Supersymmetric modified Korteweg–de Vries equation: bilinear approach

Liu, Q. P.; Hu, Xing−Biao; Zhang, Meng-Xia

doi:10.1088/0951-7715/18/4/009

Cited by 71 publications

(62 citation statements)

References 17 publications

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“…As a direct method, Hirota's bilinear method [15] proposed in 1971 has been widely used to construct multi-soliton solutions of many nonlinear PDEs like those in [5,16,29,32,45,62,63,65]. Besides, Hirota's bilinear method [15] and Darboux transformation [31] are two of the most powerful techniques for constructing rogue-wave solutions [6,28,50] of nonlinear PDEs.…”

Section: Introductionmentioning

confidence: 99%

Bilinearization and new soliton solutions of Whitham-Broer-Kaup equations with time-dependent coefficients

Zhang¹,

Wang²

2017

J. Nonlinear Sci. Appl.

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In this paper, Whitham-Broer-Kaup (WBK) equations with time-dependent coefficients are exactly solved through Hirota's bilinear method. To be specific, the WBK equations are first reduced into a system of variable-coefficient Ablowitz-KaupNewell-Segur (AKNS) equations. With the help of the AKNS equations, bilinear forms of the WBK equations are then given. Based on a special case of the bilinear forms, new one-soliton solutions, two-soliton solutions, three-soliton solutions and the uniform formulae of n-soliton solutions are finally obtained. It is graphically shown that the dynamical evolutions of the obtained one-, two-and three-soliton solutions possess time-varying amplitudes in the process of propagations.

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Section: Introductionmentioning

confidence: 99%

Bilinearization and new soliton solutions of Whitham-Broer-Kaup equations with time-dependent coefficients

Zhang¹,

Wang²

2017

J. Nonlinear Sci. Appl.

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“…As a direct method, Hirota's bilinear method [13] has been widely used to construct multi-soliton solutions of many nonlinear PDEs [23][24][25][26][27][28][29][30][31][32][33][34]. However, there is very little research work in extending Hirota's bilinear method for a whole hierarchy of nonlinear PDEs (see.…”

Section: Introductionmentioning

confidence: 99%

Bilinearization and new multi-soliton solutions of mKdV hierarchy with time-dependent coefficients

Zhang

2016

Open Physics

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In this paper, Hirota's bilinear method is extended to a new modi ed Kortweg-de Vries (mKdV) hierarchy with time-dependent coe cients. To begin with, we give a bilinear form of the mKdV hierarchy. Based on the bilinear form, we then obtain one-soliton, two-soliton and three-soliton solutions of the mKdV hierarchy. Finally, a uniform formula for the explicit N-soliton solution of the mKdV hierarchy is summarized. It is graphically shown that the obtained soliton solutions with time-dependent functions possess time-varying velocities in the process of propagation.

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“…Supersymmetric systems provide more proli c elds for mathematical and physical researchers. They exhibit the Painlevé property, the Lax representation, an innite number of conservation laws, the Bäcklund the Darboux transformations, bilinear forms and multi-soliton solutions [9][10][11][12][13][14][15]26]. However to treat the integrable systems with fermions, such as the supersymmetric integrable systems and pure integrable fermionic systems, is much more complicated than to study the integrable pure bosonic systems [17].…”

Section: Introductionmentioning

confidence: 99%

Painlevé analysis and exact solutions of bosonized N = 1 supersymmetric Burgers equation

Ren

2015

Open Physics

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Based on the bosonization approach, the N = supersymmetric Burgers (SB) system is transformed to a coupled pure bosonic system. The Painlevé property and the Bäcklund transformations (BT) of the bosonized SB (BSB) system are obtained through standard singularity analysis. Explicit solutions such as the muti-solitary waves and error function waves are provided for the BT. The exact solutions of the BSB system are obtained from the generalized tanh expansion method.

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Supersymmetric modified Korteweg–de Vries equation: bilinear approach

Abstract: A proper bilinear form is proposed for the N = 1 supersymmetric modified Korteweg-de Vries equation. The bilinear Bäcklund transformation for this system is constructed. As applications, some solutions are presented for it.

Cited by 71 publications

References 17 publications

Bilinearization and new soliton solutions of Whitham-Broer-Kaup equations with time-dependent coefficients

Bilinearization and new soliton solutions of Whitham-Broer-Kaup equations with time-dependent coefficients

Bilinearization and new multi-soliton solutions of mKdV hierarchy with time-dependent coefficients

Painlevé analysis and exact solutions of bosonized N = 1 supersymmetric Burgers equation

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