Soliton behavior of algae growth dynamics leading to the variation in nutrients concentration

Seadawy, Aly R.; Younis, Muhammad; Iqbal, Muhammad Sajid; Baber, Muhammad Zafarullah; Rizvi, Syed T. R.; Raheem, Adil

doi:10.1016/j.jksus.2022.102071

Cited by 18 publications

(2 citation statements)

References 30 publications

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“…Substituting the Eqs. ( 4) with (5) into the regarding ODE and remove all the coefficients of φ will obtain a system of algebraic equations, from which we can get the parameters a j , = (j = 1, • • • , n) and η . Solving the algebraic equations, with the known solutions of Eq.…”

Section: Step IIImentioning

confidence: 99%

Analytical study of reaction diffusion Lengyel-Epstein system by generalized Riccati equation mapping method

Ahmed,

Baber,

Iqbal

et al. 2023

Sci Rep

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In this study, the Lengyel-Epstein system is under investigation analytically. This is the reaction–diffusion system leading to the concentration of the inhibitor chlorite and the activator iodide, respectively. These concentrations of the inhibitor chlorite and the activator iodide are shown in the form of wave solutions. This is a reactionâ€ “diffusion model which considered for the first time analytically to explore the different abundant families of solitary wave structures. These exact solitary wave solutions are obtained by applying the generalized Riccati equation mapping method. The single and combined wave solutions are observed in shock, complex solitary-shock, shock singular, and periodic-singular forms. The rational solutions also emerged during the derivation. In the Lengyel-Epstein system, solitary waves can propagate at various rates. The harmony of the system’s diffusive and reactive effects frequently governs the speed of a single wave. Solitary waves can move at a variety of speeds depending on the factors and reaction kinetics. To show their physical behavior, the 3D and their corresponding contour plots are drawn for the different values of constants.

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Section: Step IIImentioning

confidence: 99%

Analytical study of reaction diffusion Lengyel-Epstein system by generalized Riccati equation mapping method

Ahmed,

Baber,

Iqbal

et al. 2023

Sci Rep

Self Cite

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“…In this modern era of research, finding soliton solutions is an important field to describe the physical behavior of the nonlinear PDEs. There are many different techniques to find the soliton solutions such as G /G expansion method https://www.journals.vu.lt/nonlinear-analysis [4,31], first integral method [5], Kudryashov method [3,8], generalized logistic equation method [22,34], Riccati mapping method [2,33], φ 6 -model expansion method [27,35], He's variational method [20], generalized exponential rational function method [12], Hirota bilinear method [11], modified exponential rational functional method [1], a new auxiliary equation [28], Riccati-Bernoulli sub-ODE method [7,16,19], etc. But in this study, we apply the new modified extended direct algebraic method and the existence of the solutions on the bistable Allen-Cahn equation with quartic potential.…”

Section: Introductionmentioning

confidence: 99%

Analysis and soliton solutions of biofilm model by new extended direct algebraic method

Iqbal¹,

İnç

Sohail

et al. 2023

NAMC

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In this paper, the examination of soliton solutions of the biofilm model with the help of a new extended direct algebraic method is expressed. Besides the exact solutions, the existence of these solutions is also discussed with the help of the Schauder fixed point theorem. The nonlinear dynamical biofilm model which we consider in this paper is basically the bistable Allen–Cahn equation with quartic potential. For more physical understanding, the 3D plots of the solutions are presented. The different types of hyperbolic, trigonometric, and rational soliton solutions are gained. In the biofilm model, different parameters belong to certain spaces and give the exact solutions by applying the technique of new extended direct algebraic method. Exact solutions of the biofilm model are highlighted along with their restriction.

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Study of lump, rogue, multi, M shaped, periodic cross kink, breather lump, kink-cross rational waves and other interactions to the Kraenkel–Manna–Merle system in a saturated ferromagnetic material

et al. 2023

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Soliton behavior of algae growth dynamics leading to the variation in nutrients concentration

Cited by 18 publications

References 30 publications

Analytical study of reaction diffusion Lengyel-Epstein system by generalized Riccati equation mapping method

Analytical study of reaction diffusion Lengyel-Epstein system by generalized Riccati equation mapping method

Analysis and soliton solutions of biofilm model by new extended direct algebraic method

Study of lump, rogue, multi, M shaped, periodic cross kink, breather lump, kink-cross rational waves and other interactions to the Kraenkel–Manna–Merle system in a saturated ferromagnetic material

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