Yong-Jiang Guo’s research while affiliated with Beijing University of Posts and Telecommunications and other places

... Different kinds of exact wave solutions are achieved in the literature by using different methods. Instantly; some exact wave solutions are obtained by applying the generalized kudryashov method in [14], different kinds of analytical wave solitons are achieved by using classical Lie-symmetry analysis in [15], distinct types of wave solitons are achieved by utilizing first integral scheme in [16], some exact wave solutions are obtained by using the Lie symmetry analysis method in [17], different types of exact soliton solutions are gained by using similarity reduction method in [18], some solutions are obtained by applying the shifted orthonormal Bernoulli polynomials in [19]. ...

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Exact wave solutions of truncated M-fractional Boussinesq-Burgers system via an effective method

... In recent years, Korteweg-de Vries (KdV)-type equations have attracted the attention of researchers, which have occurred in the fields of planetary oceans [1], atmospheres [2,3], cosmic plasmas [4][5][6] and so on [7][8][9][10][11][12][13][14][15][16][17]. In this paper, we will study a (3+1)-dimensional KdV equation with the time-dependent coefficients in a fluid [18], i.e., u yt + g 1 (t)u xxxy + g 2 (t)(u x u y ) x + g 3 (t)u x x + g 4 (t)u yy + g 5 (t)u yz = 0 , (1) where u is a differentiable function of the scaled spatial variables x, y and z and temporal variable t, the subscripts are the partial derivatives, while g (t) ( = 1, 2, · · · , 5) are the differentiable time-dependent functions. ...

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Bilinear Form, N Solitons, Breathers and Periodic Waves for a (3+1)-Dimensional Korteweg-de Vries Equation with the Time-Dependent Coefficients in a Fluid

... We will confirm the correctness of Bilinear Forms (2). In Section 3, via the Clarkson-Kruskal direct method [65,66], we will create a set of the similarity reductions for System (1) which differs from those in Refs. [21,22], so as to simplify that system to a solvable ordinary differential equation (ODE). ...

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For the Shallow Water Waves: Bilinear-Form and Similarity-Reduction Studies on a Boussinesq-Burgers System

... Researchers use various methods such as ships, satellites, submarines, moorings, aircraft, and remote vehicles to investigate the ocean's surface and depths in order to understand the physical forces that control energy transfer, mixing processes, wave movement, turbulence, circulation at different scales, and the ocean's contribution to local weather and global climate within an interconnected system [6]. ...

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Lie Subalgebras, Solutions and Conserved Vectors of a Nonlinear Geophysical Korteweg de Vries Equation in Ocean Physics and Nonlinear Mechanics with Power Law

... A scaling transformation, two hetero-Bäcklund transformations and a set of the similarity reductions for WBKEs were established in [15]. In [16,17], Bell polynomials and symbolic computation were shown to lead to two sets of auto-Bäcklund transformations and used to investigate different oceanic-water-wave dispersion. The bilinear form for WBKEs was constructed and three bilinear Bäcklund transformations with certain soliton-like solutions were formulated in [18]. ...

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Oceanic water waves via double and single convex-concave solitons in the generalized Whitham-Broer-Kaup-Boussinesq-Kupershmidt equations with a novel truncated MM-derivative

... Recent decades have seen mathematicians and scientists proposing various methods to solve exact solutions for rapidly developing NLPDEs, such as the Lie symmetry method (LSM) [7][8][9][10][11], Hirota's bilinear method [12][13][14][15][16], auto-Bäcklund transformation [17][18][19][20], the G ′ /G 2 -expansion method [21][22][23][24], Darboux transformation [25][26][27], the tan-cot technique [28,29], the generalized Riccati equation expansion method [30], Painlevé's analysis [31,32], the optimal homotopy asymptotic method (OHAM) [33], the residual power series method (RPSM) [34], the inverse scattering transform method [35], and so on [36][37][38]. Lie symmetry analysis method serves as a powerful mathematical tool for finding exact solutions of NLPDEs. ...

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A New (3+1)-Dimensional Extension of the Kadomtsev–Petviashvili–Boussinesq-like Equation: Multiple-Soliton Solutions and Other Particular Solutions

... Investigations on the shallow water waves have been belonging to the cutting-edge issues in sciences and engineering [1][2][3][4][5][6][7][8][9][10][11][12], e.g., certain Paul-Painlevé and phaseplane analyses on a generalized (3+1)-dimensional shallow water wave model [1], oceanic/laky shallow-water dynamics through a Boussinesq-Burgers system [2], bilinear form, bilinear Bäcklund transformations, breather and periodic-wave solutions for a (2+1)-dimensional shallow water equation with the time-dependent coefficients [3], breather wave solutions for a (3+1)-dimensional generalized shallow water wave equation with variable coefficients [4], soliton and periodic wave solutions for a fractional Dullin-Gottwald-Holm equation describing the water waves in a shallow regime [5], consideration on the shallow water of a wide channel or an open sea through a generalized (2+1)-dimensional dispersive long-wave system [6], local well-posedness, wave breaking data and non-existence of the sech 2 solutions for a highly nonlinear shallow water equation [8], statistical characterization of the erosion and sediment transport mechanics in the shallow tidal environments [9] and oceanic shallow-water studies on a generalized Whitham-Broer-Kaup-Boussinesq-Kupershmidt system [10]. Other recent nonlinear-fluid studies have been reported, e.g., in Refs. ...

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Auto-Bäcklund Transformation with the Solitons and Similarity Reductions for a Generalized Nonlinear Shallow Water Wave Equation

... Boussinesq-Burgers type equations have arisen in the study of shallow water waves [19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Other nonlinear evolution equations (NLEEs) have also been developed for those shallow water waves as well as some additional physical phenomena [33][34][35][36][37][38][39][40][41][42][43][44][45]. Since the solutions of the NLEEs can help people understand the relevant wave processes, researchers have employed a variety of the methods to obtain, or assist in solving some solutions for the NLEEs, such as the Bäcklund transformation [46][47][48], Hirota bilinear method [49][50][51][52], Darboux transformation [53][54][55][56] and so on. ...

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For the Shallow Water Waves: Bilinear-Form and Similarity-Reduction Studies on a Boussinesq-Burgers System

... (1a) v t À av xx À b uv ð Þ x ¼ 0; (1b) in which the real differentiable functions v(x, y, t) and u(x, y, t), respectively, imply the horizontal velocity of the water wave and the height of the water surface, a and b are the real non-zero constants, and the subscripts represent the partial derivatives concerning the scaled space variables x, y and time variable t. With symbolic computation (Anderson and Farazmand, 2024;Kovacs et al., 2024;Shen et al., 2023aShen et al., , 2023bGao et al., 2023b;Wu and Gao, 2023;Wu et al., 2023aWu et al., , 2023cWu et al., , 2023dZhou and Tian, 2022) in planning, Gao et al. (2023a) have given a set of the hetero-Bäcklund transformations, a set of the scaling transformations and four sets of the similarity reductions for system (1), whereas Liu et al. (2023) have investigated certain Lie point symmetry generators, Lie symmetry groups and symmetry reductions for system (1) with some analytic solutions. Shallow-water special cases of system (1) have been seen in Ying and Lou (2000), Li and Zhang (2004), Ma et al. (2015), Zhao and Han (2015), Kassem and Rashed (2019), Yamgou e et al. (2022), Gao et al. (2023a) as well as Liu et al. (2023). ...

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Letter to the Editor on HFF 32, 138 (2022); 32, 2282 (2022); 33, 965 (2023) and 34, 1189 (2024) for the recent shallow-water studies

... The (2 + 1) dimensional dispersion long wave equations(DLWEs) u yt + (v x + uu y ) x = 0, v t + (uv − u xy ) x = 0, (1.1) where u and v are wave amplitude functions in relation to spatial variables (x and y) and time variable (t). Eq. (1.1) is a mathematical model that describes the scenario of wide channels or open oceans with finite depth, which has substantial research significance in physics, engineering and earth science [1][2][3][4][5][6][7][8]. The DLWEs were initially introduced by Boiti in 1987 as a compatibility condition for a weak Lax pair [8]. ...

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Construction and analysis of multi-lump solutions of dispersive long wave equations via integer partitions