Analytical multi-soliton solutions of a (2+1)-dimensional breaking soliton equation

Wang, Shaofu

doi:10.1186/s40064-016-2403-2

Cited by 7 publications

(3 citation statements)

References 24 publications

(23 reference statements)

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“…In the derived solutions, parameters A 1 , A −1 , A 2 and A −2 received various specific values due to these exact solutions being converted into different solitary wave solutions in different forms, such as hyperbolic, trigonometric and rational functions (Figures 1-6). Currently several methods have been utilized to solve Equation (1) throughout the research literature [40][41][42][43][44][45][46][47][48]. Moreover, our investigated solutions are likely similar to other solutions in different research articles.…”

Section: Resultsmentioning

confidence: 91%

“…Yildiz and Daghan [43], by using two different methods, investigated exact solutions of Equation (1). Wang in [44] and Chen and Ma in [45] suggested the analytical multi-soliton solutions and exact solutions to the (2+1)-dimensional breaking soliton equation respectively. New multi-soliton solutions and Symmetries solutions of Equation ( 1) have been established in [46,47].…”

Section: Introductionmentioning

confidence: 99%

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Novel Analytical Approach for the Space-Time Fractional (2+1)-Dimensional Breaking Soliton Equation via Mathematical Methods

et al. 2021

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The aim of this work is to build novel analytical wave solutions of the nonlinear space-time fractional (2+1)-dimensional breaking soliton equations, with regards to the modified Riemann–Liouville derivative, by employing mathematical schemes, namely, the improved simple equation and modified F-expansion methods. We used the fractional complex transformation of the concern fractional differential equation to convert it for the solvable integer order differential equation. After the successful implementation of the presented methods, a comprehensive class of novel and broad-ranging exact and solitary travelling wave solutions were discovered, in terms of trigonometric, rational and hyperbolic functions. Hence, the present methods are reliable and efficient for solving nonlinear fractional problems in mathematics physics.

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Section: Resultsmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Novel Analytical Approach for the Space-Time Fractional (2+1)-Dimensional Breaking Soliton Equation via Mathematical Methods

et al. 2021

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“…Yildiz and Daghan [57] investigated solutions to the (2 þ 1)-dimensional breaking soliton equation by using two different methods. Wang [58] suggested the analytical multi-soliton solutions to the (2 þ 1)-dimensional breaking soliton equation. Symmetries of the (2 þ 1)-dimensional breaking soliton equation have been used by the authors in [59].…”

Section: Introductionmentioning

confidence: 99%

Solitary wave solutions to some nonlinear fractional evolution equations in mathematical physics

Ali

Habib

Miah

et al. 2020

Heliyon

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The objective of this article is to construct new and further general analytical wave solutions to some nonlinear evolution equations of fractional order in the sense of the modified Riemann-Liouville derivative relating to mathematical physics, namely, the space-time fractional Fokas equation, the time fractional nonlinear model equation and the space-time fractional (2 þ 1)-dimensional breaking soliton equation by exerting a rather new mechanism ðG' =G; 1 =GÞ -expansion method. We use the fractional complex transformation and associate the fractional differential equations to the solvable integer order differential equations. A comprehensive class of new and broad-ranging exact traveling and solitary wave solutions are revealed in terms of trigonometric, rational and hyperbolic functions. The attained wave solutions are sketched graphically by using Mathematica and make a comparison to the results attained by the presented technique with other techniques in a comprehensive manner. It is notable that the method can be considered as a reduction of the reputed ðG' =GÞ -expansion method commenced by Wang et al. It is noticeable that, the two variable ðG' =G; 1 =GÞ -expansion method appears to be more reliable, straightforward, computerized and user-friendly.

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Novel Localized Excitations Structures with Fusion and Fission Properties to a (2 + 1)-Dimensional Breaking Soliton Equation

Khatun

Akter

Roshid

2020

Int. J. Appl. Comput. Math

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Analytical multi-soliton solutions of a (2+1)-dimensional breaking soliton equation

Cited by 7 publications

References 24 publications

Novel Analytical Approach for the Space-Time Fractional (2+1)-Dimensional Breaking Soliton Equation via Mathematical Methods

Novel Analytical Approach for the Space-Time Fractional (2+1)-Dimensional Breaking Soliton Equation via Mathematical Methods

Solitary wave solutions to some nonlinear fractional evolution equations in mathematical physics

Novel Localized Excitations Structures with Fusion and Fission Properties to a (2 + 1)-Dimensional Breaking Soliton Equation

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