Kruskal’s simplification scheme in ferrite dynamics

Lemoula, Romuald K.K.; Kamdem, Brice A.; Kuetche, Victor K.; Noule, Raïssa S.; Defo, Jean J.; Saliou, Youssoufa

doi:10.1063/5.0048791

Cited by 9 publications

(8 citation statements)

References 67 publications

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“…Noting that when N > 1, there are 2N functions a (j) 's and b (j) 's in the two algebraic equations of Eqs. (20). In order to obtain the additional 2N −2 algebraic equations, we consider the Taylor expansion T [N ] (λ 1 ) Φ 1 (λ 1 ) | {λ 1 →λ 1 +ε} at ε = 0 in the form of…”

Section: Generalized Dts Of System (1)mentioning

confidence: 99%

“…For the ultra-short waves in a ferrite, Refs. [17][18][19][20] have studied the complex Kraenkel-Manna-Merle system that reads…”

Section: Introductionmentioning

confidence: 99%

“…Influence of damping and inhomogeneous exchange effects of System (1) has been studied [18]. Painlevé integrability, Bäcklund transformation, bilinear form and one-soliton solutions of System (1) have been presented [19,20].…”

Section: Introductionmentioning

confidence: 99%

“…However, to our knowledge, N -fold and generalized Darboux transformations (DTs) of System (1), as well as some soliton solutions different from those in Refs. [17][18][19][20] have not been reported, where N is a positive integer. In Sect.…”

Section: Introductionmentioning

confidence: 99%

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Complex Kraenkel-Manna-Merle system in a ferrite: N-fold Darboux transformation, generalized Darboux transformations and solitons

Shen

Tian

Zhou

et al. 2023

Preprint

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Ferromagnetic materials such as the ferrites are used in the electronic and energy industries. Here, we concentrate on a complex Kraenkel-Manna-Merle system for the ultra-short waves in a ferrite. An N-fold Darboux transformation of that system is presented via an existing Lax pair, where N is a positive integer. A generalized (1, N − 1)- fold Darboux transformation, which admits one spectral parameter, and a generalized (m, N − m)-fold Darboux transformation, which admits m spectral parameters, are proposed based on that N-fold Darboux transformation, where m is a positive integer. One-, two- and three-soliton solutions of that system are determined via that N-fold Darboux transformation. Double-pole and triple-pole soliton solutions of that system are derived via that (1, N − 1)-fold Darboux transformation. Those solitons are graph- ically represented for the magnetization and external magnetic field related to a ferrite.

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Section: Generalized Dts Of System (1)mentioning

confidence: 99%

“…For the ultra-short waves in a ferrite, Refs. [17][18][19][20] have studied the complex Kraenkel-Manna-Merle system that reads…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Complex Kraenkel-Manna-Merle system in a ferrite: N-fold Darboux transformation, generalized Darboux transformations and solitons

Shen

Tian

Zhou

et al. 2023

Preprint

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“…Figure 7 shows the first-order breather via Solutions (18). In each period unit, the firstorder breather in Fig.…”

Section: Breather Solutions Of System (1)mentioning

confidence: 99%

Generalized (m, N − m)-fold Darboux transformation and localized waves of the complex Kraenkel-Manna-Merle system in a ferrite

Shen,

Tian,

Zhou

et al. 2023

Preprint

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In this paper, we focus on a complex Kraenkel-Manna-Merle system, which could characterize certain short waves in a ferrite. On the basis of the existing N-fold Darboux transformation, we have determined a generalized (m, N − m)-fold Darboux transformation which admits m spectral parameters, with N and m being the positive integers. Rogue-wave, breather and mixed wave solutions of that system are derived utilizing the generalized (m, N − m)-fold Darboux transformation. We show the first-order rogue wave with one hump and two valleys, as well as the first-order rogue wave with one hump and one valley. We obtain the second-order rogue wave and also show that the second-order rogue wave divides into three first-order rogue waves which are arranged in the triangle structure. We present the third-order rogue wave and observe that the third-order rogue wave divides into six first-order rogue waves which are arranged in the triangle and pentagonal structures. The first-order breather and interaction between the two first-order breathers are illustrated. In addition, we present the interactions between the first-order/second-order rogue wave and first-order breather.

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Dynamical Study of Newly Created Analytical Solutions, Bifurcation Analysis, and Chaotic Nature of the Complex Kraenkel–Manna–Merle System

Rani,

Kumar,

Kumar

2024

Qual. Theory Dyn. Syst.

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Kruskal’s simplification scheme in ferrite dynamics

Cited by 9 publications

References 67 publications

Complex Kraenkel-Manna-Merle system in a ferrite: N-fold Darboux transformation, generalized Darboux transformations and solitons

Complex Kraenkel-Manna-Merle system in a ferrite: N-fold Darboux transformation, generalized Darboux transformations and solitons

Generalized (m, N − m)-fold Darboux transformation and localized waves of the complex Kraenkel-Manna-Merle system in a ferrite

Dynamical Study of Newly Created Analytical Solutions, Bifurcation Analysis, and Chaotic Nature of the Complex Kraenkel–Manna–Merle System

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