Dynamical forms of breathers, rogue waves, lump and their interactions for Schrödinger–Hirota equation

Ali, Ahmad; Seadawy, Aly R.; Ahmed, Sarfaraz; Rizvi, Syed T. R.

doi:10.1007/s11082-023-04998-0

Cited by 12 publications

(2 citation statements)

References 39 publications

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“…Lump solutions with higher-order rational dispersion relations were provided [69]. While the focus was on lump solutions, the interplay between lump and soliton solutions under various conditions will be explored and breathers, rogue waves, and lump interactions for the Schrödinger-Hirota equation were discussed [70]. This research will be complemented by a detailed study of soliton interactions and stability in similar and extended models.…”

Section: Introductionmentioning

confidence: 99%

Exploring the dynamic interplay of intermodal and higher order dispersion in nonlinear negative index metamaterials

Veni,

Mani Rajan,

Biswas

et al. 2024

Phys. Scr.

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Our study delves into the intricate interplay of various factors within metamaterials, with afocus on modulation instability. Through our research, we elucidate the intricate dynamics involving intermodal dispersion, self-steepening effect, higher order dispersion, and plane wave amplitude,showcasing their competition and influence on modulation instability phenomena. We aim to explorethe impact of intermodal dispersion and higher-order effects by numerically solving the generalizednonlinear Schr¨odinger equation (NLSE), which models the propagation of a few-cycle pulse in a nonlinear metamaterial. Our modulation instability (MI) analysis captures the complex dynamics thesefactors introduce. We demonstrate the spatiotemporal evolution of MI under different parametervalues, revealing how these variations influence the instability’s development and characteristics.This approach provides a detailed understanding of the system’s behavior across various conditions,highlighting the roles of intermodal dispersion and higher-order effects. We demonstrate that thebehavior of modulation instability bands and their reliance on parameters such as self-steepeningand wave amplitude is contingent upon the specific characteristics of the optical setup and mediumdispersion properties.

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Section: Introductionmentioning

confidence: 99%

Exploring the dynamic interplay of intermodal and higher order dispersion in nonlinear negative index metamaterials

Veni,

Mani Rajan,

Biswas

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…The exact solution of an equation can help us understand the properties of an equation better. Therefore, it is vital to study the Schrödinger-Hirota equation [5,6,7,8,9]. Many scholars have obtained accurate solutions for Schrödinger-Hirota equation through generalized Kudryashov algorithm, modified simple equation method, Laplace-Adomian decomposition method, etc [10,11,12].…”

Section: Introductionmentioning

confidence: 99%

The exact solutions of Schrödinger-Hirota equation based on the extended auxiliary equation method

Du,

Yin,

Pang

2023

Preprint

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The Schr\"{o}dinger-Hirota equation are studied in light transmission, optical fiber communication, and nonlinear effects in optics. The extended fourth Jacobi elliptic equation is used in this paper to seek different types of exact solutions, which include bright soliton solutions, kink solutions, periodic wave solutions, and singular traveling wave solutions via selecting appropriate parameters.The characteristics of some solutions are graphically presented using two- and three-dimensional graphs such as the real part, the imaginary part, and their modulus via providing suitable values to arbitrary parameters. Compared to other methods, the method is more direct and easier for calculations.

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Optical soliton solutions of perturbed nonlinear Schrödinger equation with parabolic law nonlinearity

Arshed,

Akram,

Sadaf

et al. 2023

Opt Quant Electron

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Dynamical forms of breathers, rogue waves, lump and their interactions for Schrödinger–Hirota equation

Cited by 12 publications

References 39 publications

Exploring the dynamic interplay of intermodal and higher order dispersion in nonlinear negative index metamaterials

Exploring the dynamic interplay of intermodal and higher order dispersion in nonlinear negative index metamaterials

The exact solutions of Schrödinger-Hirota equation based on the extended auxiliary equation method

Optical soliton solutions of perturbed nonlinear Schrödinger equation with parabolic law nonlinearity

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