Kinky breather-wave and lump solutions to the (2 + 1)-dimensional Burgers equations

Hosseini, K.; Ansari, R.; Pouyanmehr, Roozbeh; Samadani, F.; Aligoli, M.

doi:10.1007/s13324-020-00405-z

Cited by 7 publications

(5 citation statements)

References 42 publications

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“…Conserved vectors are calculated to show the integrability of CBEs. The novelty of the presented results is proven, as these are absolutely different from previous results [1][2][3][4][5][6][7][8][9][10][11]. This method highlights the usefulness of the Lie symmetry approach and provides a flexible tool for solving NPDEs.…”

Section: Discussionmentioning

confidence: 71%

“…Liu et al [8] employed the residual symmetry reduction and extended tanh function expansion technique to achieve novel Bäcklund transformations and interaction solutions between distinct solitons. Hosseini et al [9] derived kinky breather-wave and lump solutions to the (2+1)-CBEs (1.1). To extract them, they used the extended homo clinic test technique and the Hirota bilinear method.…”

Section: Review Of the Previous Workmentioning

confidence: 99%

“…The above cited contributions of different researchers [1][2][3][4][5][6][7][8][9][10][11] related to CBEs inspired the authors to get more variety of invariant solutions to the CBEs (1.1) via one-parameter classical Lie group theory . The gap in previous research [1][2][3][4][5][6][7][8][9][10][11] is bridged, and a novel class of exact solutions is exploited by the classical Lie group theory. The method inherits the invariance, ensuring the system of PDEs remains invariant.…”

Section: Motivationmentioning

confidence: 99%

“…As a result, some methods have been established with the goal of advancing further and obtaining more variety of solutions. Some of them are multi-linear variable separation method [1], Riccati equation rational expansion method [2], direct ansätz method [3], Hirota's bilinear approach [4][5][6][7], residual symmetry reduction and extended tanh function expansion technique [8], extended homo clinic test technique [9] and Lie group method .…”

Section: Introduction 1aims and Scopementioning

confidence: 99%

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Kinks and soliton solutions to the coupled Burgers equation by Lie symmetry approach

Tanwar,

Kumar

2024

Phys. Scr.

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The current research employs a novel class of invariant solutions to Painleve integrable coupled Burgers equations. Many mathematical physics domains such as fluid dynamics, traffic flow, nonlinear acoustics, turbulence phenomena, and the interaction of convection and diffusion processes, use this fundamental model. The presented investigations utilize the Lie point symmetry to yield a class of exact solutions unknown in previous findings. Lie point symmetry reduces the number of independent variables in coupled Burgers equations. For the physical visualizations of the solutions, their profiles are analysed. Since arbitrary functions and constants are available in the solutions, the derived solutions have the potential to reveal rich physical structures. We next go over kink waves, multisoliton, line multisoliton and annihilation profiles in detail. We compute conserved vectors to demonstrate the integrability of CBEs. The results demonstrate their novelty, as they diverge completely from previous findings.

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Section: Discussionmentioning

confidence: 71%

Section: Review Of the Previous Workmentioning

confidence: 99%

Section: Motivationmentioning

confidence: 99%

Section: Introduction 1aims and Scopementioning

confidence: 99%

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Kinks and soliton solutions to the coupled Burgers equation by Lie symmetry approach

Tanwar,

Kumar

2024

Phys. Scr.

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“…One can construct lump solutions by the Hirota bilinear method and the Darboux transformation [37][38][39][40][41][42][43][44][45]. Lump waves of the high-dimensional nonlinear systems are constructed by solving the Hirota bilinear method [46][47][48][49]. A symbolic computation approach is one of the useful methods to search the lump wave [31].…”

Section: Lump Solution Of the ð2 + 1þ-dimensionalmentioning

confidence: 99%

Characteristics of the Soliton Molecule and Lump Solution in the $(2 + 1)$ -Dimensional Higher-Order Boussinesq Equation

Ren

2021

Advances in Mathematical Physics

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The soliton molecules, as bound states of solitons, have attracted considerable attention in several areas. In this paper, the 2 + 1 -dimensional higher-order Boussinesq equation is constructed by introducing two high-order Hirota operators in the usual 2 + 1 -dimensional Boussinesq equation. By the velocity resonance mechanism, the soliton molecule and the asymmetric soliton of the higher-order Boussinesq equation are constructed. The soliton molecule does not exist for the usual 2 + 1 -dimensional Boussinesq equation. As a special kind of rational solution, the lump wave is localized in all directions and decays algebraically. The lump solution of the higher-order Boussinesq equation is obtained by using a quadratic function. This lump wave is just the bright form by some detail analysis. The graphics in this study are carried out by selecting appropriate parameters. The results in this work may enrich the variety of the dynamics of the high-dimensional nonlinear wave field.

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Bilinear Bäcklund transformation, Lax pair, Painlevé integrability, and different wave structures of a 3D generalized KdV equation

Hosseini,

Alizadeh,

Hinçal

et al. 2024

Nonlinear Dyn

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Kinky breather-wave and lump solutions to the (2 + 1)-dimensional Burgers equations

Cited by 7 publications

References 42 publications

Kinks and soliton solutions to the coupled Burgers equation by Lie symmetry approach

Kinks and soliton solutions to the coupled Burgers equation by Lie symmetry approach

Characteristics of the Soliton Molecule and Lump Solution in the $(2 + 1)$ -Dimensional Higher-Order Boussinesq Equation

Bilinear Bäcklund transformation, Lax pair, Painlevé integrability, and different wave structures of a 3D generalized KdV equation

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Kinky breather-wave and lump solutions to the (2 + 1)-dimensional Burgers equations

Cited by 7 publications

References 42 publications

Kinks and soliton solutions to the coupled Burgers equation by Lie symmetry approach

Kinks and soliton solutions to the coupled Burgers equation by Lie symmetry approach

Characteristics of the Soliton Molecule and Lump Solution in the 2 + 1 -Dimensional Higher-Order Boussinesq Equation

Bilinear Bäcklund transformation, Lax pair, Painlevé integrability, and different wave structures of a 3D generalized KdV equation

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Product

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Characteristics of the Soliton Molecule and Lump Solution in the $(2 + 1)$ -Dimensional Higher-Order Boussinesq Equation