Optical solitons with DNA dynamics arising in oscillator-chain of Peyrard–Bishop model

Hussain, A.; Usman, M.; Zaman, F. D.; Eldin, Sayed M.

doi:10.1016/j.rinp.2023.106586

Cited by 19 publications

(6 citation statements)

References 27 publications

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“…After plugging equation (12) into equation (10) and equating coefficients of various powers of ( ) r , we get a system of algebraic equations as given below:…”

Section: Implementation Of Methods To Fl Equationmentioning

confidence: 99%

“…Finding solutions to nonlinear problems is a difficult task. 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].…”

Section: Introductionmentioning

confidence: 99%

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

Muhammad,

Abbas,

Hussain

et al. 2024

Phys. Scr.

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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.

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“…After plugging equation (12) into equation (10) and equating coefficients of various powers of ( ) r , we get a system of algebraic equations as given below:…”

Section: Implementation Of Methods To Fl Equationmentioning

confidence: 99%

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

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“…The objective of this research is to showcase results and recent developments in the theory of evolution equations, encompassing both theoretical and practical aspects. Many researchers and mathematicians have suggested a variety of efficient methods 1 – 6 for finding exact solutions of nonlinear (NPDEs), such as Hirota’s bilinear method 7 , tanh function method 8 , the inverse scattering technique 9 , the Bäcklund transformation method 10 , modified variational iteration method 11 , the multiple exp-function approaches 12 , the Darboux transformation approach 13 , the Lie symmetry analysis 14 – 16 , the -expansion approach 17 , the Kudryashov technique 18 and the Jacobi elliptic technique 19 – 21 .…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of solitons of the (2+1)-dimensional Konopelchenko Dubrovsky system

Hussain,

Parveen,

Younis

et al. 2024

Sci Rep

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Utilizing nonlinear evolution equations (NEEs) is common practice to establish the fundamental assumptions underlying natural phenomena. This paper examines the weakly dispersed non-linear waves in mathematical physics represented by the Konopelchenko-Dubrovsky (KD) equations. The $$(G^\prime /G^2)$$ ( G ′ / G 2 ) -expansion method is used to analyze the model under consideration. Using symbolic computations, the $$(G^\prime /G^2)$$ ( G ′ / G 2 ) -expansion method is used to produce solitary waves and soliton solutions to the $$(2+1)$$ ( 2 + 1 ) -dimensional KD model in terms of trigonometric, hyperbolic, and rational functions. Mathematica simulations are displayed using two, three, and density plots to demonstrate the obtained solitary wave solutions’ behavior. These proposed solutions have not been documented in the existing literature.

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“…This technique effectively deals with nonlinear PDEs. This method has been used for the study of vast nonlinear problems, especially the study of micromorphic model 19 , Riabouchinsky Proudman Johnson equation 20 , generalized Pochhammer–Chree equation 21 , the Benney–Luke equation 22 , Peyrard–Bishop model 23 and many others 24 , 25 . The literature for the Lie symmetry analysis is well documented and one can see 26 – 28 .…”

Section: Introductionmentioning

confidence: 99%

Optimal system and dynamics of optical soliton solutions for the Schamel KdV equation

Hussain,

Chahlaoui,

Usman

et al. 2023

Sci Rep

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In this research, we investigate the integrability properties of the Schamel–Korteweg–de Vries (S-KdV) equation, which is important for understanding the effect of electron trapping in the nonlinear interaction of ion-acoustic waves. Using the optimal system, we come over reduced ordinary differential equations (ODEs). To deal with reduced ODEs for this problem, Lie symmetry analysis is combined with the modified auxiliary equation (MAE) procedure and the generalized Jacobi elliptic function expansion (JEF) method. The analytical solutions reported here are novel and have a wide range of applications in mathematical physics.

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Optical solitons with DNA dynamics arising in oscillator-chain of Peyrard–Bishop model

Cited by 19 publications

References 27 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

Dynamical behavior of solitons of the (2+1)-dimensional Konopelchenko Dubrovsky system

Optimal system and dynamics of optical soliton solutions for the Schamel KdV equation

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