Shallow-water-wave studies on a (2 + 1)-dimensional Hirota–Satsuma–Ito system: X-type soliton, resonant Y-type soliton and hybrid solutions

Shen, Yuan; Tian, Bo; Zhou, Tianyu; Gao, Xiao-Tian

doi:10.1016/j.chaos.2022.111861

Cited by 56 publications

(7 citation statements)

References 82 publications

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“…Numerical simulations show that such solutions take the shape of the capital letter Y in spatial structures. The error analysis reveals that our obtaineddata-driven fusion and fission solutions can rapidly approximate the exact ones derived by Tian and his coauthors [39]. Therefore, we conclude that the PINN method is a very effective algorithm for constructing the data-driven fusion and fission solutions for nonlinear equations.…”

Section: Introductionsupporting

confidence: 52%

Data-driven fusion and fission solutions in the Hirota–Satsuma–Ito equation via the physics-informed neural networks method

Sun,

Xing,

2023

Commun. Theor. Phys.

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Fusion and ﬁssion are two important phenomena, which have been experimentally observed in many real physical models. In this paper, we investigate the two phenomena in the (2+1)-dimensional Hirota-Satsuma-Ito (HSI) equation via the physics-informed neural networks (PINN) method. By choosing suitable physically-constrained initial boundary conditions, the data-driven fusion and ﬁssion solutions are obtained for the ﬁrst time. Dynamical behaviors and error analysis of these solutions are investigated via illustratively numerical ﬁgures, which show that good results are achieved. It is pointed out that the PINN method adopted here can be eﬀectively used to construct the data-driven fusion and ﬁssion solutions for the other nonlinear integrable equations. Based on the powerful prediction ability of the PINN method and wide applications of fusion and ﬁssion in many physical areas, it is hoped that the data-driven solutions obtained here can be helpful for experts to predict or explain some related physical phenomena.

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Section: Introductionsupporting

confidence: 52%

Data-driven fusion and fission solutions in the Hirota–Satsuma–Ito equation via the physics-informed neural networks method

Sun,

Xing,

2023

Commun. Theor. Phys.

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“…Meanwhile, the multi-soliton waves are considered as significant features to the integrable equations where the existence of soliton and multi-soliton waves is naturally used to investigate non-linear physical phenomena in the real world [1]. Recently, various versions of models have been explored, some of which are the Sawada-Kotera (SK) equation to the study of the motion of long waves in shallow water under the gravity [2], the Kadomtsev-Petviashvili (KP) equation to the study of bifurcation phenomena in fluids [3], the Hirota-Satsuma-Ito (HSI) equation to the study of shallow water wave [4][5][6][7][8][9][10][11][12], the Schrodinger equations to the study of fiber applications [13][14][15] and others [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Moreover, with the rapid development of computer calculation science, in the latest decade, many scientists have paid attention to the analytical solutions of NLEEs.…”

Section: Introductionmentioning

confidence: 99%

The applications of symbolic computation to exact wave solutions of two HSI-like equations in (2+1)-dimensional

Kuo

Günay²,

Juan³

2023

Front. Phys.

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It is renowned that Hirota–Satsuma–Ito (HSI) equation is widely used to study wave dynamics of shallow water. In this work, two new HSI-like equations are investigated which could be extended to diversify problems in natural phenomena and give admirable contributions by applying the generalized exponential rational function method (GERFM). With the aid of symbolic calculations, various constraints on the free parameters are given, while classes of wave solutions are explicitly constructed from the coefficients of the combined non-linear and dissipative terms. After specifying values for free parameters, singular, periodic singular and anti-kink waves are demonstrated in 3D figures to exhibit different kinds of wave propagations. The fact that parameters directly influence the wave amplitude and speed of traveling waves is illustrated. The derived results are innovative and have important applications in the current field of mathematical physics research. Eventually, we show that generalized exponential rational function method is effective and straightforward to solve higher-order and high-dimensional non-linear evolution equations.

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“…Fluid mechanics has been regarded as the study of the fundamental mechanisms and force of liquids, plasmas and gases, with applications in astrophysics, meteorology, oceanography and biomedical engineering [1][2][3][4]. Methods have been introduced to solve the nonlinear evolution equations, including the Bäcklund transformation, Darboux transformation and the Lie symmetry approach [5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Painlevé analysis, auto-Bäcklund transformations, bilinear forms and soliton solutions for a (2+1)-dimensional variable-coefficient modified dispersive water-wave system in fluid mechanics

Liu

Gao

2023

Commun. Theor. Phys.

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Under investigation in this paper is a (2+1)-dimensional variable-coefficient modified dispersive water-wave (vcMDWW) system in fluid mechanics. We prove the Painlevé integrability for the vcMDWW system via the Painlevé analysis. We get auto-Bäcklund transformations for the vcMDWW system via the truncated Painlevé expansions. Bilinear forms and N-soliton solutions are constructed, where N is a positive integer. We discuss the inelastic, elastic interactions and soliton resonances for the two solitons. We graphically demonstrate that velocities of the solitons are affected by the variable coefficient of that system.

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Shallow-water-wave studies on a (2 + 1)-dimensional Hirota–Satsuma–Ito system: X-type soliton, resonant Y-type soliton and hybrid solutions

Cited by 56 publications

References 82 publications

Data-driven fusion and fission solutions in the Hirota–Satsuma–Ito equation via the physics-informed neural networks method

Data-driven fusion and fission solutions in the Hirota–Satsuma–Ito equation via the physics-informed neural networks method

The applications of symbolic computation to exact wave solutions of two HSI-like equations in (2+1)-dimensional

Painlevé analysis, auto-Bäcklund transformations, bilinear forms and soliton solutions for a (2+1)-dimensional variable-coefficient modified dispersive water-wave system in fluid mechanics

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Shallow-water-wave studies on a (2 + 1)-dimensional Hirota–Satsuma–Ito system: X-type soliton, resonant Y-type soliton and hybrid solutions

Cited by 56 publications

References 82 publications

Data-driven fusion and fission solutions in the Hirota–Satsuma–Ito equation via the physics-informed neural networks method

Data-driven fusion and fission solutions in the Hirota–Satsuma–Ito equation via the physics-informed neural networks method

The applications of symbolic computation to exact wave solutions of two HSI-like equations in (2+1)-dimensional

Painlevé analysis, auto-Bäcklund transformations, bilinear forms and soliton solutions for a (2+1)-dimensional variable-coefficient modified dispersive water-wave system in fluid mechanics

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Shallow-water-wave studies on a (2 + 1)-dimensional Hirota–Satsuma–Ito system: X-type soliton, resonant Y-type soliton and hybrid solutions