A study of the generalized nonlinear advection-diffusion equation arising in engineering sciences

Adeyemo, Oke Davies; Motsepa, Tanki; Khalique, Chaudry Masood

doi:10.1016/j.aej.2021.04.066

Cited by 29 publications

(4 citation statements)

References 44 publications

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“…Fluid mechanics is a branch of physics concerning the mechanics of fluids such as liquids, gases, and plasmas and the forces on them. Applications of fluid mechanics are found in a wide range of disciplines which include civil, chemical, mechanical as well as biomedical engineering, geophysics, oceanography, astrophysics, biology and meteorology [1][2][3][4][5]. Nonlinear partial differential equations (NLPDE) in the fields of mathematics and physics play numerous important roles in theoretical sciences.…”

Section: Introductionmentioning

confidence: 99%

“…Such phenomena occur in oceanography, the aerospace industry, meteorology, nonlinear mechanics, biology, population ecology, plasma physics and fluid mechanics, to mention a few. In [1] the authors studied a generalized advection-diffusion equation which is a nonlinear partial differential equation in fluid mechanics, characterizing the motion of a buoyancy propelled plume in a bent-on absorptive medium. Moreover, in [2], a generalized Korteweg-de Vries-Zakharov-Kuznetsov equation was studied.…”

Section: Introductionmentioning

confidence: 99%

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Bifurcation Theory, Lie Group-Invariant Solutions of Subalgebras and Conservation Laws of a Generalized (2+1)-Dimensional BK Equation Type II in Plasma Physics and Fluid Mechanics

2022

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The nonlinear phenomena in numbers are modelled in a wide range of fields such as chemical physics, ocean physics, optical fibres, plasma physics, fluid dynamics, solid-state physics, biological physics and marine engineering. This research article systematically investigates a (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation. We achieve a five-dimensional Lie algebra of the equation through Lie group analysis. This, in turn, affords us the opportunity to compute an optimal system of fourteen-dimensional Lie subalgebras related to the underlying equation. As a consequence, the various subalgebras are engaged in performing symmetry reductions of the equation leading to many solvable nonlinear ordinary differential equations. Thus, we secure different types of solitary wave solutions including periodic (Weierstrass and elliptic integral), topological kink and anti-kink, complex, trigonometry and hyperbolic functions. Moreover, we utilize the bifurcation theory of dynamical systems to obtain diverse nontrivial travelling wave solutions consisting of both bounded as well as unbounded solution-types to the equation under consideration. Consequently, we generate solutions that are algebraic, periodic, constant and trigonometric in nature. The various results gained in the study are further analyzed through numerical simulation. Finally, we achieve conservation laws of the equation under study by engaging the standard multiplier method with the inclusion of the homotopy integral formula related to the obtained multipliers. In addition, more conserved currents of the equation are secured through Noether’s theorem.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bifurcation Theory, Lie Group-Invariant Solutions of Subalgebras and Conservation Laws of a Generalized (2+1)-Dimensional BK Equation Type II in Plasma Physics and Fluid Mechanics

2022

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“…For instance, the wave phenomena which has been observed in high-energy physics, biophysics, fluid mechanics, chemical kinematics as well as in optical fibres [25]. Nonetheless, nonlinear processes are not easy to control and have surfaced as one of the basic challenges because the nonlinear characteristic of the system changes sharply under small alteration of valid parameters that include time [26]. Hence, this makes the issue to be more intricate and consequently requires an ultimate solution.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, this makes the issue to be more intricate and consequently requires an ultimate solution. The study of exact explicit solutions for diverse soliton equations has become very significant in modern mathematics with ramifications to so many areas of physics, mathematics, as well as other sciences [10][11][12][13]26]. Some NPDEs can be solved with the use of different mathematical techniques.…”

Section: Introductionmentioning

confidence: 99%

Soliton solutions, travelling wave solutions and conserved quantities for a three-dimensional soliton equation in plasma physics

Khalique¹,

Adeyemo²

2021

Commun. Theor. Phys.

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Many physical systems can be successfully modelled using equations that admit the soliton solutions. In addition, equations with soliton solutions have a significant mathematical structure. In this paper, we study and analyze a three-dimensional soliton equation, which has applications in plasma physics and other nonlinear sciences such as fluid mechanics, atomic physics, biophysics, nonlinear optics, classical and quantum fields theories. Indeed, solitons and solitary waves have been observed in numerous situations and often dominate long-time behaviour. We perform symmetry reductions of the equation via the use of Lie group theory and then obtain analytic solutions through this technique for the very first time. Direct integration of the resulting ordinary differential equation is done which gives new analytic travelling wave solutions that consist of rational function, elliptic functions, elementary trigonometric and hyperbolic functions solutions of the equation. Besides, various solitonic solutions are secured with the use of a polynomial complete discriminant system and elementary integral technique. These solutions comprise dark soliton, doubly-periodic soliton, trigonometric soliton, explosive/blowup and singular solitons. We further exhibit the dynamics of the solutions with pictorial representations and discuss them. In conclusion, we contemplate conserved quantities for the equation under study via the standard multiplier approach in conjunction with the homotopy integral formula. We state here categorically and emphatically that all results found in this study as far as we know have not been earlier obtained and so are new.

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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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A study of the generalized nonlinear advection-diffusion equation arising in engineering sciences

Cited by 29 publications

References 44 publications

Bifurcation Theory, Lie Group-Invariant Solutions of Subalgebras and Conservation Laws of a Generalized (2+1)-Dimensional BK Equation Type II in Plasma Physics and Fluid Mechanics

Bifurcation Theory, Lie Group-Invariant Solutions of Subalgebras and Conservation Laws of a Generalized (2+1)-Dimensional BK Equation Type II in Plasma Physics and Fluid Mechanics

Soliton solutions, travelling wave solutions and conserved quantities for a three-dimensional soliton equation in plasma physics

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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