The Gaussian soliton in the Fermi–Pasta–Ulam chain

Liu, Cheng-shi

doi:10.1007/s11071-021-06879-1

Cited by 21 publications

(2 citation statements)

References 34 publications

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“…[30,31], we can get new solutions, they are singular rational patterns and elliptic function patterns. This method is proposed by Liu [32][33][34][35][36][37][38][39] and are widely used to solve exact solutions of mathematical physics equations [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55]. From the new patterns we obtained, we can better understand the dynamic behaviors of the model.…”

Section: Introductionmentioning

confidence: 99%

Optical solitons of Sasa-Satsuma model in birefringent fibers

Zhang¹

2022

Preprint

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This paper studies the propagation of optical solitons of the Sasa-Satsuma model in birefringent fibers. By the complete discrimination system for polynomial, we get three types of optical wave patterns for the model, where singular rational patterns and elliptic functions double periodic patterns are new propagation patterns. Besides, we show the temporal-space structures and propagation properties for some patterns with specific parameter values by drawing graphs.

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Section: Introductionmentioning

confidence: 99%

Optical solitons of Sasa-Satsuma model in birefringent fibers

Zhang¹

2022

Preprint

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“…Landau or radiation cannot damper the vibration; similarly, the Coulomb relation cannot dampen the frequency fluctuations of oscillations at extreme intervals [8,9]. Plasma destruction allows the release of condensing disturbances, resolving the Langmuir turbulence discharge amplitude problem and improving the graphical representation of Langmuir turbulence [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Faster and Slower Soliton Phase Shift: Oceanic Waves Affected by Earth Rotation

Khater

Alabdali

2021

Mathematics

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This research paper investigates the accuracy of a novel computational scheme (Khater II method) by applying this new technique to the fractional nonlinear Ostrovsky (FNO) equation. The accuracy of the obtained solutions was verified by employing the Adomian decomposition (AD) and El Kalla (EK) methods. The AD and EK methods are considered as two of the most accurate semi-analytical schemes. The FNO model is a modified version of the well-known Korteweg–de Vries (KdV) equation that considers the effects of rotational symmetry in space. However, in the KdV model, solutions to the KdV equations substitute this effect with radiating inertia gravity waves, and thus this impact is ignored. The analytical, semi-analytical, and accuracy between solutions are represented in some distinct plots. Additionally, the paper’s novelty and its contributions are demonstrated by comparing the obtained solutions with previously published results.

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Optical solitons, qualitative analysis, and chaotic behaviors to the highly dispersive nonlinear perturbation Schrödinger equation

Chen

2024

Math Methods in App Sciences

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In this paper, we study the highly dispersive nonlinear perturbation Schrödinger equation, which has arbitrary form of Kudryashov's with sextic‐power law refractive index and generalized nonlocal laws. For the equation has highly dispersive nonlinear terms and higher order derivatives, it cannot be integrated directly, so we build an integrable factor equation for the approximated equation and apply the trial equation method and the complete discrimination system for polynomial method to create new soliton solutions. On the other hand, we use the bifurcation theory to qualitatively analyze the equation and find the model has periodic solutions, bell‐shaped soliton solutions, and solitary wave solutions via phase diagrams. The topological stability of the solutions with respect to the parameters is explored in order to better understand the effect of parameters perturbations on the stability of the model's solutions. Furthermore, we analyze the modulation instability and give the corresponding linear criterion. After accounting for external perturbation terms, we analyze the chaotic behaviors of the equation through the largest Lyapunov exponents and phase diagrams.

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The Gaussian soliton in the Fermi–Pasta–Ulam chain

Cited by 21 publications

References 34 publications

Optical solitons of Sasa-Satsuma model in birefringent fibers

Optical solitons of Sasa-Satsuma model in birefringent fibers

Faster and Slower Soliton Phase Shift: Oceanic Waves Affected by Earth Rotation

Optical solitons, qualitative analysis, and chaotic behaviors to the highly dispersive nonlinear perturbation Schrödinger equation

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