Periodic propagation of complex-valued hyperbolic-cosine-Gaussian solitons and breathers with complicated light field structure in strongly nonlocal nonlinear media

Shen, Shuang; Yang, Zhenjun; Li, Xingliang

doi:10.1016/j.cnsns.2021.106005

Cited by 102 publications

(12 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The higher order SFB structures are observed in chaotic MI, with the characteristics of the noise induced peaks closely around analytic NLSE predictions [52]. In the literature, earlier works demonstrated that dynamic behaviors of localized solutions with different frame work [53][54][55][56][57][58][59][60][61]. However, numerical approach on nonautonomous rogue wave dynamics with modulation instability is not much focused.…”

Section: Introductionmentioning

confidence: 88%

Numerical investigation on nonautonomous optical rogue waves and Modulation Instability analysis for a nonautonomous system

Saravana Veni,

Mani Rajan,

Bertrand Tabi

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

In this paper, we report existence of optical rogue waves in the focussing non - autonomousnonlinear Schr ̈odinger equation (NLSE) through numerical studies of modulation instability (MI).The dynamics of non-autonomous rogue waves discussed and its associated modulation instabilitythrough linear stability analysis taken place followed by pulse splitting behaviour due to non -autonomous coefficient. We prove that the excitation of rogue waves with certain conditions in thebase band modulation instability regime. The above analysis of complex dynamics in terms of MIprocesses has allowed to experiments to excite the nonlinear superposition of rogue wave solutionsusing a modulated plane wave optical field injected into optical fiber which offer the evidence forexcitation of nonautonomous rogue waves in an inhomogeneous nonlinear medium. It is identifiedfrom the results frequency modulation on a wavefield induces modulation instability as a result ofrogue waves. We analyze the dependence of parameters coefficient of group velocity dispersion(GVD)and nonlinearity (α(z)) and non - autonomous coefficient (β(z)) and the instability of rogue waves.Our work suggests that the presence of non-autonomous coefficients can have a significant impacton the emergence of extreme events, particularly in relation to their self - steepening nature.

show abstract

Section: Introductionmentioning

confidence: 88%

Numerical investigation on nonautonomous optical rogue waves and Modulation Instability analysis for a nonautonomous system

Saravana Veni,

Mani Rajan,

Bertrand Tabi

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Inserting Equation (20) into Equation ( 2) gives the MSR with a double-kink solution to Equation (1):…”

Section: Msr With a Two-kink Solutionmentioning

confidence: 99%

“…For nonlinear partial differential equation (NLPDE) solutions, several techniques have been used in the literature. The pursuit of accurate NLPDE solutions is crucial for comprehending nonlinear physical phenomena [20][21][22][23][24][25][26]. For instance, kink-shaped tanh solutions and bell-shaped sech solutions are frequently used to simulate the nonlinear wave phenomena that are observed in optical fibers, fluid dynamics, and plasma [27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications

2023

View full text Add to dashboard Cite

We explore various analytical rational solutions with symbolic computation using the ansatz transformation functions. We gain a variety of rational solutions such as M-shaped rational solutions (MSRs), periodic cross-rationals (PCRs), multi-wave solutions, rational kink cross-solutions (RKCs), and homoclinic breather solutions (HBs), and by using the appropriate values for the relevant parameters, their dynamics are visualized in figures. Additionally, two different types of interactions between MSRs and kink waves are analyzed. Furthermore, we examine the stability of the obtained solutions and create a corresponding table. We analyze the stability of these solutions and the movement role of the wave by making graphs as two-dimensional, three-dimensional and density graphs as well as contour visual and stream plots.

show abstract

“…As far as the Lie approach is concerned, one may linearize the governing equations ( 28)- (31). There are many non-Lie procedures that are also available in the literature, for example, effective treatments of the non-linearity of differential equations have been reported in [32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Lie symmetry and exact homotopic solutions of a non-linear double-diffusion problem

Khan

Taj²,

Ahmed³

et al. 2023

Front. Phys.

View full text Add to dashboard Cite

The Lie symmetry method is applied, and exact homotopic solutions of a non-linear double-diffusion problem are obtained. Additionally, we derived Lie point symmetries and corresponding transformations for equations representing heat and mass transfer in a thin liquid film over an unsteady stretching surface, using MAPLE. We used these symmetries to construct new (Lie) similarity transformations that are different from those that are commonly used for flow and mass transfer problems. These new (Lie) similarity transformations map the partial differential equations of a mathematical model under consideration to ordinary differential equations along with boundary conditions. Lie similarity transformations are shown to lead to new solutions for the considered flow problem. These solutions are obtained using the homotopy analysis method to analytically solve the ordinary differential equations that resulted from the reduction of considered flow equations through Lie similarity transformations. With the aid of these solutions, effects of various parameters on the flow and heat transfer are discussed and presented graphically in this study.

show abstract

Periodic propagation of complex-valued hyperbolic-cosine-Gaussian solitons and breathers with complicated light field structure in strongly nonlocal nonlinear media

Cited by 102 publications

References 62 publications

Numerical investigation on nonautonomous optical rogue waves and Modulation Instability analysis for a nonautonomous system

Numerical investigation on nonautonomous optical rogue waves and Modulation Instability analysis for a nonautonomous system

Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficients and Their Applications

Lie symmetry and exact homotopic solutions of a non-linear double-diffusion problem

Contact Info

Product

Resources

About