian structure of the equations in the KdV hierarchy. All results are obtained by Hamiltonizing the appropriate Lagrangian densities recently found by us. The method is seento work for both real and complex fields. 相似文献
2.
By using the Miura transformation, from the dark soliton solutions of the mKdV equdation which are found recently by Darboux transformations, a series of new dark soliton solutions of the KdV equation is obtained. 相似文献
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4.
GUO Fu-Kui ZHANG Yu-Feng 《理论物理通讯》2006,46(4):577-579
It is common knowledge that the soliton solutions u(x, t) defined by the bell-shape form is required to satisfy the following condition lira u(x, t) = u(±∞, t) = 0. However, we think that the above condition can be modified as lim u(x, t) = u(±∞, t)^x→ = c, where c is a constant, which is called as a stationary height of u(x, t) in the present paper.^x→∞ If u(x, t) is a bell-shape solitary solution, then the stationary height of each solitary wave is just c. Under the constraint c = 0, all the solitary waves coming from the N-bell-shape-sollton solutions of the KdV equation are the same-oriented travelling. A new type of N-soliton solution with the bell shape is obtained in the paper, whose stationary height is an arbitrary constant c. Taking c ≥ 0, the resulting solitary wave is bound to be the same-oriented travelling. Otherwise, the resulting solitary wave may travel at the same orientation, and also at the opposite orientation. In addition, another type of singular rational travelling solution to the KdV equation is worked out. 相似文献
5.
By the application of the extended tanh method and the symbolic computation
system Mathematica, new soliton-like
solutions are obtained for the combined KdV and mKdV (KdV-mKdV) equation. 相似文献
6.
Some novel solutions of the KdV equation are obtained through the modified
bilinear B\"{a}cklund transformation. 相似文献
7.
New Exact Solutions to the Combined KdV and mKdV Equation 总被引:2,自引:0,他引:2
Yan-ze Peng 《International Journal of Theoretical Physics》2003,42(4):863-868
The modified mapping method is developed to obtain new exact solutions to the combined KdV and mKdV equation. The method is applicable to a large variety of nonlinear evolution equations, as long as odd- and even-order derivative terms do not coexist in the equation under consideration. 相似文献
8.
Hirota method is used to directly construct quasi-periodic wave solutions for the nonisospectral soliton equation.One and two quasi-periodic wave solutions for the variable-coefficient KdV equation are studied.The well known one-soliton solution can be reduced from the one quasi-periodic wave solution. 相似文献
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A recently proposed three-component Camassa-Holm equation is considered. It is shown that this system is a bi-Hamiltonian system. 相似文献
11.
The Korteweg-de Vries equation with a forcing term is established by recentstudies as a simple mathematical model of describing the physics of a shallow layerof fluid subject to external forcing. In the present paper, we study the analytic solutions to the KdV equation with forcing term by using Hirota's direct method. Several exact solutions are given as examples, from which one can see thatthe same type soliton solutions can be excited by different forced term. 相似文献
12.
The Korteweg-de Vries equation with a forcing term is established by recent studies as a simple mathematical model of describing the physics of a shallow layer of fluid subject to external forcing. In the present paper, we study the analytic solutions to the KdV equation with forcing term by using Hirota's direct method. Several exact solutions are given as examples, from which one can see that the same type soliton solutions can be excited by different forced term. 相似文献
13.
YAN Zhen-Ya 《理论物理通讯》2002,38(4):400-402
Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by using our extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and another three families of new doubly periodic solutions (Jacobian elliptic function solutions) are found again
by using a new transformation, which and our extended Jacobian elliptic
function expansion method form a new method still called the
extended Jacobian elliptic function expansion method. The new method can
be more powerful to be applied to other nonlinear differential equations. 相似文献
14.
YAN Zhen-Ya 《理论物理通讯》2002,38(10)
Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by usingour extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and anotherthree families of new doubly periodic solutions (Jacobian elliptic function solutions) are fbund again by using a newtransformation, which and our extended Jacobian elliptic function expansion method form a new method still called theextended Jacobian elliptic function expansion method. The new method can be more powertul to be applied to othernonlinear differential equations. 相似文献
15.
YAN Zhen-Ya 《理论物理通讯》2003,39(2)
More recently, sixteen families of Jacobian elliptic function solutions of mKdV equation have been foundby using our extended Jacobian elliptic function expansion method. In this paper, we continue to improve our methodby using another eight pairs of the closed Jacobian elliptic functions. The mKdV equation is chosen to illustrate theimproved method such that another eight families of new Jacobian elliptic function solutions are obtained again. Thenew method can be more powerful to be applied to other nonlinear differential equations. 相似文献
16.
AN Hong-Li LI Yong-Zhi CHEN Yong 《理论物理通讯》2008,50(9):568-574
In this paper, we directly extend the applications of the Adomian decomposition method to investigate the complex KdV equation. By choosing different forms of wave functions as the initial values, three new types of realistic numerical solutions: numerical positon, negaton solution, and particularly the numerical analytical complexiton solution are obtained, which can rapidly converge to the exact ones obtained by Lou et al. Numerical simulation figures are used to illustrate the efficiency and accuracy of the proposed method. 相似文献
17.
In this paper, we directly extend the
applications of the Adomian decomposition method to investigate the complex KdV equation. By choosing different forms of wave functions as the
initial values, three new types of realistic numerical solutions: numerical
positon, negaton solution, and particularly the numerical analytical
complexiton solution are obtained, which can rapidly converge to the exact
ones obtained by Lou et al. Numerical simulation figures are used
to illustrate the efficiency and accuracy of the proposed method. 相似文献
18.
YAN Zhen-Ya 《理论物理通讯》2002,38(8)
An extended Jacobian elliptic function expansion method presented recently by us is applied to the mKdVequation such that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu‘s allresults are obtained. When the modulus m → 1 or 0, we can find the corresponding six solitary wave solutions and sixtrigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian ellipticfunction solutions and can be applied to other nonlinear differential equations. 相似文献
19.
YAN Zhen-Ya 《理论物理通讯》2002,38(2):143-146
An extended Jacobian elliptic function
expansion method presented recently by us is applied to the mKdV equation such
that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu's all results are obtained. When the modulus
m→1 or 0, we can find the corresponding six solitary wave solutions and six trigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian elliptic function solutions and can be applied to
other nonlinear differential
equations. 相似文献
20.
DENG Shu-Fang 《理论物理通讯》2005,43(6):961-964
The bilinear form for a nonisospectral and variable-coefficient KdV equation
is obtained and some exact soliton solutions are derived through
Hirota method and Wronskian technique. We also derive the bilinear
transformation from its Lax pairs and find solutions with
the help of the obtained bilinear transformation. 相似文献