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1.
Using the relation between the mKdV equation and the KdV-mKdV equation, we derive non-singular rational solutions for the mKdV equation. The solutions are given in terms of Wronskians. Dynamics of some solutions is investigated by means of asymptotic analysis. Wave trajectories of high order rational solutions are asymptotically governed by cubic curves. 相似文献
2.
In a recent article(Commun. Theor. Phys. 67(2017) 207), three(2+1)-dimensional equations — KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same Kd V equation by using different transformation of variables, respectively. In this short note, by adding an adjustment item to original transformation, three more general transformation of variables corresponding to above three equations have been given.Substituting the solutions of the Kd V equation into our transformation of variables, more new exact solutions of the three(2+1)-dimensional equations can be obtained. 相似文献
3.
The Bäcklund transformation(BT) of the mKdV-sG equation is constructed by introducing a new transformation. Infinitely many nonlocal symmetries are obtained in terms of its BT. The soliton-periodic wave interaction solutions are explicitly derived by the classical Lie-group reduction method. Particularly, some special concrete soliton and periodic wave interaction solutions and their behaviours are discussed both in analytical and graphical ways. 相似文献
4.
A new method for constructing the Wronskian entries is proposed and
applied to the differential-difference
Kadomtsev-Petviashvilli (DΔKP) equation. The generalized
Wronskian solutions to it are obtained, including rational solutions
and Matveev solutions. 相似文献
5.
《Journal of Nonlinear Mathematical Physics》2013,20(2):323-336
A new type of the nonisospectral KP equation with self-consistent sources is constructed by using the source generation procedure. A new feature of the obtained nonisospectral system is that we allow y-dependence of the arbitrary constants in the determinantal solution for the nonisospectral KP equation. In order to further show integrability of the novel nonisospectral KP equation with self-consistent sources, we give a bilinear Bäcklund transformation. 相似文献
6.
Based upon the covariant prolongation
structures theory, we construct the sl(2,R)×R(ρ) prolongation structure for Konno-Asai-Kakuhata equation. By taking
two and one-dimensional prolongation spaces, we obtain the
inverse scattering equations given by Konno et al. and the
corresponding Riccati equation. The Bäcklund transformations are also presented. 相似文献
7.
In the paper we discuss the Wronskian
solutions of modified Korteweg-de Vries equation (mKdV) via the
Bäcklund transformation (BT) and a generalized Wronskian condition is
given, which allows us to substitute an arbitrary coefficient matrix
in the GN(t) for the original diagonal one. 相似文献
8.
A coupled system known as the Drinfel'd-Sokolov-Wilson equation is reexamined. With the help of a Lax operator of fourth order, its proper Darboux transformation is constructed. Also, a nonlinear superposition formula is worked out for the associated Bäcklund transformation and some solutions are calculated. 相似文献
9.
CAI Ke-Jie TIAN Bo ZHANG Cheng ZHANG Huan MENG Xiang-Hua LÜ Xing GENG Tao LIU Wen-Jun 《理论物理通讯》2008,50(5):1185-1188
By the symbolic computation and Hirota method, the bilinear form and
an auto-Bäcklund transformation for a variable-coefficient
Korteweg-de Vries equation with nonuniformities are given. Then, the
N-solitonic solution in terms of Wronskian form is obtained and
verified. In addition, it is shown that the (N-1)- and N-solitonic
solutions satisfy the
auto-Bäcklund transformation through the Wronskian technique. 相似文献
10.
In this paper,the bilinear form of a generalized Kadomtsev-Petviashvili equation is obtained by applying the binary Bell polynomials.The N-soliton solution and one periodic wave solution are presented by use of the Hirota direct method and the Riemann theta function,respectively.And then the asymptotic analysis demonstrates one periodic wave solution can be reduced to one soliton solution.In the end,the bilinear Bcklund transformations are derived. 相似文献
11.
smail Aslan 《理论物理通讯》2014,(5):595-599
The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before. 相似文献
12.
YANZhen-Ya 《理论物理通讯》2001,36(2):135-138
We obtain Backlund transformation and some new kink-like solitary wave solutions for the generalized Burgers equation in (2 1)-dimensional space,ut 1/2(uδy^-1ux)x-uxx=0,by using the extended homogeneous balance method.As is well known,the introduction of the concept of dromions (the exponentially localized solutions in (2 1)-dimensional space)has triggered renewed interest in (2 1)-dimensional soliton systems.The solutions obtained are used to show that the variable ux admits exponentially localized solutions rather than the physical field u(x,y,t) itself.In addition,it is shown that the equation passes Painleve test. 相似文献
13.
ZHANG Da-Jun WU Hua 《理论物理通讯》2008,49(4):809-814
This paper investigates in detail the dynamics of the modified KdV equation with self-consistent sources, including characteristics of one-soliton, scattering conditions and phase shifts of two solitons, degenerate case of two solitons and "ghost" solitons, etc. Co-moving coordinate frames are employed in asymptotic analysis. 相似文献
14.
Starting from the truncated Painlev′e expansion, the residual symmetry of the Alice-Bob modified Kortewegde Vries(AB-mKdV) equation is derived. The residual symmetry is localized and the AB-mKdV equation is transformed into an enlarged system by introducing one new variable. Based on Lie's first theorem, the finite transformation is obtained from the localized residual symmetry. Further, considering the linear superposition of multiple residual symmetries gives rises to N-th B?cklund transformation in the form of the determinant. Moreover, the P_sT_d(the shifted parity and delayed time reversal) symmetric exact solutions(including invariant solution, breaking solution and breaking interaction solution) of AB-mKdV equation are presented and two classes of interaction solutions are depicted by using the particular functions with numerical simulation. 相似文献
15.
The modified discrete KP equation is the Bäcklund transformation for the Hirota’s discrete KP equation or the Hirota-Miwa equation. We construct the modified discrete KP equation with self-consistent sources via source generation procedure and clarify the algebraic structure of the resulting coupled modified discrete KP system by presenting its discrete Gram-type determinant solutions. It is also shown that the commutativity between the source generation procedure and Bäcklund transformation is valid for the discrete KP equation. Finally, we demonstrate that the modified discrete KP equation with self-consistent sources yields the modified differential-difference KP equation with self-consistent sources through a continuum limit. The continuum limit of an explicit solution to the modified discrete KP equation with self-consistent sources also gives the explicit solution for the modified differential-difference KP equation with self-consistent sources. 相似文献
16.
In this paper, two types of the (2+1)-dimensional breaking soliton equations are investigated, which describe the interactions of the Riemann waves with the long waves. With symbolic computation, the Hirota bilinear forms and Bäcklund transformations are derived for those two systems. Furthermore, multisoliton solutions in terms of the Wronskian determinant are constructed, which are verified through the direct substitution of the solutions into the bilinear equations. Via the Wronskian technique, it is proved that theBäcklund transformations obtained are the ones between the (N-1)- and N-soliton solutions. Propagations and interactions of the kink-/bell-shaped solitons are presented. It is shown that the Riemann waves possess the solitonic properties, and maintain the amplitudes and velocities in the collisions only with some phase shifts. 相似文献
17.
The Qiao--Liu equation with self-consistent sources (QLESCS) and its Lax representation are derived. A reciprocal transformation for the QLESCS is given. By making use of the reciprocal transformation and the solutions of the mKdV equation with self-consistent sources (mKdVSCS), the solutions of the QLESCS are presented. 相似文献
18.
The residual symmetries of the Ablowitz–Kaup–Newell–Segur(AKNS)equations are obtained by the truncated Painleve′analysis.The residual symmetries for the AKNS equations are proved to be nonlocal and the nonlocal residual symmetries are extended to the local Lie point symmetries of a prolonged AKNS system.The local Lie point symmetries of the prolonged AKNS equations are composed of the residual symmetries and the standard Lie point symmetries,which suggests that the residual symmetry method is a useful complement to the classical Lie group theory.The calculation on the symmetries shows that the enlarged equations are invariant under the scaling transformations,the space–time translations,and the shift translations.Three types of similarity solutions and the reduction equations are demonstrated.Furthermore,several types of exact solutions for the AKNS equations are obtained with the help of the symmetry method and the Bcklund transformations between the AKNS equations and the Schwarzian AKNS equation. 相似文献
19.
HU Xiao-Rui CHEN Yong 《理论物理通讯》2008,50(11):1055-1060
On bases of the direct method developed by Clarkson and Kruskal [J. Math. Phys. 27 (1989) 2201], the (2+1)-dimensional nonisospectral Kadomtsev-Petviashvili (KP) equation has been reduced to three types of (1 +1)- dimensional partial differential equations. We focus on solving the third type of reduction and dividing them into three subcases, from which we obtain rich solutions including some arbitrary functions. 相似文献
20.
By using the variable separation approach, which is based on the corresponding Bäcklund
transformation, new exact solutions of a
(1+1)-dimensional nonlinear evolution equation are obtained.
Abundant new soliton motions of the potential field can be
found by selecting appropriate functions. 相似文献