Novel travelling wave structures for (2+1)-dimensional Sawada–Kotera equation

Wang, Xiaobo; Zhao, Q.-L.; Jia, Man; Sen-Yue, Lou

doi:10.1016/j.aml.2021.107638

Cited by 10 publications

(4 citation statements)

References 14 publications

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“…It is obvious that setting u = v = w(x, y, t) and rescaling y → x would degenerate the 2DSK type system (1) into the SK equation [34,35]. The 2DSK system (1), as a (2+1)-dimensional extension of the SK equation, serves as a model for surface water waves and may have applications in conformal field theory, quantum gravity, and nematic liquid crystals [36,37].…”

Section: Introductionmentioning

confidence: 99%

Fusion and fission phenomena in a (2+1)-dimensional Sawada-Kotera type system

Wang,

Yang,

Tang

et al. 2024

Phys. Scr.

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In this study, we extend the generalized multilinear variable separation approach to a fifth-order nonlinear evolution equation. By performing asymptotic analysis on the variable separation solution, which is composed of three lower-dimensional functions, we identify a resonant regime governing dromion-dromion/solitoff interactions. In the case of two-dromion interactions, elastic, inelastic, and completely inelastic collisions are possible, while for the dromion-solitoff interaction only inelastic and completely inelastic collisions are permitted. Furthermore, we derive two types of semi-rational solutions from the quadratic function ansatz. In particular, in the scenario of a completely resonant collision between a lump and a line-soliton pair, the lump separates from one line soliton and exists briefly before merging with the other soliton, forming a localized lump in both time and space dimensions. The fusion or fission phenomena between the dromion-dromion/solitoff interaction and the lump-line soliton interaction are shown graphically.

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Section: Introductionmentioning

confidence: 99%

Fusion and fission phenomena in a (2+1)-dimensional Sawada-Kotera type system

Wang,

Yang,

Tang

et al. 2024

Phys. Scr.

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“…( 1), all of which are constants. At present, there are many methods to find the exact solution of nonlinear partial differential equations, such as homogeneous balance method [13,14], Hirota bilinear method [15,16,17], exponential function method [18,19], Jacobi elliptic function expansion method [20,21,22,23], and other methods. The equation studied in this paper is a NLPDE with complex numbers, so it is a challenge to solve its exact solution.…”

Section: Introductionmentioning

confidence: 99%

The exact solutions of Schrödinger-Hirota equation based on the extended auxiliary equation method

Du,

Yin,

Pang

2023

Preprint

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The Schr\"{o}dinger-Hirota equation are studied in light transmission, optical fiber communication, and nonlinear effects in optics. The extended fourth Jacobi elliptic equation is used in this paper to seek different types of exact solutions, which include bright soliton solutions, kink solutions, periodic wave solutions, and singular traveling wave solutions via selecting appropriate parameters.The characteristics of some solutions are graphically presented using two- and three-dimensional graphs such as the real part, the imaginary part, and their modulus via providing suitable values to arbitrary parameters. Compared to other methods, the method is more direct and easier for calculations.

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“…has important and wide applications in conformal field theory, quantum gravity field theory and conserved current of Liouville equation [26][27][28]. Soliton solutions [29][30][31], lump solutions [32,33], travelling wave solutions [34] and some other exact solutions [35] of Eq. 1 have been detailed.…”

Section: Introductionmentioning

confidence: 99%

Multiple lump solutions of the (2+1)-dimensional sawada-kotera-like equation

et al. 2022

Front. Phys.

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In this paper, 1-lump solution and 2-lump solution of a (2 + 1)-dimensional Sawada-Kotera-like equation are obtained by means of the Hirota’s bilinear method and long wave limit method. The propagation orbits, velocities and the collisions among waves are analyzed. By setting the parameter values, the dynamic characteristics of the obtained solutions are shown in 3D and density plots. These conclusions enrich the dynamical theory of higher-dimensional nonlinear dispersive wave equations.

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Novel travelling wave structures for (2+1)-dimensional Sawada–Kotera equation

Cited by 10 publications

References 14 publications

Fusion and fission phenomena in a (2+1)-dimensional Sawada-Kotera type system

Fusion and fission phenomena in a (2+1)-dimensional Sawada-Kotera type system

The exact solutions of Schrödinger-Hirota equation based on the extended auxiliary equation method

Multiple lump solutions of the (2+1)-dimensional sawada-kotera-like equation

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