Non-Traveling Wave Solutions for the (2+1)-Dimensional Breaking Soliton System

Chen, Yuanming Chen; Ma, Song-Ya

doi:10.4236/am.2012.38122

Cited by 9 publications

(7 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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: 92%

“…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%

See 1 more Smart Citation

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

et al. 2021

View full text Add to dashboard Cite

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.

show abstract

Section: Resultsmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Many authors have obtained the analytical solutions of the deterministic breaking soliton equation by various methods such as the three-wave [23], Hirota bilinear [24], ( G G )-expansion [25], generalized auxiliary equation [26], tanh-coth [27], improved ( G G )expansion and extended tanh [28], Jacobi elliptic functions [29], and projective Riccati equation expansion [30]. The solutions to stochastic breaking soliton equations have not been obtained till now.…”

Section: Introductionmentioning

confidence: 99%

The Impact of the Wiener Process on the Analytical Solutions of the Stochastic (2+1)-Dimensional Breaking Soliton Equation by Using Tanh–Coth Method

et al. 2022

View full text Add to dashboard Cite

The stochastic (2+1)-dimensional breaking soliton equation (SBSE) is considered in this article, which is forced by the Wiener process. To attain the analytical stochastic solutions such as the polynomials, hyperbolic and trigonometric functions of the SBSE, we use the tanh–coth method. The results provided here extended earlier results. In addition, we utilize Matlab tools to plot 2D and 3D graphs of analytical stochastic solutions derived here to show the effect of the Wiener process on the solutions of the breaking soliton equation.

show abstract

“…Symmetries of the (2 þ 1)-dimensional breaking soliton equation have been used by the authors in [59]. Chen and Ma [60] introduced and investigated to extract exact solutions of non-traveling wave solutions for the (2 þ 1)-dimensional breaking soliton system. Wazwaz [61] introduced the generalized (2 þ 1)-dimensional breaking soliton equation.…”

Section: Introductionmentioning

confidence: 99%

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

Ali

Habib

Miah

et al. 2020

Heliyon

View full text Add to dashboard Cite

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.

show abstract

Non-Traveling Wave Solutions for the (2+1)-Dimensional Breaking Soliton System

Cited by 9 publications

References 21 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

The Impact of the Wiener Process on the Analytical Solutions of the Stochastic (2+1)-Dimensional Breaking Soliton Equation by Using Tanh–Coth Method

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

Contact Info

Product

Resources

About