An extended Korteweg–de Vries equation: multi-soliton solutions and conservation laws

Yaşar, Emrullah; Yaşar, Emrullah

doi:10.1007/s11071-017-3749-x

Cited by 16 publications

(7 citation statements)

References 25 publications

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“…Small amplitude ion-acoustic PWP corresponding to periodic orbit at initial point (ψ, y) = (0.1, 0) of phase portrait (figure 1(a)) is obtained numerically and shown by solid blue curves in figure 4(a)-(d). Variation of this PWP of the system (19) with respect to the mentioned parameter while keeping other parameters the same as figure 1(a) are shown in figure 4(a)-(d) by dashed black curves. It is seen that amplitude of ion-acoustic PWP increases with increase in Mach number (M) while it decreases with increase in direction cosine of the line of wave propagation with respect to z − axis (l z ).…”

Section: Numerical Solutionsmentioning

confidence: 99%

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Propagation of ion-acoustic wave and its fractal representations in spin polarized electron plasma

et al. 2023

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Propagation of small-amplitude ion-acoustic waves and its fractal representations is investigated in an electron-ion quantum plasma with separated spin electrons in the framework of the KdV and EKdV equations derived using reductive perturbation technique. The two evolution equations are transformed into planar dynamical systems by using suitable traveling wave transformation. Qualitatively diﬀerent phase portraits of these two systems are drawn with their respective Sagdeev’s pseudopotential curves and surface plots. Distinct orbits in the phase portraits give rise to distinct wave solutions. Periodic and superperiodic wave solutions are investigated numerically and solitary wave solutions are derived analytically. The eﬀect of parameters such as Mach number, direction cosine, spin polarization and frequency ratio on these wave solutions are presented. For instance, it is seen that the spin density polarization ratio has an impressive eﬀect on the amplitude of the wave solution, while the frequency ratio has no eﬀect on its amplitude. Also, we have provided a physical explanation for our ﬁnding. Further, the dynamical features of the original system and reconstructed system using fractal interpolation function are investigated under the external forcing term. Chaotic and quasiperiodic phenomena are observed for diﬀerent initial conditions. The results may help to better understand the degenerate electron gas that exists in astrophysical bodies and laboratory plasmas such as paramagnetic and ferromagnetic metals in exposing the external magnetic ﬁeld.

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Section: Numerical Solutionsmentioning

confidence: 99%

“…El-Shamy et al [18] examined solitary wave structures in a semiconductor quantum plasma under the framework of the KdV equations. The EKdV equation describes the evolution of steeper waves of shorter wavelength than does the KdV equation [19]. Both the KdV and EKdV equations are nonlinear evolution equations (NLEEs).…”

Section: Introductionmentioning

confidence: 99%

Propagation of ion-acoustic wave and its fractal representations in spin polarized electron plasma

et al. 2023

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“…As the economy and fnancial markets are nonlinear systems, nonlinear science is widely applied in constructing mathematical models to fnd deep properties of economy and fnancial problems. Most of nonlinear phenomena are generally presented in the form of nonlinear partial diferential equations (NPDEs) [6][7][8]. To conduct the mathematical models of fnance, it is imperative to determine that the models are either complex-valued or real values with wave function.…”

Section: Introductionmentioning

confidence: 99%

Solitary Wave and Singular Wave Solutions for Ivancevic Option Pricing Model

Zeng

Liang

Yuan

2022

Mathematical Problems in Engineering

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The nonlinear option pricing model presented by Ivancevic is investigated. By using travelling wave transforming method, the nonlinear option pricing equation is transformed into a differential equation with constant coefficients. By solving the differential equation with F-expansion method, a series of exact solutions have been obtained for the Ivancevic option pricing model. By choosing appropriate parameter values, the dark-soliton and dark-soliton-like solutions, periodic wave solutions, and rogue wave solutions are obtained. These solutions will enrich the types of exact waves in the existing literature of the Ivancevic option pricing model. Furthermore, they may have potential uses in describing the possible physical mechanisms for wave phenomenon in financial markets.

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“…In addition, the Boussinesq-Burgers-type system of equations, which delineates shallow water waves appearing close to lakes or ocean beaches, was studied in [4]. The list continues; see also [5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

Khalique

Plaatjie

2021

Mathematics

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In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem.

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An extended Korteweg–de Vries equation: multi-soliton solutions and conservation laws

Cited by 16 publications

References 25 publications

Propagation of ion-acoustic wave and its fractal representations in spin polarized electron plasma

Propagation of ion-acoustic wave and its fractal representations in spin polarized electron plasma

Solitary Wave and Singular Wave Solutions for Ivancevic Option Pricing Model

Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

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