Exact traveling wave solutions for the Benjamin–Bona–Mahony equation by improved Fan sub-equation method

Li, Hong; Wang, Kanmin; Li, Jibin

doi:10.1016/j.apm.2013.03.027

Cited by 15 publications

(5 citation statements)

References 10 publications

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“…To name some as example, inverse scattering method [1], the sine-cosine method and the tanh method [2][3][4]. This time, a more effective method -the approach of dynamical systems and the theory of bifurcations can help us get travelling wave solutions of a NPDE [5][6][7][8][9]. In [5], Li and He use this method to analysis a nonlinear wave equation and get its all types of solutions.…”

Section: Introductionmentioning

confidence: 99%

Bifurcations and travelling wave solutions of a (2+1)-dimensional nonlinear Schrödinger equation

Wang

Chen

Liu

2014

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

Bifurcations and travelling wave solutions of a (2+1)-dimensional nonlinear Schrödinger equation

Wang

Chen

Liu

2014

Applied Mathematics and Computation

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“…Therefore, solving NLEEs has become an essential and far-reaching topic in contemporary nonlinear scientific theory. For a long time, many scientific workers have done extensive work in the solutions of NLEEs and have proposed many valid methods which include the Lie group method [4][5][6][7][8], Bäcklund transformation [9,10], Bifurcation analysis [11][12][13][14][15][16][17], Fan sub-function method [18][19][20], Hirota bilinear method [21][22][23], Homogeneous balance method [24,25], and more [26,27].…”

Section: Introductionmentioning

confidence: 99%

Exact solutions and bifurcations for the (3+1)-dimensional generalized KdV-ZK equation

Song,

Ma,

Yang

et al. 2024

Phys. Scr.

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In this paper, a class of (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov (KdV-ZK) equation is studied by utilizing the bifurcation theory of the planar dynamical systems and the Fan sub-function method. This model can be used to explain the effects of magnetic fields on weakly nonlinear ion-acoustic waves investigated in plasma fields composed of cold and hot electrons. Under the different parameter conditions, the phase portraits and bifurcations are derived, and new exact solutions including soliton, periodic, kink and breaking wave solutions for the model are constructed. Moreover, some exact solutions, which contain soliton, kink, trigonometric function, hyperbolic function, Jacobi elliptic function solutions, are derived via the improved Fan sub-function method. The types of solutions obtained completely correspond to the types of the orbits acquiredabove, which verifies the validity of the method. Finally, the physical structures of some exact solutions are analyzed in graphical forms.

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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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Exact traveling wave solutions for the Benjamin–Bona–Mahony equation by improved Fan sub-equation method

Cited by 15 publications

References 10 publications

Bifurcations and travelling wave solutions of a (2+1)-dimensional nonlinear Schrödinger equation

Bifurcations and travelling wave solutions of a (2+1)-dimensional nonlinear Schrödinger equation

Exact solutions and bifurcations for the (3+1)-dimensional generalized KdV-ZK equation

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

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