Solitary, kink and periodic wave solutions of the (3+1)-dimensional Hirota–Satsuma–Ito-like equation

Song, Yunjia; Wang, Z; Ma, Yanzhi; Yang, Ben

doi:10.1016/j.rinp.2022.106013

Cited by 5 publications

(3 citation statements)

References 37 publications

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“…The homogeneous balance principle [30,31] is an effective method for solving NLEEs. According to this principle, we can determine in advance whether a solution of a given form exists, and if so, it can be solved by some steps.…”

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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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.

View full text Add to dashboard Cite

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“…For multi-component integrable models (see, e.g., [10,11]), other kinds of transformations need to be introduced and implemented, and for non-integrable equations, the multiple exp-function method plays a similar role as the bilinear algorithm in exploring dispersive wave solutions (see, e.g., [12,13]). Within the Hirota bilinear theory, an N-soliton solution to a nonlinear equation can be presented by solving its corresponding Hirota bilinear equation (see, e.g., [8]).…”

Section: Introductionmentioning

confidence: 99%

Lump Waves in a Spatial Symmetric Nonlinear Dispersive Wave Model in (2+1)-Dimensions

2023

Mathematics

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This paper aims to search for lump waves in a spatial symmetric (2+1)-dimensional dispersive wave model. Through an ansatz on positive quadratic functions, we conduct symbolic computations with Maple to generate lump waves for the proposed nonlinear model. A line of critical points of the lump waves is computed, whose two spatial coordinates travel at constant speeds. The corresponding maximum and minimum values are evaluated in terms of the wave numbers, and interestingly, all those extreme values do not change with time, either. The last section is the conclusion.

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“…The study of exact solutions of NFPDEs facilitates researchers to drill deeper into the physical interpretation of the solutions. For now, a large number of effective and practical methods have been applied to explore exact solutions of NFPDEs, such as the modified extended tanh-function (mETF for short) method [1,2], the improved ( ) ¢ G G method [3, 4], the two variables ( ) ¢ G G G , 1 -expansion method [5][6][7], the Darboux transformation method [8], the Kudryashov method [9,10], the exp-function method [11,12], the Hirota's bilinear method [13], the first integral method [14], the sine-cosine method [15,16], the modified ( ) ¢ G G 2 -expansion method [17][18][19] and the Bifurcation method [20][21][22], and so on [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Exact solutions and bifurcations of the time-fractional coupled Boussinesq-Burgers equation

Liu,

Xu,

Wang

2023

Phys. Scr.

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In this paper, the time-fractional coupled Boussinesq-Burgers equations are studied to construct exact solutions by utilizing the modified extended tanh-function method, the improved (G'/G) method, the two variables (G'/G,1/G)-expansion method and bifurcation analysis. Firstly, based on the modified Riemann-Liouville derivative and traveling wave transformation, the equations are rewritten as an ordinary differential equation. Some exact solutions, including singular, periodic, kink, anti-kink, soliton and periodic-singular solutions, are derived. Then, we graphically describe the 3D, density plots and solution profiles of some solutions by setting suitable parameters. Finally, the effectiveness of the methods applied is verified via bifurcation theory.

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Solitary, kink and periodic wave solutions of the (3+1)-dimensional Hirota–Satsuma–Ito-like equation

Cited by 5 publications

References 37 publications

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

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

Lump Waves in a Spatial Symmetric Nonlinear Dispersive Wave Model in (2+1)-Dimensions

Exact solutions and bifurcations of the time-fractional coupled Boussinesq-Burgers equation

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