Higher-order mixed solution and breather solution on a periodic background for the Kundu equation

Shi, Wei; Zhaqilao, Zhaqilao

doi:10.1016/j.cnsns.2023.107134

Cited by 5 publications

(2 citation statements)

References 39 publications

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“…The hybrid structures of solitons, lump solutions and rogue waves are constructed by using the Hirota bilinear method [26,27]. A hybrid structure of solitons and breathers is constructed [28]. Extended DT has been used to study hybrid rogue waves and breather waves [29][30][31], which can describe the interaction between the current-fed string and the external magnetic field and other physical phenomena [32].…”

Section: Introductionmentioning

confidence: 99%

Hybrid rogue waves and breather solutions on the double-periodic background for the Kundu-DNLS equation

Jiang,

Zhaqilao

2024

Commun. Theor. Phys.

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In this paper, by using Darboux transformation (DT) method and Taylor expansion method, a new nth-order determinant of the hybrid rogue waves and breathers solution on the double-periodic background of Kundu-DNLS equation is constructed when n is even. Breathers and rogue waves can be obtained from this determinant, respectively. Further, the hybrid rogue waves and breathers solutions on the different periodic background are given explicitly, including the single-periodic background, the double-periodic background and the plane wave background by selecting different parameters. In addition, the form of the obtained solutions is summarized.

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Section: Introductionmentioning

confidence: 99%

Hybrid rogue waves and breather solutions on the double-periodic background for the Kundu-DNLS equation

Jiang,

Zhaqilao

2024

Commun. Theor. Phys.

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“…The non-autonomous multi-rogue wave solutions of the spin-1 coupled nonlinear Gross–Pitaevskii equation with different dispersion, higher-order nonlinear terms, gain (or loss) and external potential are considered in 23 – 25 . The multiple breather solutions and mixed solutions of the Kundu equation are constructed with generalized Darboux transformation method, which have the Lax pair of Kaup–Newell system in 26 .…”

Section: Introductionmentioning

confidence: 99%

Soliton solution, breather solution and rational wave solution for a generalized nonlinear Schrödinger equation with Darboux transformation

Fan

2023

Sci Rep

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In this paper, the exact solutions of generalized nonlinear Schrödinger (GNLS) equation are obtained by using Darboux transformation(DT). We derive some expressions of the 1-solitons, 2-solitons and n-soliton solutions of the GNLS equation via constructing special Lax pairs. And we choose different seed solutions and solve the GNLS equation to obtain the soliton solutions, breather solutions and rational wave solutions. Based on these obtained solutions, we consider the elastic interactions and dynamics between two solitons.

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Dynamics of nonlinear dark waves and multi-dark wave interactions for a new extended (3+1)-dimensional Kadomtsev–Petviashvili equation

Zhong,

Tian,

Wang

et al. 2023

Nonlinear Dyn

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Higher-order mixed solution and breather solution on a periodic background for the Kundu equation

Cited by 5 publications

References 39 publications

Hybrid rogue waves and breather solutions on the double-periodic background for the Kundu-DNLS equation

Hybrid rogue waves and breather solutions on the double-periodic background for the Kundu-DNLS equation

Soliton solution, breather solution and rational wave solution for a generalized nonlinear Schrödinger equation with Darboux transformation

Dynamics of nonlinear dark waves and multi-dark wave interactions for a new extended (3+1)-dimensional Kadomtsev–Petviashvili equation

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