Nonlocal symmetry and exact solutions of the (2+1)- dimensional breaking soliton equation

Cheng, Wenguang; Li, Biao; Chen, Yong

doi:10.1016/j.cnsns.2015.05.007

Cited by 45 publications

(20 citation statements)

References 32 publications

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“…In soliton theories [1][2][3][4][5][6][7][8], as a special kind of rational solution, rogue wave has been published in different fields since Solli et al first reported the existence of optical rogue wave in 2007 [9]. Its lethality is very strong and can lead to devastated impact on the navigation.…”

Section: Introductionmentioning

confidence: 99%

Lump Solutions and Resonance Stripe Solitons to the (2+1)-Dimensional Sawada-Kotera Equation

Wang

Chen

et al. 2017

Advances in Mathematical Physics

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Based on the symbolic computation, a class of lump solutions to the (2+1)-dimensional Sawada-Kotera (2DSK) equation is obtained through making use of its Hirota bilinear form and one positive quadratic function. These solutions contain six parameters, four of which satisfy two determinant conditions to guarantee the analyticity and rational localization of the solutions, while the others are free. Then by adding an exponential function into the original positive quadratic function, the interaction solutions between lump solutions and one stripe soliton are derived. Furthermore, by extending this method to a general combination of positive quadratic function and hyperbolic function, the interaction solutions between lump solutions and a pair of resonance stripe solitons are provided. Some figures are given to demonstrate the dynamical properties of the lump solutions, interaction solutions between lump solutions, and stripe solitons by choosing some special parameters.

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Section: Introductionmentioning

confidence: 99%

Lump Solutions and Resonance Stripe Solitons to the (2+1)-Dimensional Sawada-Kotera Equation

Wang

Chen

et al. 2017

Advances in Mathematical Physics

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“…The nonlocal symmetry (6) can be also obtained by using (5) and (4) [24,25] . The Schwarzian form (5) is invariant under the Möbious transformation [5] φ →…”

Section: Nonlocal Symmetry and Its Localization For Gardner Equationmentioning

confidence: 99%

“…It is obvious that (25) can be considered as an interaction solution between explicit solitary wave and the general Painlevé II wave. The generic solutions of PII (24) are transcendental.…”

Section: Similarity Reductions Related With Nonlocal Symmetrymentioning

confidence: 99%

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Symmetry reduction related with nonlocal symmetry for Gardner equation

Ren

2017

Communications in Nonlinear Science and Numerical Simulation

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“…The interaction solutions among solitons and other nonlinear excitations can be constructed by means of the nonlocal symmetry. 7,8 Those interaction solutions are rare studied in the supersymmetric integrable systems. 9 In this paper, the bosonization method is applied to the N = 1 supersymmetric mKdVB (SmKdVB) system.…”

Section: Introductionmentioning

confidence: 99%

Painlevé analysis, nonlocal symmetry and explicit interaction solutions for supersymmetric mKdVB equation

Ren

2016

AIP Advances

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The N=1 supersymmetric mKdVB system is transformed to a coupled bosonic system by using the bosonization approach. By a singularity structure analysis, the bosonized supersymmetric mKdVB (BSmKdVB) equation admits the Painlevé property. Starting from the standard truncated Painlevé method, the nonlocal symmetry for the BSmKdVB equation is obtained. To solve the first Lie’s principle related with the nonlocal symmetry, the nonlocal symmetry is localized to the Lie point symmetry by introducing multiple new fields. Thanks to localization processes, similarity reductions for the prolonged systems are studied by the Lie point symmetry method. The interaction solutions among solitons and other complicated waves including Painlevé II waves and periodic cnoidal waves are given through the reduction theorems. The soliton-cnoidal wave interaction solutions are explicitly given by using the mapping and deformation method. The concrete soliton-cnoidal interaction solutions are displayed both in analytical and graphical ways.

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Nonlocal symmetry and exact solutions of the (2+1)- dimensional breaking soliton equation

Cited by 45 publications

References 32 publications

Lump Solutions and Resonance Stripe Solitons to the (2+1)-Dimensional Sawada-Kotera Equation

Lump Solutions and Resonance Stripe Solitons to the (2+1)-Dimensional Sawada-Kotera Equation

Symmetry reduction related with nonlocal symmetry for Gardner equation

Painlevé analysis, nonlocal symmetry and explicit interaction solutions for supersymmetric mKdVB equation

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