Analytical analysis of soliton propagation in microcavity wires

Khawaja, U. Al; Eleuch, Hichem; Bahlouli, H.

doi:10.1016/j.rinp.2018.11.019

Cited by 16 publications

(2 citation statements)

References 36 publications

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“…We can continue with the list but we mention a few. See more in , Adeyemo and Khalique (2023a), Adeyemo and Khalique (2023b), Al Khawajaa et al (2019), , Wazwaz (2017), , Ablowitz and Clarkson (1991), Adeyemo (2024), Jarad et al (2022), Khater et al (2021), Márquez et al (2023), Raza et al (2024), Khalique et al (2024), Adeyemo et al (2024), Pillay and Mason (2023), Mubai and Mason (2022), Kopcasız et al (2022), Kopcasız and Yasar (2023), Zahran et al (2024) and Rabie et al (2024). Now, having established the fact that no general technique in achieving various exact travelling wave results of NLNPDEQs has been found, mathematicians and physicists came up with some sound, effective, and efficient techniques lately so that the seemingly nagging problem could be nipped in the bud.…”

Section: Introductionmentioning

confidence: 99%

Noether symmetries, group analysis and soliton solutions of a (3+1)-dimensional generalized fifth-order Zakharov–Kuznetsov model with power, dual power laws and dispersed perturbation terms with real-world applications

Adeyemo,

Khalique,

Migranov

2024

Opt Quant Electron

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Highly important is a three-dimensional nonlinear partial differential equation because for many physical systems, one can, subject to suitable idealizations, formulate a differential equation that describes how the system changes in time. Thus, this article comprehensively reveals the investigation carried out on a (3+1)-dimensional generalized fifth-order Zakharov–Kuznetsov equation with power-law as well as dual power-law nonlinearities analytically, where the fifth-order term involved is regarded as a dispersion perturbation term. We utilize the well-celebrated Noether’s theorem to comprehensively construct conserved currents of the underlying equation. A detailed Lie group analysis of the understudied model consisting of power-law nonlinearities is further performed. This involves performing reductions of the underlying models using their Lie point symmetries. In consequence, various invariants are found. In addition, the equation reduces to diverse ordinary differential equations using its point symmetries and consequently diverse solutions of interest were achieved. Moreover, we derive some solitary wave solutions by invoking the newly introduced logistic function technique for some particular cases of the equation under consideration. In consequence, we achieve some exponential function solutions. In addition, the physical meaning of the results is put on the front burner by revealing the wave dynamics of these solutions via graphical depictions. Finally, the significance of the robust and detailed findings in the work are further corroborated with various real-world applications.

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Section: Introductionmentioning

confidence: 99%

Noether symmetries, group analysis and soliton solutions of a (3+1)-dimensional generalized fifth-order Zakharov–Kuznetsov model with power, dual power laws and dispersed perturbation terms with real-world applications

Adeyemo,

Khalique,

Migranov

2024

Opt Quant Electron

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“…For instance, to determine solitary, periodic, and compacton-like solutions, the exp-function approach is utilized [5] , a number of exact solutions for travelling waves may be produced by using the extended trial equation approach [6] , the voltage in transmission line issues can be observed by using different methods [7] , and it is also possible to build some non-topological solitons and closed-form solutions [8] . The phenomenon of travelling waves is widely investigated by means of the soliton theory which is an effective area of study for nonlinear partial differential equations like Kodomtsev–Petviashvili (KP) equation, the Schrodinger equation, Kundu-Eckhaus equation and many more that arise in disciplines like mathematical physics, nuclear physics, optics, and telecom engineering [9] , [10] , [11] . As a result, the researchers have created a wide range of analytical schemes to develop different type of solutions like the rational, rogue, breather, solitary, periodic, singular and optical wave solutions [12] .…”

Section: Introductionmentioning

confidence: 99%

Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach

Mahmood,

Srivastava,

Abbas

et al. 2023

Heliyon

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Diverse general solitary wave solutions and conserved currents of a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science

Adeyemo

2024

Math Methods in App Sciences

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This article presents an analytical investigation performed on a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science. To start with, achieving diverse solitary wave solutions to the generalized power‐law model involves using wave transformation, which reduces the model to a nonlinear ordinary differential equation. A direct integration approach is adopted to construct solutions in the beginning. This brings the emergence of interesting solutions like non‐topological solitons, trigonometric functions, exponential functions, elliptic functions, and Weierstrass functions in general structures. Besides, in a bid to secure more general exact solutions to the model, one adopts the extended Jacobi elliptic function expansion technique (for some specific cases of ). Thus, various cnoidal, snoidal, and dnoidal wave solutions to the understudied model are attained. The copolar trio explicated in a tabular form reveals that these solutions can be relapsed to various hyperbolic and trigonometric functions under certain criteria. Additionally, diverse graphical exhibitions of the dynamical attributes of the gained results are presented in a bid to have a sound understanding of the physical phenomena of the underlying model. Later, one gives the conserved vectors of the aforementioned equation by employing the standard multiplier approach.

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Analytical analysis of soliton propagation in microcavity wires

Cited by 16 publications

References 36 publications

Noether symmetries, group analysis and soliton solutions of a (3+1)-dimensional generalized fifth-order Zakharov–Kuznetsov model with power, dual power laws and dispersed perturbation terms with real-world applications

Noether symmetries, group analysis and soliton solutions of a (3+1)-dimensional generalized fifth-order Zakharov–Kuznetsov model with power, dual power laws and dispersed perturbation terms with real-world applications

Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach

Diverse general solitary wave solutions and conserved currents of a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science

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