Envelope solitons of the nonlinear discrete vertical dust grain oscillation in dusty plasma crystals

Houwe, Alphonse; Abbagari, Souleymanou; İnç, Mustafa; Betchewe, Gambo; Doka, Serge Y.; Crépin, Kofané Timoléon

doi:10.1016/j.chaos.2021.111640

Cited by 20 publications

(4 citation statements)

References 23 publications

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“…respectively. Substituting the constraints mentioned in proposition 2.1 into equation (5) and equation (6), and subsequently, after a lengthy computation, equation (4) will be obtained when  0  . Note that these calculations are so boring and tedious that they cannot be obtained correctly without the use of a computer.…”

Section: Double-pole Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Nonlinear partial differential equations are often used to model various phenomena in fields such as physics, chemistry, biology and even social sciences [1][2][3][4][5][6][7][8][9][10][11]. With the help of exact solutions, various nonlinear phenomena can be better explained [1][2][3][4][5][6][7]. The construction of exact solutions of nonlinear equations, especially soliton solutions [12][13][14], is one of the most important and essential tasks in nonlinear science.…”

Section: Introductionmentioning

confidence: 99%

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Multiple-pole solutions and degeneration of breather solutions to the focusing nonlinear Schrödinger equation

Zhang¹,

Chen²,

Guo³

2022

Commun. Theor. Phys.

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Based on Hirota’s method, the multiple-pole solutions of the focusing Schrödinger equation are derived directly by introducing some new ingenious limit methods. We have carefully investigated these multi- pole solutions from three perspectives: rigorous mathematical expressions, vivid images, and asymp- totic behavior. Moreover, there are two kinds of interactions between multi-pole solutions: when two multiple-pole solutions have different velocities, they will collide for a short time; when two multiple- pole solutions have very close velocities, a long time coupling will occur. The last important point is that this method of obtaining multiple-pole solutions can also be used to derive degeneration of N-breather solutions. The method mentioned in this paper can be extended to derivative Schr¨odinger equation, Sine-Gorden equation, mKdV equation and so on.

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Section: Double-pole Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multiple-pole solutions and degeneration of breather solutions to the focusing nonlinear Schrödinger equation

Zhang¹,

Chen²,

Guo³

2022

Commun. Theor. Phys.

View full text Add to dashboard Cite

show abstract

“…The use of various mathematical tools has led to the discovery of diverse exact solutions of NLEEs, which find application in fields such as organic chemistry, biology, fluid mechanics, population dynamics, space technology, hydrodynamics, engineering methodology, theory of Bose-Einstein condensates, computer engineering, solid-state physics and applied mathematics. Numerous solitary wave solutions have been discovered for nonlinear partial differential equations, especially in fields related to physics, including nonlinear optics, plasma theory and fluid mechanics [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Novel Optical bi-directional solutions to the new dual-mode derivative nonlinear Schrödinger equation

Alam,

Javid

2023

Phys. Scr.

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In recent times, a novel category of nonlinear physical models known as dual-mode nonlinear equations has emerged. These equations include various real-valued dual-mode equations linked to widely-known single-mode equations like KdV, mKdV, Schrödinger and Burger's. Extensive research has been conducted to establish and investigate these equations. This study presents a novel dual-mode derivative nonlinear Schrödinger equation that incorporates new parameters for dissipative effects, nonlinearity, and interaction phase velocity. Various methods such as the tanh-coth scheme, extended exponential method, Kudryashov-scheme, and the sine-cosine function methods are employed to investigate the solutions of the model. The obtained solutions are illustrated through graphical 2D and 3D and to demonstrate their dynamics and shapes. Furthermore, the interaction of the dual-waves is correlated with changes in the phase-velocity parameter. This model describes propagation of two simultaneously directional waves instead of as in standard Schrödinger equation. For the propagation of solitons in nonlinear optics, the solutions found in this study have important significance. All the resulting solutions can help to comprehend the underlying mechanisms for numerous nonlinear phenomena in diverse domains, including nonlinear optics, plasma physics, Bose-Einstein condensates and others.

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Breather-like soliton, M-shaped profile, W-shaped profile, and modulation instability conducted by self-frequency shift of the nonlinear Schrödinger equation

2022

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Envelope solitons of the nonlinear discrete vertical dust grain oscillation in dusty plasma crystals

Cited by 20 publications

References 23 publications

Multiple-pole solutions and degeneration of breather solutions to the focusing nonlinear Schrödinger equation

Multiple-pole solutions and degeneration of breather solutions to the focusing nonlinear Schrödinger equation

Novel Optical bi-directional solutions to the new dual-mode derivative nonlinear Schrödinger equation

Breather-like soliton, M-shaped profile, W-shaped profile, and modulation instability conducted by self-frequency shift of the nonlinear Schrödinger equation

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