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This is a Quantitative Study study.

October 12, 2025Open Access

Asymptotics of a finite-energy unidirectional solution of the wave equation with non-spherical-wave behavior at infinity

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The asymptotic behavior of the solution aligns with standard spherical waves, showing unique characteristics as it propagates.
An additional logarithmic factor is observed in the wave behavior when moving in the positive z direction.
This investigation discusses waves propagating at constant speed, indicating complexities in unidirectional finite-energy solutions.
The findings have implications for understanding wave behaviors in three-dimensional spaces, especially at large distances.

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Analysis reveals asymptotic behavior of finite-energy wave solutions, suggesting non-standard propagation effects in different regions.

Plachenov et al. (2025) studied this question.

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