Residual symmetries of the modified Korteweg-de Vries equation and its localization

Liu, Ping; Li, Biao; Yang, Jing

doi:10.2478/s11534-014-0488-1

Cited by 2 publications

(1 citation statement)

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“…The Lie point symmetries of the extended system 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. [18][19][20][21] The concepts of consistent Riccati expansion (CRE) and CRE solvability were proposed in 2015. [22] A system having a CRE is then defined to be CRE solvable.…”

Section: Introductionmentioning

confidence: 99%

Bäcklund transformations, consistent Riccati expansion solvability, and soliton–cnoidal interaction wave solutions of Kadomtsev–Petviashvili equation*

et al. 2020

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The famous Kadomtsev–Petviashvili (KP) equation is a classical equation in soliton theory. A Bäcklund transformation between the KP equation and the Schwarzian KP equation is demonstrated by means of the truncated Painlevé 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.

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Section: Introductionmentioning

confidence: 99%

Bäcklund transformations, consistent Riccati expansion solvability, and soliton–cnoidal interaction wave solutions of Kadomtsev–Petviashvili equation*

et al. 2020

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Bosonized Supersymmetric Sawada–Kotera Equations: Symmetries and Exact Solutions*

Liu¹,

Zhang²,

Li³

2015

Commun. Theor. Phys.

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The Bosonized Supersymmetric Sawada–Kotera (BSSK) system is constructed by applying bosonization method to a Supersymmetric Sawada–Kotera system in this paper. The symmetries on the BSSK equations are researched and the calculation shows that the BSSK equations are invariant under the scaling transformations, the space-time translations and Galilean boosts. The one-parameter invariant subgroups and the corresponding invariant solutions are researched for the BSSK equations. Four types of reduction equations and similarity solutions are proposed. Period Cnoidal wave solutions, dark solitary wave solutions and bright solitary wave solutions of the BSSK equations are demonstrated and some evolution curves of the exact solutions are figured out.

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Residual symmetries of the modified Korteweg-de Vries equation and its localization

Cited by 2 publications

References 30 publications

Bäcklund transformations, consistent Riccati expansion solvability, and soliton–cnoidal interaction wave solutions of Kadomtsev–Petviashvili equation*

Bäcklund transformations, consistent Riccati expansion solvability, and soliton–cnoidal interaction wave solutions of Kadomtsev–Petviashvili equation*

Bosonized Supersymmetric Sawada–Kotera Equations: Symmetries and Exact Solutions*

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