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1.
The matrix KP equation is a many component extension of the ordinary KP (Kodomtsev-Petvjshvilli) equation. Although the matrix KP equation is very important, however,its explicit exact solutions have not been reported up to now. In this letter we give a method to construct the matrix KP hierarchy and its exact solutions. Then we give here the explicit expressions of the exact solutions of the matrix KP equation with arbitrary soliton number. 相似文献
2.
By the application of the extended homogeneous balance
method, we derive an auto-Bäcklund transformation (BT) for
(2+1)-dimensional variable coefficient generalized KP equations. Based on
the BT, in which there are two homogeneity equations to be solved, we obtain
some exact solutions containing single solitary waves. 相似文献
3.
By virtue of the bilinear method and the KP hierarchy reduction technique, exact explicit rational solutions of the multicomponent Mel’nikov equation and the multicomponent Schrödinger–Boussinesq equation are constructed, which contain multicomponent short waves and single-component long wave. For the multicomponent Mel’nikov equation, the fundamental rational solutions possess two different behaviours: lump and rogue wave. It is shown that the fundamental (simplest) rogue waves are line localised waves which arise from the constant background with a line profile and then disappear into the constant background again. The fundamental line rogue waves can be classified into three: bright, intermediate and dark line rogue waves. Two subclasses of non-fundamental rogue waves, i.e., multirogue waves and higher-order rogue waves are discussed. The multirogue waves describe interaction of several fundamental line rogue waves, in which interesting wave patterns appear in the intermediate time. Higher-order rogue waves exhibit dynamic behaviours that the wave structures start from lump and then retreat back to it. Moreover, by taking the parameter constraints further, general higher-order rogue wave solutions for the multicomponent Schrödinger–Boussinesq system are generated. 相似文献
4.
This paper constructs more general exact solutions than $N$-soliton
solution and Wronskian solution for variable-coefficient
Kadomtsev--Petviashvili (KP) equation. By using the Hirota method
and Pfaffian technique, it finds the Grammian determinant-type
solution for the variable-coefficient KP equation (VCKP), the
Wronski-type Pfaffian solution and the Gram-type Pfaffian solutions
for the Pfaffianized VCKP equation. 相似文献
5.
B?cklund transformations,consistent Riccati expansion solvability,and soliton–cnoidal interaction wave solutions of Kadomtsev–Petviashvili equation
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《中国物理 B》2020,(2)
The famous Kadomtsev-Petviashvili(KP)equation 1 s a classical equation In soliton tneory.A Backlund transformation between the KP equation and the Schwarzian KP equation is demonstrated by means of the truncated Painlev6 expansion in this paper.One-parameter group transformations and one-parameter subgroup-invariant solutions for the extended KP equation are obtained.The consistent Riccati expansion(CRE) solvability of the KP equation is proved.Some interaction structures between soliton-cnoidal waves are obtained by CRE and several evolution graphs and density graphs are plotted. 相似文献
6.
HUANGDing-Jiang ZHANGHong-Qing 《理论物理通讯》2004,42(3):325-328
By using the extended homogeneous balance method, a new auto-Ba^ecklund transformation(BT) to the generalized Kadomtsew-Petviashvili equation with variable coefficients (VCGKP) are obtained. And making use of the auto-BT and choosing a special seed solution, we get many families of new exact solutions of the VCGKP equations, which include single soliton-like solutions, multi-soliton-like solutions, and special-soliton-like solutions. Since the KP equation and cylindrical KP equation are all special cases of the VCGKP equation, and the corresponding results of these equations are also given respectively. 相似文献
7.
We obtain a new class of exact analytic solutions of the BKP equation which are called chain solutions because they are analogous to the, soliton solutions of the KP equation. The rational solutions called lumps are shown to include in this class as a Special limiting situation. 相似文献
8.
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
9.
WEN Xiao-Yong 《理论物理通讯》2008,49(5):1235-1240
With the aid of symbolic computation system Maple, many exact solutions for the (3+1)-dimensional KP equation are constructed by introducing an auxiliary equation and using its new Jacobi elliptic function solutions, where the new solutions are also constructed. When the modulus m → 1 and m →0, these solutions reduce to the corresponding solitary evolution solutions and trigonometric function solutions. 相似文献
10.
ZHAO Qiang LIU Shi-Kuo FU Zun-Tao 《理论物理通讯》2004,42(8)
The (2 1)-dimensional Boussinesq equation and (3 1)-dimensional KP equation are studied by using the extended Jacobi elliptic-function method. The exact periodic-wave solutions for the two equations are obtained. 相似文献
11.
ZHAOQiang LIUShi-Kuo FUZun-Tao 《理论物理通讯》2004,42(2):239-241
The (2 1)-dimensional Boussinesq equation and (3 1)-dimensional KP equation are studied by using the extended Jacobi elliptic-function method. The exact periodic-wave solutions for the two equations are obtained. 相似文献
12.
BAI Cheng-Lin BAI Cheng-Jie ZHAO Hong 《理论物理通讯》2005,44(11)
A generalized variable-coefficient algebraic method is applied to construct several new families of exact solutions of physical interestfor (3 1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions. 相似文献
13.
New Multiple Soliton-like and Periodic Solutions for (2+1)-Dimensional Canonical Generalized KP Equation with Variable Coefficients 总被引:1,自引:0,他引:1
ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《理论物理通讯》2006,46(11)
In this paper, the generalized tanh function method is extended to (2 1)-dimensional canonical generalized KP (CGKP) equation with variable coefficients. Taking advantage of the Riccati equation, many explicit exact solutions,which contain multiple soliton-like and periodic solutions, are obtained for the (2 1)-dimensional CGKP equation with variable coefficients. 相似文献
14.
BAI Cheng-Lin BAI Cheng-Jie ZHAO Hong 《理论物理通讯》2005,44(5):821-826
A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions. 相似文献
15.
ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《理论物理通讯》2006,46(5):793-798
In this paper, the generalized ranch function method is extended to (2+1)-dimensianal canonical generalized KP (CGKP) equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the (2+1)-dimensional OGKP equation with variable coetffcients. 相似文献
16.
HUANG Ding-Jiang ZHANG Hong-Qing 《理论物理通讯》2004,42(9)
By using the extended homogeneous balance method, a new auto-Backlund transformation(BT) to thegeneralized Kadomtsev-Petviashvili equation with variable coefficients (VCGKP) are obtained. And making use of theauto-BT and choosing a special seed solution, we get many families of new exact solutions of the VCGKP equations,which include single soliton-like solutions, multi-soliton-like solutions, and special-soliton-like solutions. Since the KPequation and cylindrical KP equation are all special cases of the VCGKP equation, and the corresponding results ofthese equations are also given respectively. 相似文献
17.
Studying compactons, solitons, solitary patterns and periodic solutions is important in nonlinear phenomena. In this paper we study nonlinear variants of the Kadomtsev–Petviashvili (KP) and the Korteweg–de Vries (KdV) equations with positive and negative exponents. The functional variable method is used to establish compactons, solitons, solitary patterns and periodic solutions for these variants. This method is a powerful tool for searching exact travelling solutions in closed form. 相似文献
18.
Based on the extended mapping deformation method and symbolic
computation, many exact travelling wave solutions are found for
the (3+1)-dimensional JM equation and the (3+1)-dimensional KP
equation. The obtained solutions include solitary solution, periodic wave solution,
rational travelling wave solution, and Jacobian and Weierstrass
function solution, etc. 相似文献
19.
In this paper, we first consider
exact solutions for Lienard equation
with nonlinear terms of any order.
Then, explicit exact bell and kink profile solitary-wave solutions
for many nonlinear evolution equations are obtained by means of
results of the Lienard equation and proper deductions, which transform
original partial differential equations into the Lienard one.
These nonlinear equations include compound KdV, compound KdV-Burgers,
generalized Boussinesq, generalized KP and Ginzburg-Landau
equation. Some new solitary-wave solutions are found. 相似文献
20.
New doubly periodic and multiple soliton solutions of the generalized (3+l)-dimensional KP equation with variable coefficients
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A new generalized Jacobi elliptic function method is used to construct the exact travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation which has more new solutions. More new doubly periodic and multiple soliton solutions are obtained for the generalized (3+1)-dimensional Kronig-Penny (KP) equation with variable coefficients. This method can be applied to other equations with variable coefficients. 相似文献