The constraint of the Kadomtsev-Petviashvili equation and its special solutions

Cheng, Yi; Li, Yishen

doi:10.1016/0375-9601(91)90403-u

Cited by 279 publications

(126 citation statements)

References 10 publications

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“…Initial solution as a parameter is introduced to Eq. (20). We assume that the u 0 is an initial solution of Eq.…”

Section: Introducing Parameters and Small Perturbation Methodsmentioning

confidence: 99%

“…The velocity of a wave variable as a parameter is introduced to Eq. (20). We can assume that ξ = z − αt in Eq.…”

Section: Introducing Parameters and Small Perturbation Methodsmentioning

confidence: 99%

“…The spatiotemporal variety in exact two-wave and multi-wave propagation will be investigated and numerically simulated. In this chapter, some important models such as shallow water wave propagation models under the transverse long-wave disturbance Potential Kadomtsev-Petviashvili equation [13][14][15][16][17], Kadomtsev-Petviashvili [18][19][20][21][22][23][24][25][26][27] equation, and specially, Kadomtsev-Petviashvili with positive dispersion equation are considered. Applied new methods to these equations, some new two-wave and multi-wave are obtained and spatiotemporal variety in multi-wave propagation is investigated and numerically simulated.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spatio-Temporal Feature in Two-Wave and Multi-Wave Propagations

Dai¹,

Li²,

Mu³

et al. 2012

Wave Processes in Classical and New Solids

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“…Initial solution as a parameter is introduced to Eq. (20). We assume that the u 0 is an initial solution of Eq.…”

Section: Introducing Parameters and Small Perturbation Methodsmentioning

confidence: 99%

“…The velocity of a wave variable as a parameter is introduced to Eq. (20). We can assume that ξ = z − αt in Eq.…”

Section: Introducing Parameters and Small Perturbation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spatio-Temporal Feature in Two-Wave and Multi-Wave Propagations

Dai¹,

Li²,

Mu³

et al. 2012

Wave Processes in Classical and New Solids

View full text Add to dashboard Cite

“…Solutions of the governing nonlinear equations can shed light on these phenomena. There are various systematical methods for constructing solutions, for example, nonlinearization method of Lax pairs [1][2][3], extended -expansion method [4][5][6] and homogeneous balance method [7][8][9][10], and dressing method and generalized dressing method [11][12][13][14][15][16]. It is well known that the Hirota method with the aid of Riemann-theta function is a good method to obtain periodic and quasiperiodic solutions.…”

Section: Introductionmentioning

confidence: 99%

Theta Function Solutions of the 3 + 1‐Dimensional Jimbo‐Miwa Equation

Dai

2017

Mathematical Problems in Engineering

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“…Either (2+1)-dimensional soliton equations [1], [2] or (1+1) -dimensio -nal soliton equations [3], [4] can be decomposed into two compatible finite-dimensional integrable systems. It is known that a crucial idea in carrying out symmetry constraints is the nonlinearization of Lax pairs for soliton hierarchies.…”

Section: Introductionmentioning

confidence: 99%

Bargmann Symmetry Constraint and Binary Nonlinearization of Super Guo Hierarchy

Tao¹

2013

IJAPM

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Abstract-An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Guo hierarchy. Under the obtained symmetry constraint, the n-th flow of the super Guo hierarchy is decomposed into two super finite -dimensional integrable Hamiltonian systems, which defined over the super symmetry manifold R 4N|2N with the corresponding dynamical variables x and t n . The integrals of motion required for Liouville integrability are explicitly given.Index Terms-Symmetry constraint, binary nonlinearization, super guo hierarchy, super finitee-dimensional integrable hamiltonian systems. I. INTRODUCTIONFor almost twenty years, much attention has been paid to the construction of finite-dimensional integrable systems from soliton equations by using symmetry constraints. Either [19]. In this paper, we would like to consider the binary nonlinearization of the super Guo hierarchy. This paper is organized as follows. In the next section, we will recall the super Guo soliton hierarchy and its super Hamiltonian structure. Then in Section III, we compute a Bargmann symmetry constraint for the potential of the super Guo hierarchy. In Section IV, we apply the binary nonlinearization method to super Guo hierarchy, and then obtain super finite-dimensional integrable Hamiltonian hierarchy on the super symmetry manifold ℝ 4 |2 , whose integrals of motion are explicitly given. II. THE SUPER GUO HIERARCHYwhere is a spectral parameter, q and r are even variables, and and are odd variables(see [20] ). Taking If we setthen (2) Si-Xing TaoBargmann Symmetry Constraint and Binary Nonlinearization of Super Guo Hierarchy

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The constraint of the Kadomtsev-Petviashvili equation and its special solutions

Cited by 279 publications

References 10 publications

Spatio-Temporal Feature in Two-Wave and Multi-Wave Propagations

Spatio-Temporal Feature in Two-Wave and Multi-Wave Propagations

Theta Function Solutions of the 3 + 1‐Dimensional Jimbo‐Miwa Equation

Bargmann Symmetry Constraint and Binary Nonlinearization of Super Guo Hierarchy

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