Employing Hirota’s bilinear form to find novel lump waves solutions to an important nonlinear model in fluid mechanics

Hirota's bilinear form for the Complex Modified Korteweg-de Vries-II equation (CMKdV-II) is derived. We obtain one- and two-soliton solutions analytically for the CMKdV-II. One-soliton solution of the CMKdV-II equation is obtained by using finite difference method by implementing an iterative method.

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Soliton Solutions, Bäcklund Transformation and Wronskian Solutions for the (2+1)-Dimensional Variable-Coefficient Konopelchenko–Dubrovsky Equations in Fluid Mechanics

Zeitschrift für Naturforschung A ◽

10.5560/zna.2011-0071 ◽

2012 ◽

Vol 67 (3-4) ◽

pp. 132-140

Author(s):

Peng-Bo Xu ◽

Yi-Tian Gao

Keyword(s):

Shear Flow ◽

Fluid Mechanics ◽

Shallow Water ◽

Bilinear Form ◽

Water Waves ◽

Variable Coefficient ◽

Soliton Solutions ◽

Shallow Water Waves ◽

Stratified Shear Flow ◽

Dimensional Variable

This paper is to investigate the (2+1)-dimensional variable-coefficient Konopelchenko- Dubrovsky equations, which can be applied to the phenomena in stratified shear flow, internal and shallow-water waves, plasmas, and other fields. The bilinear-form equations are transformed from the original equations, and soliton solutions are derived via symbolic computation. Soliton solutions and collisions are illustrated. The bilinear-form B¨acklund transformation and another soliton solution are obtained. Wronskian solutions are constructed via the B¨acklund transformation and solution

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The study of complexitons and periodic solitary-wave solutions with fifth-order KdV equation in (2+1) dimensions

Modern Physics Letters B ◽

10.1142/s0217984919504116 ◽

2019 ◽

Vol 33 (33) ◽

pp. 1950411 ◽

Cited By ~ 3

Author(s):

Muhammad Tahir ◽

Aziz Ullah Awan

Keyword(s):

Solitary Wave ◽

Bilinear Form ◽

Kdv Equation ◽

Three Dimensional ◽

Solitary Wave Solutions ◽

Test Technique ◽

Wave Solutions ◽

Complexiton Solutions ◽

Hirota’S Bilinear Form ◽

Fifth Order

In this paper, the generalized fifth-order (2[Formula: see text]+[Formula: see text]1)-dimensional KdV equation is scrutinized via the extended homoclinic test technique (EHTT) and extended transformed rational function (ETRF) method. With the aid of Hirota’s bilinear form, various exact solutions comprising, periodic solitary-wave, kinky-periodic solitary-wave, periodic soliton and complexiton solutions are constructed. Moreover, the mechanical features and dynamic characteristics of the obtained solutions are presented by three-dimensional plots.

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Lump, periodic lump and interaction lump stripe solutions to the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation

Modern Physics Letters B ◽

10.1142/s0217984918501063 ◽

2018 ◽

Vol 32 (07) ◽

pp. 1850106 ◽

Cited By ~ 17

Author(s):

Pinxia Wu ◽

Yufeng Zhang ◽

Iqbal Muhammad ◽

Qiqi Yin

Keyword(s):

Energy Distribution ◽

Bilinear Form ◽

Dynamic Process ◽

Propagation Direction ◽

Horizontal Velocity ◽

Lump Solutions ◽

Petviashvili Equation ◽

Hirota’S Bilinear Form ◽

Bkp Equation

In this paper, the Hirota’s bilinear form is employed to investigate the lump, periodic lump and interaction lump stripe solutions of the (2+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation. Many results are obtained by dynamic process of figures. We analyze the propagation direction and horizontal velocity of lump solutions to find some constraint conditions which include positiveness and localization. In the process of the travel of the periodic lump solutions, it appears that the energy distribution is not symmetrical. The interaction lump stripe solutions of non-elastic indicate that the lump solitons are dropped and swallowed by the stripe soliton.

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Lump solitons and interaction phenomenon to a (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation

Modern Physics Letters B ◽

10.1142/s0217984919503950 ◽

2019 ◽

Vol 33 (32) ◽

pp. 1950395 ◽

Cited By ~ 3

Author(s):

Na Liu ◽

Yansheng Liu

Keyword(s):

Symbolic Computation ◽

Bilinear Form ◽

Nonlinear Waves ◽

Soliton Solutions ◽

Lump Solutions ◽

Interaction Solutions ◽

Hirota’S Bilinear Form ◽

Interaction Phenomenon

This paper studies lump solutions and interaction solutions for a (3[Formula: see text]+[Formula: see text]1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation. With the help of symbolic computation and Hirota’s bilinear form, we obtain bright–dark lump solutions, lump-soliton solutions, and lump-kink solutions. Meanwhile, the dynamics of the obtained three classes of solutions are analyzed and exhibited mathematically and graphically. These results provide us with useful information to grasp the propagation processes of nonlinear waves.

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