The improved Fan sub-equation method and its application to the SK equation

Feng, Dahe; Luo, Guoxi

doi:10.1016/j.amc.2009.07.045

Cited by 16 publications

(7 citation statements)

References 17 publications

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“…Feng studied the bifurcation of phase portraits of () and obtained all possible exact traveling wave solutions (bounded and unbouned) for all possible parameters

{\omega}_j

. As a result, more types of new exact solutions for some NPDEs were obtained [21–23].…”

Section: Introductionmentioning

confidence: 99%

Exact traveling wave solutions of the generalized fifth‐order dispersive equation by the improved Fan subequation method

Wang

2023

Math Methods in App Sciences

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In this paper, the improved Fan subequation method is employed to construct exact traveling wave solutions for a generalized fifth‐order dispersive equation. By making use of bifurcation theory of dynamical systems, we have succeeded to obtain the phase portraits of the subequations involving all possible parameter conditions, and many different types of traveling wave solutions as well, which include more general soliton solutions, kink solutions, triangular function solutions, rational solutions, and Jacobian elliptic function solutions with double periods and so on. Furthermore, as all parameters in the representations of exact solutions are free variables, the solutions obtained show more complex dynamical behaviors and could be applicable to explain diversity in qualitative features of wave phenomena.

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“…Feng studied the bifurcation of phase portraits of () and obtained all possible exact traveling wave solutions (bounded and unbouned) for all possible parameters

{\omega}_j

. As a result, more types of new exact solutions for some NPDEs were obtained [21–23].…”

Section: Introductionmentioning

confidence: 99%

Exact traveling wave solutions of the generalized fifth‐order dispersive equation by the improved Fan subequation method

Wang

2023

Math Methods in App Sciences

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“…In addition, in many practical cases, Eq. ( 1) also has opposite analog wave propagation directions [15][16][17][18]. Therefore, the study of the bSK equation is of great interest.…”

Section: Introductionmentioning

confidence: 99%

Spatial Self-Bending Soliton Phenomenon of (2+1) Dimensional bidirectional Sawada-Kotera Equation

Wang¹

2023

Preprint

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In this paper, we mainly study the spatial self-bending soliton phenomenon of the (2+1) dimensional bidirection-al Sawada-Kotera equation. The bilinear form of the (2+1)-dimensional bidirectional Sawada-Kotera equation is obtained by Hirota bilinear method, and then the N-soliton solution is obtained through special parameter constraints (e A js = 0), the spatial self-bending soliton is derived from the N-soliton solution, and the curvature of the spatial self-bending soliton is given furthermore, the interaction solution of spatial self-bending soliton and respiratory wave is obtained, and the interaction solution of spatial self-bending soliton and higher-order lump wave is obtained by using the method of long wave limit.

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“…Fan [33] developed a new sub-equation method to attain analytical exact solutions of NLEEs. Numerous authors presented the extended Fan sub-equation method by employing various sub-equations and realized plentiful new exact solutions of nonlinear equations [34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Traveling, periodic and localized solitary waves solutions of the (4+1)-dimensional nonlinear Fokas equation

Khatri¹,

Malik

Gautam

2020

SN Appl. Sci.

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By utilizing the three distinctive approaches specifically, the extended Fan sub-equation method, the exp[−G()]-function expansion method, and the fractional transformation method, the traveling waves and soliton solutions of the (4+1)-dimensional nonlinear Fokas equation are extracted. Meanwhile, some parametric constraint conditions are described. The acquired solutions are singular and nonsingular soliton solutions, periodic solutions, breather solution, rational solutions, trigonometric periodic wave solutions, hyperbolic solutions, Weierstrass, and Jacobi elliptic doubly periodic wave solutions. The dynamics of some of the obtained solutions are investigated and described in 2-dimensional figures by choosing appropriate parameter values. The comparison of our obtained results with the other solutions in literature shows that the obtained solutions of this paper are new and have not been formulated before by other techniques. We believe that all these results are useful to enrich the knowledge of the important physical phenomenon characterized by the Fokas equation. The reported solutions illustrate the straightforwardness, reliability, and effectiveness of the used techniques that can be further employed to higher-dimensional nonlinear evolution equations.

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The improved Fan sub-equation method and its application to the SK equation

Cited by 16 publications

References 17 publications

Exact traveling wave solutions of the generalized fifth‐order dispersive equation by the improved Fan subequation method

Exact traveling wave solutions of the generalized fifth‐order dispersive equation by the improved Fan subequation method

Spatial Self-Bending Soliton Phenomenon of (2+1) Dimensional bidirectional Sawada-Kotera Equation

Traveling, periodic and localized solitary waves solutions of the (4+1)-dimensional nonlinear Fokas equation

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