Theoretical analysis demonstrates the existence of classical solutions for one-dimensional shallow water equations, suggesting improved predictive modeling for fluid dynamics.
The one-dimensional shallow water wave equations represent a fundamental model in fluid dynamics and is widely used to describe various practical problems. Existence of classical solutions to the wave equation provide valuable understanding and predictive power for phenomena observed in nature and engineering applications. This paper is focused on existence of one or more classical solutions to shallow water equations. To this end a novel way of integral representation of the solutions is introduced. The provided example supports the main findings in this paper.
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Georgiev et al. (2026) studied this question.
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