The Formation of Invariant Exact Optical Soliton Solutions of Landau-Ginzburg-Higgs Equation via Khater Analytical Approach

Faridi, Waqas Ali; AlQahtani, Salman A.

doi:10.1007/s10773-024-05559-1

Int J Theor Phys

2024

DOI: 10.1007/s10773-024-05559-1

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The Formation of Invariant Exact Optical Soliton Solutions of Landau-Ginzburg-Higgs Equation via Khater Analytical Approach

Waqas Ali Faridi,

Salman A. AlQahtani

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2024

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Exact solutions of the Landau–Ginzburg–Higgs equation utilizing the Jacobi elliptic functions

Çulha Ünal

2024

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The Landau–Ginzburg–Higgs equation is one of the significant evolution equation in physical phenomena. In this work, the exact solutions of this equation are gained by applying an analytical method depends on twelve Jacobi elliptic functions. This equation is turned into an ordinary differential equation by the proposed method. When solving the Landau–Ginzburg–Higgs equation, an auxiliary ordinary differential equation is considered. Some theorems and corollaries utilized in the solutions of this auxiliary equation are given. Using these solutions, the elliptic and elementary solutions of the Landau–Ginzburg–Higgs equation are obtained and illustrated by tables. Many solutions are given in the form of the complex, rational, hyperbolic, and trigonometric functions. The soliton solutions and the complex valued solutions are also found by proposed method. These solutions include the largest set of solutions in the literature. Some of them are shown graphically by 2-dimensional and 3-dimensional with the help of Mathematica software. The obtained solutions are beneficial for the farther development of a concerned model. The presented method does not need initial and boundary conditions, perturbation, or linearization. Besides, this method is easy, efficient, and reliable for solutions of many partial differential equations.

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Exact solutions of the Landau–Ginzburg–Higgs equation utilizing the Jacobi elliptic functions

Çulha Ünal

2024

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The Formation of Invariant Exact Optical Soliton Solutions of Landau-Ginzburg-Higgs Equation via Khater Analytical Approach

Cited by 1 publication

References 40 publications

Exact solutions of the Landau–Ginzburg–Higgs equation utilizing the Jacobi elliptic functions

Exact solutions of the Landau–Ginzburg–Higgs equation utilizing the Jacobi elliptic functions

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