Bright, dark, kink, singular and periodic soliton solutions of Lakshmanan–Porsezian–Daniel model by generalized projective Riccati equations method

Akram, Ghazala; Sadaf, Maasoomah; Arshed, Saima; Sameen, Fizza

doi:10.1016/j.ijleo.2021.167051

Cited by 60 publications

(3 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The traveling wave solution has applications in engineering, mathematical physics, plasma physics, and optical fibers has increased recently. It has been demonstrated that many nonlinear physical systems have traveling wave solutions such as combo-singular kink, single kink, cusp, rough, combined, and other types of solitons [29][30][31][32][33]. The traveling wave solutions of nonlinear physical models have been discovered by some authors using a variety of methods, including the extended G G2 ( ) ¢ -expansion approach [34], new general extended direct algebraic method [35], and many additional analytical methods [36].…”

Section: Introductionmentioning

confidence: 99%

Dynamical features and sensitivity visualization of thin-film Polarisation equation

Fatima,

Abbas,

Muhammad

2023

Phys. Scr.

View full text Add to dashboard Cite

The present investigation describes the dynamical behavior, multi-stability, and traveling wave solutions of thin-film polarisation equations (TFPE) which describes the propagation of waves in thin-film ferroelectric materials. The extended direct algebraic technique is used to construct the traveling wave patterns. Visual representations of a few randomly selected solutions are provided for physical comprehension. The ordinary differential equation can be expressed in the planar dynamical system using the Galilean transformation. Using various initial conditions for the unperturbed dynamical system, phase portraits with various sorts of trajectories are created. Additionally, the Runge-Kutta method is used to plot nonlinear periodic waves and super nonlinear waves. Additionally, the Hamiltonian function for this undisturbed dynamical system is computed and shown. It also included the source term with amplitude and frequency parameters for the chaotic and quasi-periodic behaviors, and the system is also stated in the non-autonomous form. For the dynamical system under investigation, multi-stability is also thoroughly described. Furthermore, a full inspection of the sensitivity of the perturbed dynamical structure under various initial conditions has been conducted.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamical features and sensitivity visualization of thin-film Polarisation equation

Fatima,

Abbas,

Muhammad

2023

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…The freak wave solutions of the nonlinear Schrödinger equation are determined using Darboux transformation combined with separation of variable method [ 18 ]. Two exact solution methods are applied on Lakshmanan-Porsezian-Daniel model to extract soliton solutions in [ 19 , 20 ]. The exp-function method is applied to solve some nonlinear partial differential equations (NLPDEs) [ 21 ].…”

Section: Introductionmentioning

confidence: 99%

Numerical simulations of the soliton dynamics for a nonlinear biological model: Modulation instability analysis

et al. 2023

Self Cite

View full text Add to dashboard Cite

This article deals with studying the dynamical behavior of the DNA model proposed by Peyrard and Bishop. The proposed model is investigated using the unified method (UM). Unified method successfully extracts solutions in the form of polynomial and rational functions. The solitary wave solutions and soliton solutions are constructed. An investigation of modulation instability is also presented in this paper. 3D and 2D plots are presented to exhibit the physical behavior of some of the obtained solutions.

show abstract

“…The LPD model is one of the significant evolution equations used in physics and other science fields. During the past few years, the LPD model has been investigated using different techniques such as the modified simple equation method [15], modified auxiliary equation method [16,17], extended trial equation technique [18], modified extended direct algebraic technique [19], improved Adomian decomposition technique [20], and generalized projective Riccati equation technique [21].In this study, the optical solitons of the LPD model are retrieved using the extended ( G′ G 2 )-expansion technique along with other traveling wave solutions. The LPD model is a useful model for the description of nonlinear waves through optical media in many real-life problems [15].…”

Section: Introductionmentioning

confidence: 99%

Dynamic investigation of the Laksmanan–Porsezian–Daniel model with Kerr, parabolic, and anti-cubic laws of nonlinearities

et al. 2022

Self Cite

View full text Add to dashboard Cite

The Laksmanan–Porsezian–Daniel model is one of the useful models used in nonlinear optics. The extended G′G2-expansion method is used to discuss the dynamical behavior of the proposed model. Many novel solitary wave solutions are obtained using the considered model. To deal with the nonlinearity of this model, three laws of nonlinearity are used, namely, Kerr law, parabolic law, and anti-cubic law. Three-dimensional surface, two-dimensional contour, density, and two-dimensional-line plots of some retrieved solutions are drawn using Maple software. The graphical simulations show the shape and structure of the wave profile corresponding to the obtained results.

show abstract

Bright, dark, kink, singular and periodic soliton solutions of Lakshmanan–Porsezian–Daniel model by generalized projective Riccati equations method

Cited by 60 publications

References 38 publications

Dynamical features and sensitivity visualization of thin-film Polarisation equation

Dynamical features and sensitivity visualization of thin-film Polarisation equation

Numerical simulations of the soliton dynamics for a nonlinear biological model: Modulation instability analysis

Dynamic investigation of the Laksmanan–Porsezian–Daniel model with Kerr, parabolic, and anti-cubic laws of nonlinearities

Contact Info

Product

Resources

About