Breather, multi-shock waves and localized excitation structure solutions to the Extended BKP–Boussinesq equation

Roshid, Harun-Or; Noor, N. F. M.; Khatun, Mst. Shekha; Başkonuş, Hacı Mehmet; Belgacem, Fethi Bin Muhammad

doi:10.1016/j.cnsns.2021.105867

Cited by 13 publications

(7 citation statements)

References 18 publications

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“…investigation are new and have been listed for the first time. The authors' suggestion for future works is employing newly well-organized methods [38][39][40][41][42][43][44] to acquire other wave structures of STOBE.…”

Section: Declaration Of Competing Interestmentioning

confidence: 99%

The Sharma–Tasso–Olver–Burgers equation: its conservation laws and kink solitons

Hosseini¹,

Akbulut²,

Băleanu³

et al. 2022

Commun. Theor. Phys.

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The present paper deals with the Sharma–Tasso–Olver–Burgers equation (STOBE) and its conservation laws and kink solitons. More precisely, the formal Lagrangian, Lie symmetries, and adjoint equations of the STOBE are firstly constructed to retrieve its conservation laws. Kink solitons of the STOBE are then extracted through adopting a series of newly well-designed approaches such as Kudryashov and exponential methods. Diverse graphs in 3D postures are formally portrayed to reveal the dynamical features of kink solitons. According to the authors’ knowledge, the outcomes of the current investigation are new and have been listed for the first time.

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Section: Declaration Of Competing Interestmentioning

confidence: 99%

The Sharma–Tasso–Olver–Burgers equation: its conservation laws and kink solitons

Hosseini¹,

Akbulut²,

Băleanu³

et al. 2022

Commun. Theor. Phys.

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“…Strain condition for the validity of the complex solution is also established. Moreover, Roshida et al 8 has studied an extended BKP‐Boussinesq equation to construct localized excitation solution, breather, and shock wave. The original model is transferred to the bilinear form by the transformation

u&#x0003D;2{(lnf)}_x

.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of rational and semi‐rational solution for a new extended (3 + 1)‐dimensional Kadomtsev‐Petviashvili equation

Yan

Xie

2022

Math Methods in App Sciences

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This paper proposes a new extended (3 + 1)-dimensional Kadomtsev-Petviashvili equation that portrays a unique dispersion effect about x, z. Its integrability is confirmed via the WTC-Kruskal algorithm in Painlevé sense.N-soliton, breather, and O-type solitary wave are derived systematically at first. Then, the mixed solution composed of soliton and breather is obtained. In addition, the "long wave" limit is employed to construct rational and semi-rational solution. The rational solution can be classified as rogue wave, T-type solitary wave, and lump wave. The semi-rational solution has the form a hybrid of two solitons, a hybrid of rogue wave and soliton, a hybrid of lump and soliton(s), and a hybrid of lump and breather. The results may help simulate complex waves and their interactions in fluid.

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“…Nonlinear partial differential equations have received wide attention because they can describe the common phenomena in the objective world more realistically. With the profound studies of researchers, many effective methods have been used to study the exact solution of nonlinear integer order evolution equation, such as first integral method [1], Hirota bilinear method [2], homogeneous balance method [3], Lie group method [4], function expansion method [5]. Nowadays, abundant classical mechanical techniques have been applied to the study of conservative system, however, majority of the processes discovered in physics are non-conservative.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis and Travelling Wave Solution for a Generalized Time Fractional KdV Equation

Wang¹,

Yang²,

Yang

et al. 2022

J. Phys.: Conf. Ser.

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By using bifurcation theory of planar dynamic system to a generalized time fractional KdV equation, a large number of solutions including irrational function solution, Jacobian elliptic function solution, trigonometric function solution, solitary solution as well as compacton solution are derived. Under different parametric selection, various kinds of sufficient conditions and numerical simulations are demonstrated to visualize their mechanism.

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Breather, multi-shock waves and localized excitation structure solutions to the Extended BKP–Boussinesq equation

Cited by 13 publications

References 18 publications

The Sharma–Tasso–Olver–Burgers equation: its conservation laws and kink solitons

The Sharma–Tasso–Olver–Burgers equation: its conservation laws and kink solitons

Dynamical analysis of rational and semi‐rational solution for a new extended (3 + 1)‐dimensional Kadomtsev‐Petviashvili equation

Bifurcation Analysis and Travelling Wave Solution for a Generalized Time Fractional KdV Equation

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