On Survey of the Some Wave Solutions of the Non-Linear Schrödinger Equation (NLSE) in Infinite Water Depth

TAZGAN, Tuğba; Çelık, Ercan; Yel, Gülnur

doi:10.35378/gujs.1016160

Cited by 8 publications

(4 citation statements)

References 38 publications

(25 reference statements)

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“…Nonlinear partial differential equations (PDEs) have been a popular subject in the field of nonlinear science and have been used to describe problems in a variety of areas, including ecology and economic systems, image processing, quantum physics, and epidemiology. PDEs are frequently utilized in a variety of physical applications, such as supersonic and turbulent flow, magnetohydrodynamic movement through pipes, wave dispersion and propagation, computational fluid dynamics, magnetic resonance imaging, population modeling, medical imaging, electrically signaling nerves, and others [6][7][8]. To learn more, consider the reference mentioned in [9].…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of the Fractional Partial Differential Equations via Novel Transform

2023

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In comparison to fractional-order differential equations, integer-order differential equations generally fail to properly explain a variety of phenomena in numerous branches of science and engineering. This article implements efficient analytical techniques within the Caputo operator to investigate the solutions of some fractional partial differential equations. The Adomian decomposition method, homotopy perturbation method, and Elzaki transformation are used to calculate the results for the specified issues. In the current procedures, we first used the Elzaki transform to simplify the problems and then applied the decomposition and perturbation methods to obtain comprehensive results for the problems. For each targeted problem, the generalized schemes of the suggested methods are derived under the influence of each fractional derivative operator. The current approaches give a series-form solution with easily computable components and a higher rate of convergence to the precise solution of the targeted problems. It is observed that the derived solutions have a strong connection to the actual solutions of each problem as the number of terms in the series solution of the problems increases. Graphs in two and three dimensions are used to plot the solution of the proposed fractional models. The methods used currently are simple and efficient for dealing with fractional-order problems. The primary benefit of the suggested methods is less computational time. The results of the current study will be regarded as a helpful tool for dealing with the solution of fractional partial differential equations.

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Section: Introductionmentioning

confidence: 99%

A Comparative Study of the Fractional Partial Differential Equations via Novel Transform

2023

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“…Pandir et al employed the modified exponential function technique [11]. Yazgan et al handled the sine-Gordon expansion method [12,13]. Ghanbari and Gomez Aguilar utilized the generalized exponential function procedure [14], Kudryashov employed the simplest equation method to the Chavy-Waddy-Kolokolnikov model [15], Sebogodi et al applied the symmetry reduction method to (2+1)-dimensional combined potential Kadomtsev-Petviashvili-B-type Kadomtsev-Petviashvili [16], Sebogadi et al used the ansatz method to obtain the traveling wave solutions of the generalized Chaffee-Infante equation in (1+3) dimensions [17], Podile et al applied the multiple exp-function technique to the e (2+1)-dimensional Hirota-Satsuma-Ito equation [18], and so on [19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Some Latest Families of Exact Solutions to Date–Jimbo–Kashiwara–Miwa Equation and Its Stability Analysis

Akbulut,

Alqahtani,

Alharthi

2023

Mathematics

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The present study demonstrates the derivation of new analytical solutions for the Date–Jimbo–Kashiwara–Miwa equation utilizing two distinct methodologies, specifically the modified Kudryashov technique and the (g′)-expansion procedure. These innovative concepts employ symbolic computations to provide a dynamic and robust mathematical procedure for addressing a range of nonlinear wave situations. Additionally, a comprehensive stability analysis is performed, and the acquired results are visually represented through graphical representations. A comparison between the discovered solutions and those already found in the literature has also been performed. It is anticipated that the solutions will contribute to the existing literature related to mathematical physics and soliton theory.

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“…, 2019), sine-Gordon expansion method (Yel, 2020; Yazgan et al. , 2022, 2023), Jacobi elliptic function (Yazgan et al. , 2022), conservation laws (Gandarias et al.…”

Section: Introductionmentioning

confidence: 99%

“…The various solutions of Eq. ( 2) have been proposed via F-expansion method (Silambarasan et al, 2019), sine-Gordon expansion method (Yel, 2020;Yazgan et al, 2022Yazgan et al, , 2023, Jacobi elliptic function (Yazgan et al, 2022), conservation laws (Gandarias et al, 2020), invariant preserving schemes (Kolkovska and Vucheva, 2019), Sardar sub-equation method (Rehman et al, 2022), etc. Additionally, asymptotic profile of solutions (Wang and Chen, 2016), instability and stability properties (Erbay et al, 2016) and non-uniqueness (Yang et al, 2015) are studied in the literature.…”

Section: Introductionmentioning

confidence: 99%

The solutions of dissipation-dispersive models arising in material science

Pınar

2022

MMMS

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PurposeThe aim of this work is to obtain periodic waves of Eq. (1) via ansatz-based methods. So, the open questions are replied and the gap will be filled in the literature. Additionally, the comparison of the considered models (Eq. (1) and Eq. (2)) due to their performance. Although it is extremely difficult to find the exact wave solutions in Eq. (1) and Eq. (2) without any assumptions, the targeted solutions have been obtained with the chosen method.Design/methodology/approachMaterial science is the today's popular research area. So, the well-known model is the dissipation double dispersive nonlinear equation and, in the literature, open queries have been seen. The aim of this work is to reply open queries by obtaining wave solutions of the dissipation double dispersive model, double dispersive model and double dispersive model for Murnaghan's material via ansatz-based methods.FindingsThe results have been appeared for the first time in this communication work and they may be valuable for developing uses in material science.Originality/valueThe exact wave solutions of Eq. (1) and Eq. (2) without any assumptions have been obtained with via ansatz-based method. So, the open questions are replied and the gap will be filled in the literature.

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On Survey of the Some Wave Solutions of the Non-Linear Schrödinger Equation (NLSE) in Infinite Water Depth

Cited by 8 publications

References 38 publications

A Comparative Study of the Fractional Partial Differential Equations via Novel Transform

A Comparative Study of the Fractional Partial Differential Equations via Novel Transform

Some Latest Families of Exact Solutions to Date–Jimbo–Kashiwara–Miwa Equation and Its Stability Analysis

The solutions of dissipation-dispersive models arising in material science

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