New exact solutions for the (2 + 1)-dimensional Sawada–Kotera equation

Shi, Ye; Li, Donglong

doi:10.1016/j.compfluid.2012.08.005

Cited by 15 publications

(12 citation statements)

References 21 publications

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“…On the basis of the bilinear equation (3), we find the periodic wave-type solutions through the three-wave method 31,32 for the extended (3+1)-dimensional JM equation by setting the form…”

Section: Periodic Wave-type Solutions To the Extended (3+1)-dimensionmentioning

confidence: 99%

On integrability of the extended (3+1)‐dimensional Jimbo‐Miwa equation

Liu

Yang

Feng

2019

Math Methods in App Sciences

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By applying the binary bell polynomial scheme, the bilinear form, Bäcklund Transformations, and lax pairs of an extended (3+1)-dimensional Jimbo-miwa (JM) equation are constructed. Next, periodic wave-type solutions can also be obtained to the extended (3+1)-dimensional JM equation through the three-wave method with the help of maple. Finally, a test function of the sech-function method is utilized to get solitary waves of this study problem. These new results can help us better understand interesting physical phenomena and mechanism. KEYWORDS binary bell polynomial scheme, extended (3+1)-dimensional JM equation, bäcklund transformations and Lax pairs, periodic wave-Type solutions, Solitary Waves MSC CLASSIFICATION 35L05; 35C08; 35Q35 This equation was firstly proposed by A. M. Wazwaz to study its one-soliton solution, two-soliton solution, and multi-soliton solutions of Equation (1) by utilizing the simplified Hirota bilinear method. 25 Meanwhile, Sun and Chen obtained the lump solutions of Equation (1). 26 Manafian 27 used the Hirota bilinear method of a new combination of exponential function, trigonometric function, and hyperbolic functions to obtain new periodic solitary wave solutions, etc. 27-29

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“…On the basis of the bilinear equation (3), we find the periodic wave-type solutions through the three-wave method 31,32 for the extended (3+1)-dimensional JM equation by setting the form…”

Section: Periodic Wave-type Solutions To the Extended (3+1)-dimensionmentioning

confidence: 99%

On integrability of the extended (3+1)‐dimensional Jimbo‐Miwa equation

Liu

Yang

Feng

2019

Math Methods in App Sciences

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“…where , are free parameters. Substituting (10) into Eq. (9) yields the following wave solution of Eq.…”

Section: The Bilinear Form Of 5th Order Kdv Equationmentioning

confidence: 99%

“…Also, Dai et al [8] proposed extended three-soliton method. Then, Shi et al [9][10][11] constructed a novel approach, namely, multi-wave method to find new exact solutions for nonlinear problems and extend Dai et al's work [8].…”

Section: Introductionmentioning

confidence: 99%

The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations

Pandır

Ulusoy²

2017

Journal of Engineering Technology and Applied Sciences

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In this research, we use the multi-wave method to obtain new exact solutions for generalized forms of the 5 th order KdV equation and the fifth order KdV (fKdV) equation with power law nonlinearity. Computations are performed with the help of the mathematics software Mathematica. Then periodic wave solutions, bright soliton solutions and rational function solutions with free parameters are obtained by this approach. It is shown that this method is very useful and effective.

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“…If α = 1, then Equation (1) reduces into the (2 + 1)-dimensional integro-differential SK equation [30][31][32][33][34][35][36], which was initially established by Konopelcheno and Dubrovsky [37], using the inverse scattering transform method. The (2 + 1)-dimensional SK equation has been investigated extensively and intensively in a number of studies in the literature because of its significance and various applications in two-dimensional quantum gravity field theory, conformal field theory, and conserved current of Liouville equation [38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Applications of the (G′/G2)-Expansion Method for Solving Certain Nonlinear Conformable Evolution Equations

et al. 2021

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The core objective of this article is to generate novel exact traveling wave solutions of two nonlinear conformable evolution equations, namely, the (2+1)-dimensional conformable time integro-differential Sawada–Kotera (SK) equation and the (3+1)-dimensional conformable time modified KdV–Zakharov–Kuznetsov (mKdV–ZK) equation using the (G′/G2)-expansion method. These two equations associate with conformable partial derivatives with respect to time which the former equation is firstly proposed in the form of the conformable integro-differential equation. To the best of the authors’ knowledge, the two equations have not been solved by means of the (G′/G2)-expansion method for their exact solutions. As a result, some exact solutions of the equations expressed in terms of trigonometric, exponential, and rational function solutions are reported here for the first time. Furthermore, graphical representations of some selected solutions, plotted using some specific sets of the parameter values and the fractional orders, reveal certain physical features such as a singular single-soliton solution and a doubly periodic wave solution. These kinds of the solutions are usually discovered in natural phenomena. In particular, the soliton solution, which is a solitary wave whose amplitude, velocity, and shape are conserved after a collision with another soliton for a nondissipative system, arises ubiquitously in fluid mechanics, fiber optics, atomic physics, water waves, and plasmas. The method, along with the help of symbolic software packages, can be efficiently and simply used to solve the proposed problems for trustworthy and accurate exact solutions. Consequently, the method could be employed to determine some new exact solutions for other nonlinear conformable evolution equations.

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New exact solutions for the (2 + 1)-dimensional Sawada–Kotera equation

Cited by 15 publications

References 21 publications

On integrability of the extended (3+1)‐dimensional Jimbo‐Miwa equation

On integrability of the extended (3+1)‐dimensional Jimbo‐Miwa equation

The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations

Applications of the (G′/G2)-Expansion Method for Solving Certain Nonlinear Conformable Evolution Equations

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