共查询到20条相似文献,搜索用时 46 毫秒
1.
The generalized (2+1)-dimensional KP, cKP and mKP are decomposed into the known (1+1)-dimensional soliton equations. Then, we show that the (1+1)-dimensional soliton equations give rise to the explicit soliton solutions of the generalized KP, cKP and mKP. 相似文献
2.
First, a new multi-component modified Kadomtsev-Petviashvill (mKP) spectral problem is constructed by k-constraint imposed on a general pseudo-differential operator. Then, two hierarchies of multi-component mKP equations are derived, including positive non-isospectral mKP hierarchy and negative non-isospectral mKP hierarchy. Moreover, new integrable couplings of the resulting mKP soliton hierarchies are constructed by enlarging the associated matrix spectral problem. 相似文献
3.
Three types of generalized Kadomtsev-Petviashvili equations arising from baroclinic
potential vorticity equation
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
By means of the reductive perturbation method, three types
of generalized (2+1)-dimensional Kadomtsev--Petviashvili (KP)
equations are derived from the baroclinic potential vorticity (BPV)
equation, including the modified KP (mKP) equation, standard KP equation
and cylindrical KP (cKP) equation. Then some solutions of
generalized cKP and KP equations with certain conditions are given
directly and a relationship between the generalized mKP equation and
the mKP equation is established by the symmetry group direct method
proposed by Lou et al. From the relationship and the solutions
of the mKP equation, some solutions of the generalized mKP equation can be
obtained. Furthermore, some approximate solutions of the baroclinic
potential vorticity equation are derived from three types of
generalized KP equations. 相似文献
4.
Via the elementary Darboux transformation (DT) of the modified Kadomtsev--Petviashvili (mKP) equation, a binary Darboux transformation (BDT) of the mKP equation is constructed. 相似文献
5.
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
![点击此处可从《中国物理快报》网站下载免费的PDF全文](/ch/ext_images/free.gif)
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
6.
B. A. Kupershmidt 《Communications in Mathematical Physics》1995,167(2):351-371
Apart from the case of the KP hierarchy, all known Miura maps between integrable Hamiltonian systems had been proven to be canonical. The remaining KP case is settled below. As a corollary, it is shown that the KP hierarchy is a factor — hierarchy of the mKP one, with the kernel consisting of a single scalar field. A discrete mKP hierarchy and the associated Miura map are constructed, and the latter is shown to be canonical as well. As in the continuous case, this implies that one can extend the discrete KP hierarchy by a single new field into an extended discrete KP hierarchy in such a way that the extended discrete Miura map mKPeKP is a canonical isomorphism. 相似文献
7.
Franco Magri Marco Pedroni Jorge P. Zubelli 《Communications in Mathematical Physics》1997,188(2):305-325
We tackle the problem of interpreting the Darboux transformation for the KP hierarchy and its relations with the modified
KP hierarchy from a geometric point of view. This is achieved by introducing the concept of a Darboux covering. We construct
a Darboux covering of the KP equations and obtain a new hierarchy of equations, which we call the Darboux-KP hierarchy (DKP).
We employ the DKP equations to discuss the relationships among the KP equations, the modified KP equations, and the discrete
KP equations. Our approach also handles the various reductions of the KP hierarchy.
We show that the KP hierarchy is a projection of the DKP, the mKP hierarchy is a DKP restriction to a suitable invariant submanifold,
and that the discrete KP equations are obtained as iterations of the DKP ones.
Received: 23 July 1996 / Accepted: 6 January 1997 相似文献
8.
A method is proposed to construct a new extended KP hierarchy, which includes two types of KP equation with self-consistent sources and admits reductions to k-constrained KP hierarchy and to Gelfand-Dickey hierarchy with sources. It provides a general way to construct soliton equations with sources and their Lax representations. 相似文献
9.
Fajun Yu 《Physics letters. A》2008,372(24):4353-4360
In [W.X. Ma, J. Phys. A: Math. Theor. 40 (2007) 15055], Prof. Ma gave a beautiful result (a discrete variational identity). In this Letter, based on a discrete block matrix spectral problem, a new hierarchy of Lax integrable lattice equations with four potentials is derived. By using of the discrete variational identity, we obtain Hamiltonian structure of the discrete soliton equation hierarchy. Finally, an integrable coupling system of the soliton equation hierarchy and its Hamiltonian structure are obtained through the discrete variational identity. 相似文献
10.
The Grammian determinant solutions of the non-isospectral modified Kadomtsev-Petviashvili (mKP) equation are presented. Moreover, a new non-isospectral coupled system is constructed by using the Pfaffianization procedure. Furthermore, Gramm-type Pfaffian solutions of the non-isospectral coupled system are obtained. 相似文献
11.
For two-dimensional unmagnetized dusty plasmas with many different
dust grain species, a Kadomtsev--Petviashvili (KP) equation, a
modified KP (mKP) equation and a coupled KP(cKP) equation for small,
but finite amplitude dust-acoustic solitary waves are obtained for
different physical conditions respectively. The influence of an
arbitrary dust size distribution described by a polynomial
expressed function on the properties of dust-acoustic solitary waves
is investigated numerically. How dust size distribution affects
the sign and the magnitude of nonlinear coefficient A(D) of KP
(mKP) equation is also discussed in detail. It is noted that
whether a compressive or a rarefactive solitary wave exists
depends on the dust size distribution in some dusty
plasmas. 相似文献
12.
We present a new symmetry flow of the Kadomtsev-Petviashvili (KP) hierarchy, which origins from the rescaling of whole “multi-time“ valuables. This flow describes the deformation of solutions of the KP hierarchy with respect to a noncommutative parameter. It is shown that the introduced rescaling symmetry flow does not commute with the ordinary evolution flows of the KP hierarchy, but commutes with the evolution flows with respect to slow-variables. 相似文献
13.
A Hierarchy of New Nonlinear Evolution Equations Associated with a 3×3 Matrix Spectral Problem
下载免费PDF全文
![点击此处可从《中国物理快报》网站下载免费的PDF全文](/ch/ext_images/free.gif)
A 3×3 matrix spectral problem with three potentials and the corresponding hierarchy of new nonlinear evolution equations are proposed. Generalized Hamiltonian structures for the hierarchy of nonlinear evolution equations are derived with the aid of trace identity. 相似文献
14.
15.
Xi-Xiang Xu 《Physics letters. A》2008,372(20):3683-3693
Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems. 相似文献
16.
Claudio Altafini 《Reports on Mathematical Physics》2003,52(3):381-400
For the unitary operator, solution of the Schrödinger equation corresponding to a time-varying Hamiltonian, the relation between the Magnus and the product of exponentials expansions can be expressed in terms of a system of first-order differential equations in the parameters of the two expansions. A method is proposed to compute such differential equations explicitly and in a closed form. 相似文献
17.
ZHANG Da-Jun WU Hua DENG Shu-Fang BI Jin-Bo 《理论物理通讯》2008,49(6):1393-1396
Some general formulas in the Sato theory related to the nonisospectral KP and mKP hierarchies are derived for simplifying calculations. 相似文献
18.
Hong-Xiang Yang 《Physics letters. A》2009,373(7):741-748
Starting from a new discrete iso-spectral problem, we derive a hierarchy of Hamiltonian lattice equations. A Darboux transformation is established for the lattice soliton hierarchy. As applications, the soliton solutions of resulted lattice hierarchy are given. 相似文献
19.
By considering a discrete iso-spectral problem, a hierarchy of bi-Hamiltonian relativistic Toda type lattice equations are revisited. After introducing a semi-direct sum Lie algebras of four by four matrices, integrable coupling system associated with the relativistic Toda type lattice are derived. It is shown that the resulting lattice soliton hierarchy possesses Hamiltonian structures and infinitely many common commuting symmetries as well infinitely many conserved functions. The Liouville integrability of the resulting system is then demonstrated. 相似文献