The exact solutions of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si14.svg"><mml:mrow><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math>–dimensional Kadomtsev–Petviashvili equation with variable coefficients by extended generalized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si15.svg"><mml:mrow><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml

Mohanty, Shruti; Kravchenko, O. V.; Deka, Manoj Kr.; Dev, Apul N.; Churikov, D. V.

doi:10.1016/j.jksus.2022.102358

Cited by 35 publications

(7 citation statements)

References 32 publications

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“…In this equation, the coefficients a 0 , a 1 and b 1 are constants that need to be decided. Scenario I. λ > 0 (For trigonometric) To obtain the solutions for Equation ( 17), we use Equations ( 4) and ( 6) and replace Equation (17) with Equation (23). With this technique, a polynomial with ℊ and F is created from the left side of Equation ( 17).…”

Section: Application For Kerr Lawmentioning

confidence: 99%

“…Numerous researchers have developed various methodologies to derive precise solutions for NLSEs, employing diverse approaches such as the G ′ G ′ +G+A method [7,8], the Sardar subequation method [9,10], the Riccati equation method [11,12], the Hirota bilinear method [13,14], the Lie group method [15,16], the (G ′ /G)-expansion technique [17,18], the extended Jacobi elliptic function method [19,20], the functional variable technique [21,22], the homogeneous balance method [23,24], the Hirota bilinear formulation with N-soliton [25,26], the new auxiliary equation method [27,28], the tanh-function method [29][30][31], the tanh-coth method [32,33], the generalized Kudryshov method [34,35], the exp(−φ(ξ)) -expansion method [36,37], the unified method [38,39], the multiple exp-function method [40,41] and so on.…”

Section: Introductionmentioning

confidence: 99%

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Abundant New Optical Soliton Solutions to the Biswas–Milovic Equation with Sensitivity Analysis for Optimization

Hossain,

Alsharif,

Miah

et al. 2024

Mathematics

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This study extensively explores the Biswas–Milovic equation (BME) with Kerr and power law nonlinearity to extract the unique characteristics of optical soliton solutions. These optical soliton solutions have different applications in the field of precision in optical switching, applications in waveguide design, exploration of nonlinear optical effects, imaging precision, reduced intensity fluctuations, suitability for optical signal processing in optical physics, etc. Through the powerful (G′/G, 1/G)-expansion analytical method, a variety of soliton solutions are expressed in three distinct forms: trigonometric, hyperbolic, and rational expressions. Rigorous validation using Mathematica software ensures precision, while dynamic visual representations vividly portray various soliton patterns such as kink, anti-kink, singular soliton, hyperbolic, dark soliton, and periodic bright soliton solutions. Indeed, a sensitivity analysis was conducted to assess how changes in parameters affect the exact solutions, aiding in the understanding of system behavior and informing decision-making, especially in accurately designing or analyzing real-world optical phenomena. This investigation reveals the significant influence of parameters λ, τ, c, B, and Κ on the precise solutions in Kerr and power law nonlinearities within the BME. Notably, parameter λ exhibits consistently high sensitivity across all scenarios, while parameters τ and c demonstrate pronounced sensitivity in scenario III. The outcomes derived from this method are distinctive and carry significant implications for the dynamics of optical fibers and wave phenomena across various optical systems.

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Section: Application For Kerr Lawmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Abundant New Optical Soliton Solutions to the Biswas–Milovic Equation with Sensitivity Analysis for Optimization

Hossain,

Alsharif,

Miah

et al. 2024

Mathematics

View full text Add to dashboard Cite

show abstract

“…In (Ma et al, 2023), the extended (2+1)-dimensional KP equation was solved using conjugate complex and long-wave limit methods. In (Mohanty et al, 2023) In this article, the optical solitons of the extended (2+1)dimensional KP equation are investigated using the unified Riccati equation expansion method (UREEM) (Sirendaoreji 2017), (Zayed et al 2020).…”

Section: Introductionmentioning

confidence: 99%

An Investigation for Soliton Solutions of the Extended (2+1)-Dimensional Kadomtsev–Petviashvili Equation

ÇINAR

2024

Afyon Kocatepe University Journal of Sciences and Engineering

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This article presents an investigation for soliton solutions of the extended (2+1)-dimensional Kadomtsev–Petviashvili equation which describes wave behavior in shallow water. We utilize the unified Riccati equation expansion method. By employing the powerful method, many soliton solutions are successfully derived, and it is verified by Wolfram Mathematica that the solutions satisfy the main equation. Additionally, Matlab is utilized to generate plots and examine the properties of the obtained solitons. The results reveal that the considered equation exhibits a wide range of soliton solutions, including dark, bright, singular, and periodic solutions. This comprehensive investigation of soliton solutions for the Kadomtsev–Petviashvili equation holds significant relevance in various fields such as oceanography and nonlinear optics, contributing to practical applications.

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“…The soliton solutions derived from FNLEE have practical and commercial applications in various fields such as optical fiber technology, telecommunications, signal processing, image processing, system identification, water purification, plasma physics, medical device sterilization, chemistry, and other related domains [1,2]. Various dynamic approaches have been introduced and implemented in the literature to solve nonlinear fractional differential equations (NFDES) and obtain analytical traveling wave solutions, for example, the exp-function method [3], the Modified Exp-function method [4], the inverse scattering transformation method [5,6], the Bäcklund transformation method [7], the homogenous balance method [8,9], the Jacobi elliptic function method [10], the unified algebraic method [11], the sine-cosine method [12,13], the tanh-coth method [14,15], improved modified extended tanh-function method [16,17], the Lie symmetry analysis method [18], the extended generalized (G /G)-expansion method [19], the modified simple equation method [20], the generalized Kudryashov method [21,22], the sine-Gordon expansion method [23], the Riccati-Bernoulli equation method [24,25], the new extended direct algebraic method [26,27], and the new auxiliary equation method [28].…”

Section: Introductionmentioning

confidence: 99%

The Extended Direct Algebraic Method for Extracting Analytical Solitons Solutions to the Cubic Nonlinear Schrödinger Equation Involving Beta Derivatives in Space and Time

2023

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In the field of nonlinear optics, quantum mechanics, condensed matter physics, and wave propagation in rigid and other nonlinear instability phenomena, the nonlinear Schrödinger equation has significant applications. In this study, the soliton solutions of the space-time fractional cubic nonlinear Schrödinger equation with Kerr law nonlinearity are investigated using an extended direct algebraic method. The solutions are found in the form of hyperbolic, trigonometric, and rational functions. Among the established solutions, some exhibit wide spectral and typical characteristics, while others are standard. Various types of well-known solitons, including kink-shape, periodic, V-shape, and singular kink-shape solitons, have been extracted here. To gain insight into the internal formation of these phenomena, the obtained solutions have been depicted in two- and three-dimensional graphs with different parameter values. The obtained solitons can be employed to explain many complicated phenomena associated with this model.

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The exact solutions of the2+1–dimensional Kadomtsev–Petviashvili equation with variable coefficients by extended generalized

Cited by 35 publications

References 32 publications

Abundant New Optical Soliton Solutions to the Biswas–Milovic Equation with Sensitivity Analysis for Optimization

Abundant New Optical Soliton Solutions to the Biswas–Milovic Equation with Sensitivity Analysis for Optimization

An Investigation for Soliton Solutions of the Extended (2+1)-Dimensional Kadomtsev–Petviashvili Equation

The Extended Direct Algebraic Method for Extracting Analytical Solitons Solutions to the Cubic Nonlinear Schrödinger Equation Involving Beta Derivatives in Space and Time

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