N-lump and interaction solutions of localized waves to the (2+1)-dimensional generalized KDKK equation

Zhou, Xuejun; İlhan, Onur Alp; Manafian, Jalil; Singh, Gurpreet; Tuguz, Nalbiy Salikhovich

doi:10.1016/j.geomphys.2021.104312

Cited by 34 publications

(11 citation statements)

References 42 publications

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“…7. Interaction between the two first-order breathers via Solutions (19) under Constraints (3) with Next, we discuss some special cases of the second-order breather solutions as follows:…”

Section: The Higher-order Breather and Y/x-type Breather Solutions Fo...mentioning

confidence: 99%

“…Refs. [15][16][17][18][19][20][21][22][23][24][25][26] have considered a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (gKDKK) system in fluid mechanics and plasma physics,…”

Section: Introductionmentioning

confidence: 99%

“…The higher-order lump, breather and hybrid solutions for System (1) have been given [18]. Hybrid solutions of the localized waves for System (1) have been investigated [19]. Multiple-rogue-wave solutions for System (1) have been constructed [20].…”

Section: Introductionmentioning

confidence: 99%

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Bilinear form, Pfaffian, soliton and breather solutions for a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics

Cheng

Tian

Shen

et al. 2022

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In this paper, a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics is studied. Bilinear form under certain constraints is given via the Hirota method. The Nth-order Pfaffian solutions are proved via the Pfaffian technique, where N is a positive integer. N-soliton and the higher-order breather solutions are derived from the Nth-order Pfaffian solutions. Y/X-type solitons are constructed via adding some conditions to the N-soliton solutions. Elastic and inelastic interactions between the two solitons are presented graphically. Y/X-type breathers are constructed via adding some conditions to the higher-order breather solutions. Y-type breathers describe the inelastic interactions between the two breathers, and the X-type breathers describe the different two-breather structure. We investigate the influence of the coefficients in the system on those solitons and breathers as follows: the amplitudes of those solitons and breathers are related to l1 and l2; the periods of those breathers are related to l1, l2, l3 and l5, where l1, l2, l3 and l5 are the constant coefficients in the system.

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“…7. Interaction between the two first-order breathers via Solutions (19) under Constraints (3) with Next, we discuss some special cases of the second-order breather solutions as follows:…”

Section: The Higher-order Breather and Y/x-type Breather Solutions Fo...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bilinear form, Pfaffian, soliton and breather solutions for a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics

Cheng

Tian

Shen

et al. 2022

Preprint

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“…Feng et al studied periodic wave solutions and asymptotic behaviors [36]. Zhou et al gained N-lump and interaction solutions of localized waves [37].…”

Section: Introductionmentioning

confidence: 99%

Fission and Fusion Solutions to the (2+1)-Dimensional Generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt Equation Arising in Fluid Mechanics and Plasma Physics

Gao

Deng

2022

Preprint

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Fission and fusion are common phenomena in nature, they usually occur in physical and biological fields. In this paper, we will give new constraint to obtain fission and fusion solutions which have the shape of the letter Y . In combination with velocity resonance method, mode resonance method and long-wave limit method, we construct the interaction solutions of y-type molecules with soliton molecules, breather molecules and lump molecules respectively. We also obtain a novel solution containing a mixture of lump molecules, breather molecules and y-type molecules. At the same time, we analyze the dynamic behaviors of these interaction solutions and give the problems waiting to be solved.

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“…The fractional generalized CBS-BK equation is