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This paper explores a comprehensive theory for both linear and non-linear dispersive waves.

A general approach to linear and non-linear dispersive waves using a Lagrangian

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Theoretical framework describes non-uniform wave trains in dispersive waves, suggesting new insights on wave dynamics.

This paper explores a comprehensive theory for both linear and non-linear dispersive waves.
Developed a theoretical framework based on a variational principle with a Lagrangian.
Focused on non-uniform wave trains with slowly varying amplitudes and wave-numbers.
Utilized Boussinesq's equations for long water waves as a practical example.
Established a general theory applicable to both linear and non-linear dispersive waves.
Provided insights into the behavior of non-uniform wave trains.
Demonstrated the applicability of the variational principle in deriving dispersive equations.

G. B. Whitham (1965) studied this question.

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