共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, bilinear form of a negative order AKNS equation hierarchy is given. The soliton solutions are obtained through Hiorta's direct method. 相似文献
2.
In this short paper, bilinear form of a negative order AKNS equation
is given. The N-soliton solutions are obtained through Hiorta's direct method. 相似文献
3.
In this paper, bilinear form of a negative order AKNS equation hierarchy is given. The soliton solutions are obtained through Hiorta's direct method. 相似文献
4.
Bilinear form of the nonisospectral AKNS equation is given. The
N-soliton solutions are obtained through Hirota's method. 相似文献
5.
6.
It is well-known that the finite-gap solutions of the KdV equationcan be generated by its recursion operator.We generalize the result to a special form of Lax pair,from which a method to constrain the integrable system to alower-dimensional or fewer variable integrable system is proposed.A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depictedby a series of ordinary differential equations (ODEs), which may be gotten by a simple but unfamiliar Lax pair. Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies. The key is a special form of Lax pair for the AKNS hierarchy. It is proved that under the constraints all equations of the AKNS hierarchy are linearizable. 相似文献
7.
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
8.
Song-lin Zhao 《Journal of Nonlinear Mathematical Physics》2016,23(4):544-562
Generalized Cauchy matrix approach is used to investigate a discrete negative Ablowitz–Kaup–Newell–Segur (AKNS) equation. Several kinds of solutions more than multi-soliton solutions to this equation are derived by solving determining equation set. Furthermore, applying an appropriate continuum limit we obtain a semidiscrete negative AKNS equation and after a second continuum limit we derive the nonlinear negative AKNS equation. The reductions to discrete, semi-discrete and continuous sine-Gordon equations are also discussed. 相似文献
9.
BAI ChengLin 《理论物理通讯》2000,34(4):729-732
Using the extended homogeneous balance method, which is very concise and primary, we find the multiple soliton solutions of the high order Broer-Kaup equations. The method can be generalized to dealing with high-dimensional Broer-Kaup equations and other class of nonlinear equations. 相似文献
10.
The bilinear form of the (2+1)-dimensional non-isospectral AKNS
system is derived. Its N-soliton solutions are obtained by using
the Hirota method. As a reduction, a (2+1)-dimensional non-isospectral
Schrödinger equation and its N-soliton solutions are constructed. 相似文献
11.
By means of the generalized direct method, a relationship is
constructed between the new solutions and the old ones of the
(3+1)-dimensional breaking soliton equation. Based on the
relationship, a new solution is obtained by using a given
solution of the equation. The symmetry is also obtained for the
(3+1)-dimensional breaking soliton equation. By using the equivalent
vector of the symmetry, we construct a seven-dimensional symmetry
algebra and get the optimal system of group-invariant solutions. To
every case of the optimal system, the (3+1)-dimensional breaking
soliton equation is reduced and some solutions to the reduced
equations are obtained. Furthermore, some new explicit solutions are
found for the (3+1)-dimensional breaking soliton equation. 相似文献
12.
Two basic Darboux transformations of a spectral problem associated with a classical Boussinesq-Burgers equation are presented in this letter. They are used to generate new solutions of the classical Boussinesq-Burgers equation. 相似文献
13.
By using the generally projective Riccati equation method, a series of
doubly periodic solutions (Jacobi elliptic function solution) for a class
of nonlinear partial differential equations are obtained in a
unified way. When the module m→1, these solutions exactly
degenerate to the soliton solutions of the equations. Then we
reveal the relationship between the soliton-like solutions
obtained by other authors and these soliton solutions of the
equations. 相似文献
14.
《理论物理通讯》2011,(1):20-24
15.
GUO Fu-Kui 《理论物理通讯》2008,49(6):1397-1398
A new three-dimensional Lie algebra and its corresponding loop algebra are constructed, from which a modified AKNS soliton-equation hierarchy is obtained. 相似文献
16.
17.
YANG Jian-Rong MAO Jie-Jian 《理论物理通讯》2008,49(1):22-26
With Hirota's bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift. 相似文献
18.
The (2+1)-dimensional breaking soliton equation describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the
x-axis. In this paper, with the aid of symbolic computation, six
kinds of new special exact soltion-like solutions of
(2+1)-dimensional breaking soliton equation are obtained by using
some general transformations and the further generalized
projective Riccati equation method. 相似文献
19.
With the aid of the truncated Painlevé expansion, a set of rational solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov (GNNV) equation with the quadratic function which contains one lump soliton is derived. By combining this quadratic function and an exponential function, the fusion and fission phenomena occur between one lump soliton and a stripe soliton which are two kinds of typical local excitations. Furthermore, by adding a corresponding inverse exponential function to the above function, we can derive the solution with interaction between one lump soliton and a pair of stripe solitons. The dynamical behaviors of such local solutions are depicted by choosing some appropriate parameters. 相似文献
20.
In this paper, the short-wave model equations are investigated, which are associated with the Camassa- Holm (CH) and Degasperis Procesi (DP) shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformatioas back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems. 相似文献