Lie Analysis and Novel Analytical Solutions for the Time-Fractional Coupled Whitham–Broer–Kaup Equations

Through the commutator table and the adjoint table between the infinitesimals, we apply two stages of Lie symmetry reduction to reduce the (2[Formula: see text]+[Formula: see text]1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation to ordinary differential equations (ODE’s). Some of these ODE’s had no quadrature. We derive several new solutions for these non-solvable ODE’s using Integrating Factors property.

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“…• The Integrating Factors method overcome the problems as depicted in Ref. 8 of Lie symmetry reduction method (back substitution problems).…”

Section: Discussionmentioning

confidence: 99%

Families of analytic solutions for (2+1) model in unbounded domain via optimal Lie vectors with integrating factors

Sadat

Kassem

2019

Mod. Phys. Lett. B

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“…First family: There are three cases relying on b. Case 1: If b = 0, then the solution of (8), by using ( 11) and (15), is…”

Section: Re-methodsmentioning

confidence: 99%

“…Consequently, it is essential in mathematical physics to seek exact solutions for FDEs. In recent years, multiple approaches for dealing with FDEs have been devised, such as the (G /G)-expansion method [8,9], Kudryashov method [10], first-integral method [11], sine-cosine method [12,13], exp(−φ(ς))-expansion [14], direct algebraic method [15], perturbation method [16,17], tanh-sech [18,19], sine-Gordon expansion [20], Jacobi elliptic function [21], etc.…”

Section: Introductionmentioning

confidence: 99%

Effects of the Wiener Process and Beta Derivative on the Exact Solutions of the Kadomtsev–Petviashvili Equation

Al-Askar,

Cesarano,

Mohammed

2023

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We take into account the (2 + 1)-dimensional stochastic Kadomtsev–Petviashvili equation with beta-derivative (SKPE-BD) in this paper. To develop new hyperbolic, trigonometric, elliptic, and rational solutions, the Riccati equation and Jacobi elliptic function methods are employed. Because the KP equation is required for explaining the development of quasi-one-dimensional shallow-water waves, the solutions obtained can be used to interpret various attractive physical phenomena. To display how the multiplicative white noise and beta-derivative impact the exact solutions of the SKPE-BD, we plot a few graphs in MATLAB and display different 3D and 2D figures. We deduce how multiplicative noise stabilizes the solutions of SKPE-BD at zero.

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“…However, solving nonlinear partial differential equations has long been a tough but critical endeavor. As a result, many brilliant scientists in the domains of science and engineering have developed a number of strong approaches for acquiring exact solutions, for instance, improved tan (ϕ/2)-expansion [9], such as the (G /G)-expansion method [10,11], the Kudryashov method [12], the firstintegral method [13], the sine-cosine [14,15], the exp(−φ(ς))-expansion [16], the direct algebraic [17], the perturbation method [18,19], the tanh-sech [20,21], the sine-Gordon expansion [22], the Jacobi elliptic function [23], and so on.…”

Section: Introductionmentioning

confidence: 99%

The Analytical Solutions to the Fractional Kraenkel–Manna–Merle System in Ferromagnetic Materials

et al. 2023

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In this article, we examine the Kraenkel–Manna–Merle system (KMMS) with an M-truncated derivative (MTD). Our goal is to obtain rational, hyperbolic, and trigonometric solutions by using the F-expansion technique with the Riccati equation. To our knowledge, no one has studied the exact solutions to the KMMS in the presence/absence of a damping effect with an M-truncated derivative, using the F-expansion technique. The magnetic field propagation in a zero-conductivity ferromagnet is described by the KMMS; hence, solutions to this equation may provide light on several fascinating scientific phenomena. We use MATLAB to display figures in a variety of 3D and 2D formats to demonstrate the influence of the M-truncated derivative on the exact solutions to the KMMS.

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Lie Analysis and Novel Analytical Solutions for the Time-Fractional Coupled Whitham–Broer–Kaup Equations

Cited by 17 publications

References 29 publications

Families of analytic solutions for (2+1) model in unbounded domain via optimal Lie vectors with integrating factors

Families of analytic solutions for (2+1) model in unbounded domain via optimal Lie vectors with integrating factors

Effects of the Wiener Process and Beta Derivative on the Exact Solutions of the Kadomtsev–Petviashvili Equation

The Analytical Solutions to the Fractional Kraenkel–Manna–Merle System in Ferromagnetic Materials

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