Exact Traveling-Wave Solutions for One-Dimensional Modified Korteweg–de Vries Equation Defined on Cantor Sets

Gao, Feng; Yang, Xiao‐Jun; Ju, Yang

doi:10.1142/s0218348x19400103

Cited by 38 publications

(17 citation statements)

References 25 publications

(13 reference statements)

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“…The result of an exact solutions are expressed in the form of Jacobi elliptic functions, hyperbolic functions, and trigonometric functions with some of the solutions are the same as previous studies but there are also several different variations. In addition, several other methods have also been used by previous researchers to construct the exact solutions of the mKdV wave equation (Chai et al, 2014;Islam et al, 2015;Ji & Zhu, 2017;Nuruddeen, 2018;Gao et al, 2019). However, the exact solutions obtained in previous studies were expressed in the form of functions that were different from this study.…”

Section: Table 2 General Solutions Of Equation (8)mentioning

confidence: 97%

“…Many methods have been used by researchers to construct the solution of the mKdV wave equation. Some of them are the F-expansion method (Bashir & Alhakim, 2013), the exp-function method (Chai et al, 2014), the (G'/G)-expansion method (Islam et al, 2015), the inverse scattering transform (Ji & Zhu, 2017), conformable fractional derivative (Nuruddeen, 2018), and the local fractional derivative (Gao et al, 2019) with results in the form of exact solutions. In addition, there are also researchers who use numerical methods such as the Adomian Pade approximation method (Abassy et al, 2004), the numerical inverse scattering (Trogdon et al, 2012), differential quadrature method (Başhan et al, 2016), and a lumped Galerkin method based on cubic B-spline interpolation functions (Ak et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

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Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

Apriliani

Maulidi

Azhari

2020

ajpm

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One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations.

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Section: Table 2 General Solutions Of Equation (8)mentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

Apriliani

Maulidi

Azhari

2020

ajpm

View full text Add to dashboard Cite

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“…With the help of solving different kinds of equations, Liu and Yang et al studied wave‐type solution of different expressions . By transforming the traveling wave solutions, Gao and Yang et al discussed the nondifferentiable traveling‐wave solutions in detail …”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

Jiang

Yang

Sun

et al. 2020

Math Methods in App Sciences

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Based on the methods of complex function, conformal mapping, and multipolar coordinate system, dynamic response of an elliptical inclusion embedded in an anisotropic half space is investigated. In order to find the solution of SH waves, the governing equation is transferred into its normalized form. Then, the scattering wave induced by the inclusion and the standing wave in the inclusion is deduced. Different incident wave angles and the corresponding anisotropy of the half space are considered to obtain the reflected waves. The elliptical inclusion is transferred into a unit circle by conformal mapping method, and then the undetermined coefficients in scattering wave and standing wave are solved by using the continuous condition at the boundary of the inclusion. Subsequently, the dynamic stress concentration factor (DSCF) around the inclusion is calculated and analyzed. Numerical results demonstrate that the distribution of the DSCF is mainly influenced by the incident wave angle and the incident wave number. It is affected by anisotropic parameters as well. KEYWORDSanisotropy, complex function method, dynamic stress concentration factor (DSCF), elliptical inclusion, wave scattering MSC CLASSIFICATION 74J20Math Meth Appl Sci. 2020;43:6888-6902. wileyonlinelibrary.com/journal/mma

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“…The exact traveling wave solutions for the fractional equations and the heat transfer equations are worked out in Refs. [41][42][43][44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal-derivative NLS equations and group-invariant soliton solutions

Yao

Huang

2020

Adv Differ Equ

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A coupled Chen-Lee-Liu (CLL) system is proposed and its linear Lax pair is given. Many kinds of nonlocal-derivative NLS (DNLS) equations arise from the group symmetry reductions of the coupled CLL system.PTĈ-symmetry invariant one-soliton solution and periodic two-soliton solution of a two-place DNLS (TDNLS) system are obtained. A group symmetry invariant two-soliton solution of a four-place DNLS (FDNLS) system is worked out. New characteristics of the two-soliton interactions for the TDNLS system and FDNLS system are analyzed.

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Exact Traveling-Wave Solutions for One-Dimensional Modified Korteweg–de Vries Equation Defined on Cantor Sets

Cited by 38 publications

References 25 publications

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

Dynamic analysis of anisotropic half space containing an elliptical inclusion under SH waves

Nonlocal-derivative NLS equations and group-invariant soliton solutions

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