New kinds of analytical solitary wave solutions for ionic currents on microtubules equation via two different techniques

Khater, Mostafa M. A.; Jhangeer, Adil; Rezazadeh, Hadi; Akinyemi, Lanre; Akbar, M. Ali; Ahmad, Harith

doi:10.1007/s11082-021-03267-2

Cited by 61 publications

(10 citation statements)

References 54 publications

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“…After substituting equation (25) along with (26) in equation (24), we get an algebraic system by equating the coefficients of distinct powers of ( )…”

Section: Exact Solutions For the Gpre Methods With Graphical Represen...mentioning

confidence: 99%

“…Various techniques and methods are available for obtaining accurate soliton solutions in non-linear PDEs. These methodologies encompass a variety of approaches, including the unified auxiliary equation method used by Mathanaranjan et al [22], the sine-Gordon expansion method [23], the simple extended [24], the bilinear neural network method [25], variational iteration techniques [26], the extended exponential function technique [27], the power series methodology [28], the Hirota bilinear technique [29]. Numerous others [30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

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Formation of solitary waves solutions and dynamic visualization of the nonlinear schrödinger equation with efficient techniques

Majid,

Asjad,

Faridi

2024

Phys. Scr.

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This article investigates the non-linear generalized geophysical KdV equation, which describes shallow water waves in an ocean. The proposed generalized projective Riccati equation method and modified auxiliary equation method extract a more efficient and broad range of soliton solutions. These include U-shaped, W-shaped, singular, periodic, bright, dark, kink-type, breather soliton, multi-singular soliton, singular soliton with high amplitude, multiple periodic, multiple lump wave soliton, and flat kink-type soliton solutions. The travelling wave patterns of the model are graphically presented with suitable parameter values using the modern software Maple and Wolfram Mathematica. The visual representation of the solutions in 3D, 2D, and contour surfaces enhances understanding of parameter impact. Sensitivity and modulation instability analyses were performed to offer insights into the dynamics of the examined model. The observed dynamics of the proposed model were presented, revealing quasi-periodic chaotic, periodic systems, and quasi-periodic behaviour. This analysis confirms the effectiveness and reliability of the method employed, demonstrating its applicability in discovering travelling wave solitons for a wide range of nonlinear evolution equations.

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“…After substituting equation (25) along with (26) in equation (24), we get an algebraic system by equating the coefficients of distinct powers of ( )…”

Section: Exact Solutions For the Gpre Methods With Graphical Represen...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Formation of solitary waves solutions and dynamic visualization of the nonlinear schrödinger equation with efficient techniques

Majid,

Asjad,

Faridi

2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…where a 2 , a 0 , a 2 , b 1 , ψ 0 , α 0 , α 1 , α 2 are variable. As a result, using all of the above determined values, equation (10) produces…”

Section: Collision Between Lump Wave and Strip Solitonmentioning

confidence: 99%

“…Using modern computer programmes like Mathematica, Maple, or Matlab, many travelling wave solutions have been estimated in scientific papers [6][7][8]. They appeared to be many ways to study the dynamical structures of many prominent nonlinear models, including the extended adaptive auxiliary equation mapping approach [9], the extended simple equation approach [10], the logistic equation method [11], the direct perturbation method [12], the Kudryashov method [13], the inverse scattering method [14], the exp (−f(ξ)) expansion method [15], the tanh method [16], the Hirota bilinear method [17], the generalised exponential rational function method [18], the exp-function method [19], the extended direct algebraic technique with modifications [20], and the homogeneous balancing method.…”

Section: Introductionmentioning

confidence: 99%

Lumps, solitons and stability analysis for the (3 + 1)-dimensional fractional potential-YTSF-like model in weakly dispersive medium

Badshah,

Tariq,

Wazwaz

et al. 2023

Phys. Scr.

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In this study, the fractional (3 + 1)-dimensional potential Yu-Toda-Sasa-Fukuyama (YTSF)-like model is being investigated analytically and semi-analytically. The given model is converted into a bilinear form using the Hirota bilinear method. Which refers to the development of lump waves, collisions between lump waves and periodic waves, collisions between lump waves and single- and double-kink soliton solutions, and collisions between lump, periodic, and single- and double-kink soliton solutions. Furthermore, the Adomian technique and the modified extended Tanh function technique are applied to obtain several forms of innovative combinations for the governing dynamical fractional model. In addition, it has been confirmed that the established results are stable, and it has been helpful to validate the calculations. Moreover, multiple intriguing exact solutions are utilized to illustrate the physical nature of 3D, contour, and 2D graphs. A collection of bright, dark, periodic, rational, and elliptic function solutions are obtained for the solution.

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“…There are multiple approaches andschemessuch as the sine-Gordon expansion scheme [26], the Kudryashov method [27], the simply extended equation method [28] and the bilinear neural network technique [29],…”

Section: Introductionmentioning

confidence: 99%

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

Asjad¹,

Ashaq²,

Faridi³

et al. 2023

Preprint

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In this article, the new extended direct algebraic method is used to build the exact travellingwave solutions for the non-linear time-fractional Clannish Random Walker’s Parabolic equation.This study establishes the framework in which periodic, singular, dark, bright and kink-typewave solitons are obtained with exact solutions offered by the mixed hyperbolic and trigonom-etry solutions, mixed periodic and periodic solutions, plane solutions, shock solutions, mixedtrigonometric solutions, mixed singular solutions, mixed shock single solutions, complex solitarysingular solutions, shock solutions and shock wave solutions. The exact soliton solutions of thetime-fractional clannish random walker’s parabolic equation model is graphically presented atdifferent values of involved parameters by Wolfram Mathematica software. The propagating behaviours display in 3-D, contour and 2-D surfaces of the obtained results to visualise the im-pact of the involved parameters. The sensitivity analysis is demonstrated for the wave profilesof the designed dynamical framed structure, where the soliton wave number parameter regulatesthe water wave singularity. This analysis illustrates that the utilized method is efficient andreliable and can be useful to find appropriate solutions in closed-form solitary soliton to a wide range of non-linear evolution equations. These techniques can also be utilised to find new exact travelling wave solutions for any class of integer or fractional differential equations thatarise in mathematical physics.

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New kinds of analytical solitary wave solutions for ionic currents on microtubules equation via two different techniques

Cited by 61 publications

References 54 publications

Formation of solitary waves solutions and dynamic visualization of the nonlinear schrödinger equation with efficient techniques

Formation of solitary waves solutions and dynamic visualization of the nonlinear schrödinger equation with efficient techniques

Lumps, solitons and stability analysis for the (3 + 1)-dimensional fractional potential-YTSF-like model in weakly dispersive medium

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

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