Optical solitons and conservation laws for the concatenation model: Power–law nonlinearity

This paper investigates the significance of the dispersive concatenation model, incorporating the Kerr law of self-phase modulation in the presence of white noise. Our methodology relies on the enhanced direct algebraic method for integration. We reveal that intermediate solutions are expressed in terms of Jacobi's elliptic functions, leading to soliton solutions as the modulus of ellipticity approaches unity. This discovery culminates in the emergence of a diverse range of optical solitons. Our findings contribute novelty to the existing literature by offering insights into the behavior of optical solitons within the dispersive concatenation model, presenting a significant advancement in understanding this complex phenomenon.

Section: The Enhanced Direct Algebraic Method: a Quick Recapitulationmentioning

confidence: 99%

“…A considerable amount of results has been subsequently reported for this model during the past couple of years [6][7][8][9][10]. These include the retrieval of optical soliton solutions and the conservation laws that were recovered by means of multipliers approach.…”

Section: Introductionmentioning

confidence: 99%

Optical Solitons with Dispersive Concatenation Model Having Multiplicative White Noise by the Enhanced Direct Algebraic Method

Arnous,

Biswas,

Yildirim

et al. 2024

“…In its dimensionless representation, the perturbed edition of the concatenation model includes both STD and the white noise effect, as detailed in references [3][4][5][6][7][8][9]: iq aq bq c q q c q q q q q q q q q q q δ δ δ δ δ δ…”

Section: Governing Modelmentioning

confidence: 99%

“…In 2012, Ankiewicz et al introduced a new governing model that combines the nonlinear Schrödinger's equation (NLSE), Lakshmanan-Porsezian-Daniel (LPD) model, and the Sasa-Satsuma equation (SSE) [1][2]. Known as the concatenation model, it has yielded significant results in recent years, recovering and reporting optical solitons under Kerr law of self-phase modulation (SPM) and power-law of SPM [3][4][5][6][7][8][9]. These results include the retrieval of optical solitons using the method of undetermined coefficients, identification of conservation laws through the multiplier approach, discovery of quiescent solitons with nonlinear chromatic dispersion (CD), numerical analysis through Laplace-Adomian decomposition, and more.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Perturbation of Optical Solitons for the Concatenation Model with Power-Law of Self-Phase Modulation Having Multiplicative White Noise

Arnous,

Biswas,

Yildirim

et al. 2024

Addressing the concatenation model, this paper explores the incorporation of power-law self-phase modulation and spatio-temporal dispersion, in addition to the chromatic dispersion. The inclusion of the white noise effect, along with deterministic Hamiltonian perturbation terms of arbitrary intensity, is also examined. Two integration approaches are applied to recover the soliton solutions, leading to the observation that the white noise effect remains confined to the phase component of these solutions.

“…emerged. A few of the topics that have been touched base upon for the model are conservation laws, Painleve analysis, magneto-optic solitons, quiescent solitons for nonlinear chromatic dispersion, numerical analysis, bifurcation analysis, birefringent fibers, just to enlist a few [3][4][5][6][7][8]. While the previous round of bifurcation analysis of the model is with Kerr law of self-phase modulation (SPM), the current paper is a generalized version of the previous counterpart [6].…”

mentioning

confidence: 99%

Bifurcation Analysis and Chaotic Behavior of the Concatenation Model with Power-Law Nonlinearity

Tang,

Biswas,

Yildirim

et al. 2023

This paper presents a comprehensive analysis of the concatenation model with power-law nonlinearity. The research encompasses multiple key aspects, providing a detailed exploration of the model's behavior and implications within the context of nonlinear dynamics and optics. The study commences with an in-depth bifurcation analysis, aiming to unravel the intricate dynamics and transitions within the system. This analysis not only uncovers the system's behavior under varying conditions but also sheds light on its stability and the emergence of bifurcation phenomena. Our research delves into the retrieval of soliton solutions within the model. The exploration of solitons is of paramount significance, offering insights into localized, self-sustaining waveforms that often play a crucial role in nonlinear systems. These soliton solutions are identified, characterized, and their relevance to the model is established. The paper addresses the complex dynamics of the system in the presence of perturbation terms. By incorporating perturbations into the analysis, we elucidate how external influences impact the system's behavior and lead to chaotic phenomena. This analysis helps uncover the system's sensitivity to external factors and provides a deeper understanding of chaotic behavior.