Symmetries, associated first integrals and successive reduction of Schrödinger type and other second order difference equations

Hussain, A.; Kara, A. H.; Zaman, F. D.

doi:10.1016/j.ijleo.2023.171080

Cited by 18 publications

(7 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several approaches have been suggested, including the improved F-expansion method [7], the variational iteration method [8], the inverse scattering technique [9], the tanh-coth function technique [10], the Jacobi elliptic function expansion technique [11,12] and disciplines, and opened up new avenues. Many of the techniques created for the analysis of NLPDEs exhibit a level of sophistication that makes it challenging for many researchers to access them [14][15][16][17][18]. Today, in many different domains, including plasma physics, optics, biological systems, plasma physics, chemical systems, etc., NLPDEs are ubiquitous and have come to define them [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Dynamical features and traveling wave structures of the perturbed Fokas-Lenells equation in nonlinear optical fibers

Muhammad,

Abbas,

Hussain

et al. 2024

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

In this study, the new complex wave solutions of the perturbed Fokas-Lenells (p-FL) equation, which has applications in nonlinear optical fibers are obtained using a new extended direct algebraic method. This model represents recent electronic communications like Internet blogs, facebook communication and twitter comments. The obtained solutions are the different classes of traveling wave structures with singular solutions Type-I \& II, dark-singular, dark, and dark-bright solutions. Furthermore, stability conditions for the computed structures are reported. Also, graphical representations of some particular structures are shown by taking the specific values of the constants. The ordinary differential equation (ODE) obtained from a traveling wave transformation is converted into a dynamical system using Galilean transformation. The phase plane analysis is done for different values of the controlled parameters $d_1$ and $d_3$. A perturbation term is added to analyze the chaotic dynamics, and plots indicate that the system shows the chaotic dynamics. Also, sensitivity analysis shows that the system is sensitive to initial conditions. The conclusion is accounted for toward the end.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamical features and traveling wave structures of the perturbed Fokas-Lenells equation in nonlinear optical fibers

Muhammad,

Abbas,

Hussain

et al. 2024

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Notably, this approach maintains the symmetry structure inherent in differential equations, distinguishing it from alterations typically associated with differential equations in the presence of transforming lattices. There are some applications of these techniques in Hussain et al [15], Folly-Gbetoula et al [16,17], and [18,19]; in the latter, the conservation laws for the discrete sine-Gordon equation and discrete Liouville equation were thoroughly addressed. Also, some third order difference equations were studied using that technique.…”

Section: Introductionmentioning

confidence: 99%

First integrals, conserved vectors of nonlinear partial difference equations

Hussain,

Kara,

Zaman

2024

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

We perform a symmetry analysis of some nonlinear partial difference equations (nP$\triangle$Es), where the discrete version is obtained using some discretization approach. The discrete versions of the wave, diffusion, Fisher and Huxley equations are the subject of this research. At first, the initial invariance approach is the Lie symmetry approach. The first integrals technique that Hydon introduced to be used with discrete ordinary difference equations (O$\triangle$Es) serves as our inspiration in this situation. We develop a similar technique for generating the first integral vectors of the nP$\triangle$Es without recourse to symmetry generators.

show abstract

“…Many approaches have been applied in recent years to examine nonlinear problems. Some of these are the Jacobi elliptic function method [10][11][12], the sub-equation approach [13], the exponential rational function method [14], new extended direct algebraic method [15] as well as symmetry approaches [16][17][18][19][20][21], and others [22][23][24][25][26]. Solitons, which are nonlinear confined solitary waves that preserve their shape while traveling at a constant speed, are a part of numerous nonlinear physical systems.…”

Section: Introductionmentioning

confidence: 99%

Dispersive modified Benjamin-Bona-Mahony and Kudryashov-Sinelshchikov equations: non-topological, topological, and rogue wave solitons

Usman,

Hussain,

Ali

et al. 2024

International Journal of Mathematics and Computer in Engineering

View full text Add to dashboard Cite

This study delves into the exploration of three distinct envelope solitons within the nonlinear dispersive modified Benjamin Bona Mahony (NDMBBM) equation, originating from seismic sea waves, and the Kudryashov-Sinelshchikov (KS) equation. The solitons emerge naturally during the derivation process, and their existence is scrutinized using the ansatz approach. The findings reveal the presence of non-topological (bright), topological (dark) solitons, and rogue wave (singular) solitons, presenting significant applications in applied research and engineering. Additionally, two-dimensional and three-dimensional revolution plots are employed with varying parameter values to scrutinize the physical characteristics of these solitons.

show abstract

Symmetries, associated first integrals and successive reduction of Schrödinger type and other second order difference equations

Cited by 18 publications

References 7 publications

Dynamical features and traveling wave structures of the perturbed Fokas-Lenells equation in nonlinear optical fibers

Dynamical features and traveling wave structures of the perturbed Fokas-Lenells equation in nonlinear optical fibers

First integrals, conserved vectors of nonlinear partial difference equations

Dispersive modified Benjamin-Bona-Mahony and Kudryashov-Sinelshchikov equations: non-topological, topological, and rogue wave solitons

Contact Info

Product

Resources

About