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Soliton Dynamics of the Generalized Shallow Water Like Equation in Nonlinear Phenomenon
Frontiers in Physics, 2022 The generalized shallow water like equation is investigated in this research paper. Exact solutions of generalized shallow water like equation are extracted using modified auxiliary equation (MAE) method and extended (G′G2)-expansion method.
Ghazala Akram +2 more
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An extended linear shallow-water equation [PDF]
Journal of Fluid Mechanics, 2019 An extension to the classical shallow-water equation (SWE) is derived that exactly satisfies the bed condition and can be regarded as an approximation to wave scattering at the next order in the small parameter $(h/\unicode[STIX]{x1D706})^{2}$ (depth to ...
R. Porter
semanticscholar +4 more sources
Global Weak Solutions for a Shallow Water Equation
Communications in Mathematical Physics, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Adrian Constantin +2 more
exaly +3 more sources
Exact solutions of the generalized (2+1)-dimensional shallow water wave equation
Results in Physics, 2022 In this paper, we construct abundant exact solutions of generalized (2+1)-dimensional shallow water wave equation via the Hirota bilinear method and test functions. We obtain exact interaction solutions, such as solitons, lump solutions and lump-periodic
Shan Yu, Lin Huang
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Optimal Control of a Viscous Shallow Water Equation [PDF]
Advances in Mathematical Physics, 2013 This paper is concerned with a viscous shallow water equation, which includes both the viscous Camassa-Holm equation and the viscous Degasperis-Procesi equation as its special cases.
Wenbin Zhang, Jiangbo Zhou
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Results in Physics, 2023 Results Phys. 43, 106048 (2022) has amusingly retrieved some solitonic and other analytic solutions for a shallow water wave equation presented there. In this Letter, we suggest that such an equation be moreover studied in line with Results Phys.
Xin-Yi Gao, Yong-Jiang Guo, Wen-Rui Shan
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Peakon solutions of the shallow water equation
Applied Mathematics Letters, 2001 This paper deals with the shallow water equation \[ U_t+ 3UU_x= U_{xxt}+ 2U_x U_{xx}- 2KU_x.\tag{1} \] The authors consider singular limits of quasiperiodic solutions when the spectral curve becomes singular and its arithmetic genus drops to zero. The solutions are then expressed in terms of purely exponential \(\tau\)-functions and they describe the ...
Mark S. Alber, Charles Miller
exaly +2 more sources
THE SIMULATION OF ONE-DIMENSIONAL SHALLOW WATER WAVE EQUATION WITH MACCORMACK SCHEMES
Barekeng, 2022 Many practical problems can be modeled using the one-dimensional shallow water wave equation. Therefore, the solution to the one-dimensional shallow water wave equation will be discussed to solve this problem.
Iffah Nurlathifah Fikri, Sumardi Sumardi
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Fractional-stochastic shallow water equations and its analytical solutions
Results in Physics, 2023 In this paper, the stochastic shallow water wave equation with M-Truncated derivative is taken into account. New rational, trigonometric and hyperbolic solutions are produced using the He’s semi-inverse method and modified extended tanh-function method ...
Amjad E. Hamza +3 more
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