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- W4384164020 abstract "In this paper, the nonlocal residual symmetries of Whitham–Broer–Kaup equations with time-dependent variable coefficients are derived by using truncated Painlevé analysis. Since it is discovered that the variable coefficient Whitham–Broer–Kaup (vcWBK) equations with two physical quantities can be simplified to the variable coefficient Burgers equation which owns only one field quantity, then the nonlocal symmetries of the vcWBK equations are reduced to that of variable coefficient Burgers equation. In order to acquire the symmetry reduction solutions, the nonlocal symmetry of variable coefficient Burgers equation is further localized to the Lie point symmetries of an enlarged variable coefficient Burgers system. On the basis of the obtained similarity reduction solutions, we design various different exact solutions of different shapes for vcWBK equations via fixing the arbitrary variable coefficients as some specific functions, and display the dynamical behaviors of these solutions by illustrating their images." @default.
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- W4384164020 date "2023-08-15" @default.
- W4384164020 modified "2023-09-25" @default.
- W4384164020 title "Similarity Reductions Related to Nonlocal Symmetries for Whitham–Broer–Kaup Equations with Variable Coefficients" @default.
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- W4384164020 doi "https://doi.org/10.7566/jpsj.92.084003" @default.
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