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In an Ocean or a River: Bilinear Auto-Bäcklund Transformations and Similarity Reductions on an Extended Time-Dependent (3+1)-Dimensional Shallow Water Wave Equation
In an Ocean or a River: Bilinear Auto-Bäcklund Transformations and Similarity Reductions on an Extended Time-Dependent (3+1)-Dimensional Shallow Water Wave Equation
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In an Ocean or a River: Bilinear Auto-Bäcklund Transformations and Similarity Reductions on an Extended Time-Dependent (3+1)-Dimensional Shallow Water Wave Equation
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In an Ocean or a River: Bilinear Auto-Bäcklund Transformations and Similarity Reductions on an Extended Time-Dependent (3+1)-Dimensional Shallow Water Wave Equation
In an Ocean or a River: Bilinear Auto-Bäcklund Transformations and Similarity Reductions on an Extended Time-Dependent (3+1)-Dimensional Shallow Water Wave Equation

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In an Ocean or a River: Bilinear Auto-Bäcklund Transformations and Similarity Reductions on an Extended Time-Dependent (3+1)-Dimensional Shallow Water Wave Equation
In an Ocean or a River: Bilinear Auto-Bäcklund Transformations and Similarity Reductions on an Extended Time-Dependent (3+1)-Dimensional Shallow Water Wave Equation
Journal Article

In an Ocean or a River: Bilinear Auto-Bäcklund Transformations and Similarity Reductions on an Extended Time-Dependent (3+1)-Dimensional Shallow Water Wave Equation

2025
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Overview
With respect to oceanic fluid dynamics, certain models have appeared, e.g., an extended time-dependent (3+1)-dimensional shallow water wave equation in an ocean or a river, which we investigate in this paper. Using symbolic computation, we find out, on one hand, a set of bilinear auto-Bäcklund transformations, which could connect certain solutions of that equation with other solutions of that equation itself, and on the other hand, a set of similarity reductions, which could go from that equation to a known ordinary differential equation. The results in this paper depend on all the oceanic variable coefficients in that equation.