Generalized optical soliton solutions to the (3+1)-dimensional resonant nonlinear Schrödinger equation with Kerr and parabolic law nonlinearities

Sedeeg, Abdelilah Kamal H.; Nuruddeen, Rahmatullah Ibrahim; Gómez-Aguilar, J. F.

doi:10.1007/s11082-019-1889-6

Cited by 32 publications

(8 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Different structures of oblique resonant optical solitons have been obtained by using the generalized exp ÀΦ ξ ðÞ ðÞ -expansion method. Furthermore, Sedeeg et al [28] studied the two models of 3D-RNLS equation given in (2) and (3) by applying the modified extended tanh method. Optical soliton solutions including dark, singular and combo solitons are extracted in addition to periodic solutions.…”

Section: Introductionmentioning

confidence: 99%

Resonant Optical Solitons in (3 + 1)-Dimensions Dominated by Kerr Law and Parabolic Law Nonlinearities

Al-Ghafri¹

2022

The Nonlinear Schrödinger Equation

View full text Add to dashboard Cite

This study investigates the optical solitons of of (3+1)-dimensional resonant nonlinear Schrödinger (3D-RNLS) equation with the two laws of nonlinearity. The two forms of nonlinearity are represented by Kerr law and parabolic law. Based on complex transformation, the traveling wave reduction of the governing model is derived. The projective Riccati equations technique is applied to obtain the exact solutions of 3D-RNLS equation. Various types of waves that represent different structures of optical solitons are extracted. These structures include bright, dark, singular, dark-singular and combined singular solitons. Additionally, the obliquity effect on resonant solitons is illustrated graphically and is found to cause dramatic variations in soliton behaviors.

show abstract

Section: Introductionmentioning

confidence: 99%

Resonant Optical Solitons in (3 + 1)-Dimensions Dominated by Kerr Law and Parabolic Law Nonlinearities

Al-Ghafri¹

2022

The Nonlinear Schrödinger Equation

View full text Add to dashboard Cite

show abstract

“…For example, the heat conduction NPE is a differential equation that describes the dispersion of atmospheric pollutant concentration, coastal salinity, and the law of fluid motion, while the delay NPE is also widely used, such as in the fields of population dynamics, ecology, and environmental science. The data simulation problems can be reduced to a delay NPE [ 1 ]. There are many variables in the NPE.…”

Section: Introductionmentioning

confidence: 99%

Multivariable Linear Algebraic Discretization of Nonlinear Parabolic Equations for Computational Analysis

Zuo¹,

Mei²

2022

Computational Intelligence and Neuroscience

View full text Add to dashboard Cite

Since the nonlinear parabolic equation has many variables, its calculation process is mostly an algebraic operation, which makes it difficult to express the discrete process concisely, which makes it difficult to effectively solve the two grid algorithm problems and the convergence problem of reaction diffusion. The extended mixed finite element method is a common method for solving reaction-diffusion equations. By introducing intermediate variables, the discretized algebraic equations have great nonlinearity. To address this issue, the paper proposes a multivariable linear algebraic discretization method for NPEs. First, the NPE is discretized, the algebraic form of the nonlinear equation is transformed into the vector form, and the rough set (RS) and information entropy (IE) are constructed to allocate the weights of different variable attributes. According to the given variable attribute weight, the multiple variables in the equation are discretized by linear algebra. It can effectively solve the two grid algorithm problems and the convergence problem of reaction diffusion and has good adaptability in this field.

show abstract

“…Korteweg-DeVries equation [14] can be a good example for dispersive waves. There are many equations developed for determining the wave behavior of a dynamical system [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. For a small intersection of a spatiotemporal system the dynamics can be assumed as linear.…”

Section: Introductionmentioning

confidence: 99%

Wave behaviors of Kundu–Mukherjee–Naskar model arising in optical fiber communication systems with complex structure

et al. 2021

View full text Add to dashboard Cite

Rogue waves are very mysterious and extra ordinary waves. They appear suddenly even in a calm sea and are hard to be predicted. Although nonlinear Schrödinger equation (NLS) provides a perspective, it alone can neither detect rogue waves nor provide a complete solution to problems. Therefore, some approximations are still mandatory for both obtaining an exact solution and predicting rogue waves. Such as Kundu-Mukherjee-Naskar (KMN) model which allows obtaining lump-soliton solutions considered as rogue waves. In this study the functional variable method is utilized to obtain the analytical solutions of KMN model that corresponds to the propagation of soliton dynamics in optical fiber communication system.

show abstract

Generalized optical soliton solutions to the (3+1)-dimensional resonant nonlinear Schrödinger equation with Kerr and parabolic law nonlinearities

Cited by 32 publications

References 30 publications

Resonant Optical Solitons in (3 + 1)-Dimensions Dominated by Kerr Law and Parabolic Law Nonlinearities

Resonant Optical Solitons in (3 + 1)-Dimensions Dominated by Kerr Law and Parabolic Law Nonlinearities

Multivariable Linear Algebraic Discretization of Nonlinear Parabolic Equations for Computational Analysis

Wave behaviors of Kundu–Mukherjee–Naskar model arising in optical fiber communication systems with complex structure

Contact Info

Product

Resources

About