Investigation of wave solutions and conservation laws of generalized Calogero–Bogoyavlenskii–Schiff equation by group theoretic method

Jarad, Fahd; Jhangeer, Adil; Awrejcewicz, Jan; Riaz, Muhammad Bilal; Junaid-U-Rehman, M.

doi:10.1016/j.rinp.2022.105479

Cited by 22 publications

(3 citation statements)

References 26 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

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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

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“…The new auxiliary method 35 , 36 is a recently proposed method for solving challenging nonlinear PDEs. This method involves introducing an auxiliary variable and constructing a system of coupled equations involving both the original variables and the auxiliary variable.…”

Section: Introductionmentioning

confidence: 99%

Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms

Junaid-U-Rehman

Kudra

Awrejcewicz

2023

Sci Rep

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Nonlinear chains of atoms (NCA) are complex systems with rich dynamics, that influence various scientific disciplines. The lie symmetry approach is considered to analyze the NCA. The Lie symmetry method is a powerful mathematical tool for analyzing and solving differential equations with symmetries, facilitating the reduction of complexity and obtaining solutions. After getting the entire vector field by using the Lie scheme, we find the optimal system of symmetries. We have converted assumed PDE into nonlinear ODE by using the optimal system. The new auxiliary scheme is used to find the Travelling wave solutions, while graphical behaviour visually represents relationships and patterns in data or mathematical models. The multiplier method enables the identification of conservation laws, and fundamental principles in physics that assert certain quantities remain constant over time.

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“…The new auxiliary method [10,11] is a recently proposed method for solving challenging nonlinear PDEs. This method involves introducing an auxiliary variable and constructing a system of coupled equations involving both the original variables and the auxiliary variable.…”

Section: Introductionmentioning

confidence: 99%

Conservation Laws, Solitary Wave Solutions, and Lie Analysis for the Nonlinear Chains of Atoms

Rehman

Awrejcewicz

Kudra

2023

Preprint

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Nonlinear chains of atoms(NCA) are complex systems with rich dynamics, influencing various scientific disciplines. Lie symmetry approach is considered to analyze the NCA. The Lie symmetry method is a powerful mathematical tool for analyzing and solving differential equations with symmetries, facilitating the reduction of complexity and obtaining solutions. After getting the entire vector field by using the Lie scheme, we find the optimal system of symmetries. Using the optimal system we have converted assumed PDE into nonlinear ODE. The new auxiliary scheme introduces novel approaches to complement existing techniques, enhancing accuracy and simplifying computations. Travelling wave solutions describe wave-like propagation in systems, while graphical behavior visually represents relationships and patterns in data or mathematical models. The multiplier method enables the identification of conservation laws, fundamental principles in physics that assert certain quantities remain constant over time. Understanding these concepts contributes to a deeper comprehension of nonlinear chains of atoms and their dynamics, fostering advancements in related fields.

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Investigation of wave solutions and conservation laws of generalized Calogero–Bogoyavlenskii–Schiff equation by group theoretic method

Cited by 22 publications

References 26 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

Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms

Conservation Laws, Solitary Wave Solutions, and Lie Analysis for the Nonlinear Chains of Atoms

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