Non-Lie symmetry groups of (2+1)-dimensional nonlinear systems obtained from a simple direct method

Sen-Yue, Lou; Ma, Hongcai

doi:10.1088/0305-4470/38/7/l04

Cited by 131 publications

(86 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For many types of nonlinear systems the method can be used to find all possible similarity reductions. In [3], Lou and Ma modified the C-K direct method to find the generalized Lie and non-Lie symmetry groups for the well-known KP equation. Here we will use this modified direct method to discuss (1).…”

Section: Lie Symmetry Group Of the Nonisospectral Kp Equation Obtainementioning

confidence: 99%

“…Remark: In [3], Lou and Ma have obtained the full symmetry group of the complex KP equation. It can be divided into six sectors.…”

Section: Lie Symmetry Group Of the Nonisospectral Kp Equation Obtainementioning

confidence: 99%

“…David, Kamran, Levi and Winternitz [2] studied the Lie point symmetry group of the KP equation via the traditional Lie group approach. Lou and Ma [3] developed the direct method presented by Clarkson and Kruskal (C-K) [4] to construct the finite symmetry group of the KP equation. However, recently more and more people study the nonisospectral and variable coefficient generalizations of completely integrable nonlinear evolution equations.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Lie Symmetry Group of the Nonisospectral Kadomtsev-Petviashvili Equation

Chen

2009

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

The classical symmetry method and the modified Clarkson and Kruskal (C-K) method are used to obtain the Lie symmetry group of a nonisospectral Kadomtsev-Petviashvili (KP) equation. It is shown that the Lie symmetry group obtained via the traditional Lie approach is only a special case of the symmetry groups obtained by the modified C-K method. The discrete group analysis is given to show the relations between the discrete group and parameters in the ansatz. Furthermore, the expressions of the exact finite transformation of the Lie groups via the modified C-K method are much simpler than those obtained via the standard approach.

show abstract

Section: Lie Symmetry Group Of the Nonisospectral Kp Equation Obtainementioning

confidence: 99%

“…Remark: In [3], Lou and Ma have obtained the full symmetry group of the complex KP equation. It can be divided into six sectors.…”

Section: Lie Symmetry Group Of the Nonisospectral Kp Equation Obtainementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Lie Symmetry Group of the Nonisospectral Kadomtsev-Petviashvili Equation

Chen

2009

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

show abstract

“…For many types of nonlinear systems, the method can be used to find all the possible similarity reductions. Recently, Lou and Ma [11,12] generalized a new simple direct method basing on CK's method, which is much simpler than the traditional Lie-point symmetry group.…”

Section: Introductionmentioning

confidence: 99%

Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water

Tian¹

2016

PAMJ

View full text Add to dashboard Cite

Abstract:In this paper, a simple direct method is presented to find equivalence transformation of a nonlinear WhithamBroer-Kaup equations. Applying this equivalence transformation, we can obtain the symmetry group theorem of the Whitham-Broer-Kaup equations and then derive series of new exact and explicit solutions of the Whitham-Broer-Kaup equations according to solutions of the previous references.

show abstract

“…Especially, the Lie group technique is an important method in the nonlinear system fields. The classical Lie group approach [15], the non-classical Lie group approach [16] and the Clarkson-Kruskal (CK) direct method [17] are powerful and effective methods to obtain the explicit exact solutions [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of supersymmetric Burgers equation with Bosonization procedure

Ren

Gao

et al. 2015

Open Mathematics

View full text Add to dashboard Cite

Using bosonization approach, the N D 1 supersymmetric Burgers (SB) system is changed to a system of coupled bosonic equations. The difficulties caused by intractable anticommuting fermionic fields can be effectively avoided with the approach. By solving the coupled bosonic equations, the traveling wave solutions of the SB system can be obtained with the mapping and deformation method. Besides, the richness of the localized excitations of the supersymmetric integrable system is discovered. In the meanwhile, the similarity reduction solutions of the SB system are also studied with the Lie point symmetries theory.

show abstract

Non-Lie symmetry groups of (2+1)-dimensional nonlinear systems obtained from a simple direct method

Cited by 131 publications

References 15 publications

Lie Symmetry Group of the Nonisospectral Kadomtsev-Petviashvili Equation

Lie Symmetry Group of the Nonisospectral Kadomtsev-Petviashvili Equation

Exact and Explicit Solutions of Whitham-Broer-Kaup Equations in Shallow Water

Exact solutions of supersymmetric Burgers equation with Bosonization procedure

Contact Info

Product

Resources

About