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

Akbulut, Arzu; Alqahtani, Rubayyi T.; Alharthi, Nadiyah Hussain

doi:10.3390/math11194176

Mathematics

2023

DOI: 10.3390/math11194176

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

Arzu Akbulut,

Rubayyi T. Alqahtani,

Nadiyah Hussain Alharthi

Abstract: 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 thr… Show more

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2024

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Cited by 3 publications

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Dynamics of the traveling wave solutions of conformable time-fractional ISLW and DJKM equations via a new expansion method

Kırcı,

Koç,

Bulut

2024

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This work searches the new wave solutions of the time-fractional ion sound and Langmuir waves (ISLWs) equation and the time-fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation with the conformable derivative. The $$\left( m+\frac{1}{G^\prime }\right)$$ m + 1 G ′ -expansion method is employed for these models for the first time. Getting support from symbolic software, some new solutions are presented, which will be constructive for studies in the field of nonlinear physical phenomena. New wave solutions obtained by using the $$\left( m+\frac{1}{G^\prime }\right)$$ m + 1 G ′ -expansion method have applications in engineering, physics, and other scientific fields. The regarded method may provide a framework for the exact solutions of several evolution equations in applied sciences. Moreover, the graphical illustrations are also demonstrated to observe the dynamical behaviours of the solutions, which may benefit the development of new technologies.

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Dynamics of the traveling wave solutions of conformable time-fractional ISLW and DJKM equations via a new expansion method

Kırcı,

Koç,

Bulut

2024

Opt Quant Electron

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New algorithm for deriving rational form solutions in the generalized Date-Jimbo-Kashiwara-Miwa model

Darweesh,

Alquran

2024

Phys. Scr.

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This paper introduces, for the ﬁrst time, the application of rational form solutions involving sine-cosine and sinh-cosh functions to address a nonlinear model emerging in the realm of plasma physics. The model under consideration is derived from the KP hierarchy and is denoted as the Date-Jimbo-Kashiwara-Miwa equation. In this study, the proposed model is extended to incorporate arbitrary coeﬃcients, encompassing both nonlinearity and dispersion factors. The solutions obtained are presented through 2D and 3D plots, revealing three distinct types of solitary wave propagation: moving singular-periodic, kink, and singular solutions. These solutions, as reported in this work, have the potential for broader applications, including optics and quantum physics.

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Solitonic structures and chaotic behavior in the geophysical Korteweg–de Vries equation: A μ-symmetry and g′-expansion approach

Kopçasız,

Yaşar

2024

Mod. Phys. Lett. B

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This study discusses the [Formula: see text] and Lie symmetries, [Formula: see text]-conservation laws, analytical solutions, chaotic phenomena, and sensitivity analysis of the geophysical Korteweg–de Vries equation (GKdVE). The GKdVE describes the propagation of long waves in geophysical systems like oceans, taking into account the influence of the Coriolis force due to Earth’s rotation. We aim to understand the behavior of waves better in geophysical settings and their potential applications across fields like oceanography, meteorology, and climate science. By using the similarity variables, the GKdVE is transformed into a reduced ordinary differential equation (RODE). We employ the ([Formula: see text])-expansion procedure in one of the RODEs to obtain soliton solutions. Thanks to the ([Formula: see text])-expansion procedure, we discover six wave solutions. Through the implementation of the variational problem strategy, we derive both the Lagrangian and the [Formula: see text]-conservation law ([Formula: see text]-CL). Additionally, we revisit the planar dynamical system associated with the equation of interest, conducting a sensitive inspection to assess its sensitivity. Moreover, the introduction of a perturbed term reveals chaotic and quasi-periodic behaviors across a range of parameter values. Furthermore, we provide visual demonstrations of these properties through figures depicting the exact solutions.

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

Cited by 3 publications

References 45 publications

Dynamics of the traveling wave solutions of conformable time-fractional ISLW and DJKM equations via a new expansion method

Dynamics of the traveling wave solutions of conformable time-fractional ISLW and DJKM equations via a new expansion method

New algorithm for deriving rational form solutions in the generalized Date-Jimbo-Kashiwara-Miwa model

Solitonic structures and chaotic behavior in the geophysical Korteweg–de Vries equation: A μ-symmetry and g′-expansion approach

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