Abundant Lump Solutions and Interaction Phenomena to the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation

Lü, Jianqing; Bilige, Sudao; Gao, Xiaoqing; Bai, Yuexing; Zhang, Runfa

doi:10.4236/jamp.2018.68148

Cited by 44 publications

(16 citation statements)

References 45 publications

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“…In Figures 1 and 2, the solution () is plotted for a appropriate option of the parameters a , b , c , and d at space x =−2,0,2, respectively. Seeing the expression of (), we discover that f 2 is a positive quadratic function with the condition a >0, which is compatible with the findings in Lü et al 54 …”

Section: New M‐lump Solutions Of the Annv Equationsupporting

confidence: 90%

N‐lump and interaction solutions of localized waves to the (2 + 1)‐dimensional asymmetrical Nizhnik–Novikov–Veselov equation arise from a model for an incompressible fluid

Manafian

İlhan

Avazpour

et al. 2020

Math Methods in App Sciences

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The present article deals with M-soliton solution and N-soliton solution of the (2 + 1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation by virtue of Hirota bilinear operator method. The obtained solutions for solving the current equation represent some localized waves including soliton, breather, lump, and their interactions, which have been investigated by the approach of the long-wave limit. Mainly, by choosing the specific parameter constraints in the M-soliton and N-soliton solutions, all cases of the one breather or one lump can be captured from the two, three, four, and five solitons. In addition, the performances of the mentioned technique, namely, the Hirota bilinear technique, are substantially powerful and absolutely reliable to search for new explicit solutions of nonlinear models. Meanwhile, the obtained solutions are extended with numerical simulation to analyze graphically, which results in localized waves and their interaction from the two-, three-, four-, and five-soliton solutions profiles. They will be extensively used to report many attractive physical phenomena in the fields of acoustics, heat transfer, fluid dynamics, classical mechanics, and so on.

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Section: New M‐lump Solutions Of the Annv Equationsupporting

confidence: 90%

N‐lump and interaction solutions of localized waves to the (2 + 1)‐dimensional asymmetrical Nizhnik–Novikov–Veselov equation arise from a model for an incompressible fluid

Manafian

İlhan

Avazpour

et al. 2020

Math Methods in App Sciences

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“…a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a 2 2 2 2 4 8 9 4 8 8 9 2 3 4 5 5 6 7 2 9 9 9 2 2 8 9 14 8 14 8 8 9 9 10 10 11 12 13 2 9 9 14 14 15 15 16 16 1 1 2 2 3 3 0, , , , , 0, , , , , , 0, , , , , , , , a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a with the condition 9 0 a ≠ . To search the periodic solution of the KPB-like equation, for example, let's try to substitute the solution (32) into the expression (31). Then through the expression (31) and the transformation (2), we get the periodic solitary wave solution of the KPB-like equation,…”

Section: Casementioning

confidence: 99%

“…are real parameters to be determined later. With the help of Maple, substituting(31) into Equation(3), we obtain a set of algebraic equations in algebraic equations, we can find the following sets of solutions and these set leads to the corresponding periodic solitary wave solutions of the KPB-like equation.…”

mentioning

confidence: 99%

Diversity of New Three-Wave Solutions and New Periodic Waves for the (3 + 1)-Dimensional Kadomtsev-Petviashvili-Boussinesq-Like Equation

Li¹,

Bilige²,

Zhang³

et al. 2020

JAMP

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Based on the generalized bilinear method, diversity of exact solutions of the (3 + 1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like equation is successfully derived by using symbolic computation with Maple. These new solutions, named three-wave solutions and periodic wave have greatly enriched the existing literature. Via the three-dimensional images, density images and contour plots, the physical characteristics of these waves are well described. The new three-wave solutions and periodic solitary wave solutions obtained in this paper, will have a wide range of applications in the fields of physics and mechanics.

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“…Based on the semi‐inverse variational principle and by multiplying Equation with u ′ and integrating brings about the stationary integral

J = \int_{- \infty}^{\infty} ((), \frac{- m c}{2} {false(u^{'} false)}^{2} + m^{3} false(m α + n β false) ([], u^{'} u^{' ″} - \frac{1}{2} {false(u^{''} false)}^{2}) + \frac{2}{3} m^{2} false(3 m α + 4 n β false) {false(u^{'} false)}^{3}) d ξ .

…”

Section: Application Of Sivp For Equation (12)mentioning

confidence: 99%

Breather wave, periodic, and cross‐kink solutions to the generalized Bogoyavlensky‐Konopelchenko equation

Manafian

Ivatloo

Abapour

2019

Math Methods in App Sciences

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The present article deals with multi-waves and breather wave solutions of the generalized Bogoyavlensky-Konopelchenko equation by virtue of the Hirota bilinear operator method and the semi-inverse variational principle. The obtained solutions for solving the current equation represent some localized waves including soliton, periodic, and cross-kink solutions in which have been investigated by the approach of the bilinear method. With certain parameter constraints in the multi-waves and breather, all cases of the periodic and cross-kink solutions can be captured from the one and two soliton(s). The obtained solutions are extended with numerical simulation to analyze graphically, which results into 1-and 2-soliton solutions and also periodic and cross-kink solutions profiles, that will be extensively used to report many attractive physical phenomena in the fields of acoustics, heat transfer, fluid dynamics, classical mechanics, and so on. KEYWORDS generalized Bogoyavlensky-Konopelchenko equation, Hirota bilinear operator method, multi-waves and breather, periodic and cross-kink solutions, semi-inverse variational principle, solitons MSC CLASSIFICATION

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Abundant Lump Solutions and Interaction Phenomena to the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation

Cited by 44 publications

References 45 publications

N‐lump and interaction solutions of localized waves to the (2 + 1)‐dimensional asymmetrical Nizhnik–Novikov–Veselov equation arise from a model for an incompressible fluid

N‐lump and interaction solutions of localized waves to the (2 + 1)‐dimensional asymmetrical Nizhnik–Novikov–Veselov equation arise from a model for an incompressible fluid

Diversity of New Three-Wave Solutions and New Periodic Waves for the (3 + 1)-Dimensional Kadomtsev-Petviashvili-Boussinesq-Like Equation

Breather wave, periodic, and cross‐kink solutions to the generalized Bogoyavlensky‐Konopelchenko equation

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