共查询到20条相似文献,搜索用时 46 毫秒
1.
It is well known that the Kadomtsev-Petviashvili (KP) equation is the two-dimensional analogue of the Korteweg—de Vries (KdV) equation. We reconsider the derivation of the KP equation, modified to include the effects of rotation, in order to determine the nature of the initial conditions. The motivation for this is that if the solutions of the modified KP equation are assumed to be locally confined, then they satisfy a certain constraint, which appears to restrict considerably the class of allowed initial conditions. The outcome of the analysis presented here is that in general it is not permissible to assume that solutions of the modified KP equation are locally confined, and hence the constraint cannot be applied. The reason for this is the radiation of Poincaré waves, which appear behind the main part of the solution described by the modified KP equation. 相似文献
2.
We propose an algebro-geometric method for constructing solutions of the discrete KP equation over a finite field. We also perform the corresponding reduction to the finite-field version of the discrete KdV equation. We write formulas that allow constructing multisoliton solutions of the equations starting from vacuum wave functions on an arbitrary nonsingular curve. 相似文献
3.
《Chaos, solitons, and fractals》2000,11(5):711-719
Nonlinear wave propagation through a 2D lattice is investigated. Using reductive perturbation method, we show that this can be described by Kadomtsev–Petviashvili (KP) equation for quadratic nonlinearity and modified KP equation for cubic nonlinearity, respectively. With quadratic and cubic nonlinearities together, the system is governed by an integro-differential equation. We have also checked the integrability of these equations using singularity analysis and obtained solitary wave solutions. 相似文献
4.
In this paper, the first integral method is used to construct exact solutions of the modified KdV–KP equation and the Burgers–Kadomtsev–Petviashvili (Burgers–KP) equation. This method can be applied to nonintegrable equations as well as to integrable ones. This method is based on the theory of commutative algebra. 相似文献
5.
In this paper, we clarify the connection of the Fokas–Lenells (FL) equation to the Kadomtsev–Petviashvili (KP)–Toda hierarchy by using a set of bilinear equations as a bridge and confirm multidark soliton solution to the FL equation previously given by Matsuno (J. Phys. A 2012 45 (475202). We also show that the set of bilinear equations in the KP–Toda hierarchy can be generated from a single discrete KP equation via Miwa transformation. Based on this finding, we further deduce the multibreather and general rogue wave solutions to the FL equation. The dynamical behaviors and patterns for both the breather and rogue wave solutions are illustrated and analyzed. 相似文献
6.
Propagation of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions is analyzed. The Kadomtsev–Petviashivili (KP) equation is derived by using the reductive perturbation theory. A Sagdeev potential for this system has been proposed. This potential is used to study the stability conditions and existence of solitonic solutions. Also, it is shown that a rarefactive soliton can be propagates in most of the cases. The soliton energy has been calculated and a linear dispersion relation has been obtained using the standard normal-modes analysis. The effects of variable dust charge on the amplitude, width and energy of the soliton and its effects on the angular frequency of linear wave are discussed too. It is shown that the amplitude of solitary waves of KP equation diverges at critical values of plasma parameters. Solitonic solutions of modified KP equation with finite amplitude in this situation are derived. 相似文献
7.
Yaming Chen Songhe SongHuajun Zhu 《Journal of Computational and Applied Mathematics》2011,236(6):1354-1369
In this paper, the multi-symplectic Fourier pseudospectral (MSFP) method is generalized to solve two-dimensional Hamiltonian PDEs with periodic boundary conditions. Using the Fourier pseudospectral method in the space of the two-dimensional Hamiltonian PDE (2D-HPDE), the semi-discrete system obtained is proved to have semi-discrete multi-symplectic conservation laws and a global symplecticity conservation law. Then, the implicit midpoint rule is employed for time integration to obtain the MSFP method for the 2D-HPDE. The fully discrete multi-symplectic conservation laws are also obtained. In addition, the proposed method is applied to solve the Zakharov-Kuznetsov (ZK) equation and the Kadomtsev-Petviashvili (KP) equation. Numerical experiments on soliton solutions of the ZK equation and the KP equation show the high accuracy and effectiveness of the proposed method. 相似文献
8.
In this paper, we introduce a Frobenius Painlevé IV equation and the corresponding Hamilton system, and we give the symmetric form of the Frobenius Painlevé IV equation. Then, we construct the Lax pair of the Frobenius Painlevé IV equation. Furthermore, we recall the Frobenius modified KP hierarchy and the Frobenius KP hierarchy by bilinear equations, then we show how to get Frobenius Painlevé IV equation from the Frobenius modified KP hierarchy. In order to study the different aspects of the Frobenius Painlevé IV equation, we give the similarity reduction and affine Weyl group symmetry of the equation. Similarly, we introduce a Frobenius Painlevé II equation and show the connection between the Frobenius modified KP hierarchy and the Frobenius Painlevé II equation. 相似文献
9.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(8):3024-3032
The non-isospectral variable-coefficient KP equation with self-consistent sources and its Grammian solutions are obtained for the first time by using the source generation procedure. Moreover, a new coupled system of the non-isospectral variable-coefficient KP equation with self-consistent sources is constructed by applying the source generation procedure and the coupled non-isospectral variable-coefficient KP equation without sources. The novel coupled system with sources cannot only be reduced to the coupled non-isospectral variable-coefficient KP equation, but also reduced to the non-isospectral variable-coefficient KP equation with self-consistent sources. 相似文献
10.
In this work, we study a completely integrable dissipative equation. The Burgers equation is extended by using the sense of the Kadomtsev–Petviashvili (KP) equation. The new established Burgers–KP equation is studied by using the tanh–coth method to obtain kink solutions and periodic solutions. We also apply the powerful Hirota’s bilinear method to establish exact N-soliton solutions for the derived integrable equation. 相似文献
11.
《Journal of Computational and Applied Mathematics》2012,236(6):1354-1369
In this paper, the multi-symplectic Fourier pseudospectral (MSFP) method is generalized to solve two-dimensional Hamiltonian PDEs with periodic boundary conditions. Using the Fourier pseudospectral method in the space of the two-dimensional Hamiltonian PDE (2D-HPDE), the semi-discrete system obtained is proved to have semi-discrete multi-symplectic conservation laws and a global symplecticity conservation law. Then, the implicit midpoint rule is employed for time integration to obtain the MSFP method for the 2D-HPDE. The fully discrete multi-symplectic conservation laws are also obtained. In addition, the proposed method is applied to solve the Zakharov–Kuznetsov (ZK) equation and the Kadomtsev–Petviashvili (KP) equation. Numerical experiments on soliton solutions of the ZK equation and the KP equation show the high accuracy and effectiveness of the proposed method. 相似文献
12.
We study the (2+1)-dimensional model proposed by Kadomtsev and Petviashvili (KP) to describe slowly varying nonlinear waves in a dispersive medium. Applying an appropriate Lie transformation and following the method introduced by Tajiri et al., the KP equation is reduced to a one-dimensional equation, that is, to a certain version of the Boussinesq equation (BqE). Then, we solve the BqE by the Hirota method, and finally we use the inverse transformation in order to obtain de KP solutions. We Analyze some remarkable properties of the solutions found in this work. 相似文献
13.
本文从约化的角度考虑BKP方程族的Pfaffian形式的解.证明了通过施加适当的微分约束,KP方程族的格拉姆行列式的解很自然的约化为BKP方程族的解. 相似文献
14.
We construct Virasoro-type additional symmetries of a kind of constrained multicomponent Kadomtsev–Petviashvili (KP) hierarchy and obtain the Virasoro flow equation for the eigenfunctions and adjoint eigenfunctions. We show that the algebraic structure of the Virasoro symmetry is retained under discretization from the constrained multicomponent KP hierarchy to the discrete constrained multicomponent KP hierarchy. 相似文献
15.
§1. IntroductionNonlinearintegrablediscretesystemsarenowattractingmuchattention.Amongthem,thediscretePainlevéequationsareexpectedtobethemostfundamentalonesinanalogytothecontinuouscase.Closerstudiesarehowrevealingtheirrichmathematicalstructures,suchas… 相似文献
16.
We study the evolution of small-amplitude water waves when the fluid motion is three dimensional. An isotropic pseudodifferential equation that governs the evolution of the free surface of a fluid with arbitrary, uniform depth is derived. It is shown to reduce to the Benney-Luke equation, the Korteweg-de Vries (KdV) equation, the Kadomtsev-Petviashvili (KP) equation, and to the nonlinear shallow water theory in the appropriate limits. We compute, numerically, doubly periodic solutions to this equation. In the weakly two-dimensional long wave limit, the computed patterns and nonlinear dispersion relations agree well with those of the doubly periodic theta function solutions to the KP equation. These solutions correspond to traveling hexagonal wave patterns, and they have been compared with experimental measurements by Hammack, Scheffner, and Segur. In the fully two-dimensional long wave case, the solutions deviate considerably from those of KP, indicating the limitation of that equation. In the finite depth case, both resonant and nonresonant traveling wave patterns are obtained. 相似文献
17.
Antonín Slavík 《Journal of Difference Equations and Applications》2018,24(3):425-437
We introduce a new class of discrete Bessel functions and discrete modified Bessel functions of integer order. After obtaining some of their basic properties, we show that these functions lead to fundamental solutions of the discrete wave equation and discrete diffusion equation. 相似文献
18.
19.
Song-lin Zhao 《Journal of Difference Equations and Applications》2013,19(8):1134-1148
We establish a discrete model for the potential Ablowitz–Kaup–Newell–Segur equation via a generalized Cauchy matrix approach. Soliton solutions and Jordan block solutions of this equation are presented by solving the determining equation set. By applying appropriate continuum limits, we obtain two semi-discrete potential Ablowitz–Kaup–Newell–Segur equations. The reductions to real and complex discrete and semi-discrete potential modified Korteweg-de Vries equations are also discussed. 相似文献
20.
Kwasi Boateng Weiguo Yang David Yaro Michael Ezra Otoo 《Mathematical Methods in the Applied Sciences》2020,43(6):3457-3472
The fully integrable KP equation is one of the models that describes the evolution of nonlinear waves, the expansion of the well-known KdV equation, where the impacts of surface tension and viscosity are negligible. This paper uses the Modified Extended Direct Algebraic (MEDA) method to build fresh exact, periodic, trigonometric, hyperbolic, rational, triangular and soliton alternatives for the (2 + 1)-dimensional Gardner KP equation. These solutions that we discover in this article will help us understand the phenomena of the (2 + 1)-dimensional Gardner KP equation. Comparing the study in this paper and existing work, we find more exact solutions with soliton and periodic structures and the rational function solution in this paper is more general than the rational solution in existing literature. Most of the Jacobi elliptic function solutions and the mixed Jacobi elliptic function solutions to the (2 + 1)-dimensional Gardner KP equation discovered in this paper, to the best of our highest understanding are not seen in any existing paper until now. 相似文献