Abstract
A few more remarks about the origin of the discrepancies between the results obtained by the method of multiple scales and the averaged Lagrangian method are in order. I t must be mentioned that the latter method does not apparently compare well on matters of rigor because the notion of slow variation is never quantified there precisely. On this account, it is quite probable that the averaged Lagrangian method has underestimated the amplitude dispersion in the transverse direction, and may be this is the cause of the forementioned discrepancies. Nonetheless, the evolution equation produced by the averaged Lagrangian method does have some interesting properties, as demonstrated in the above paper, and as such it could be accepted as another model equation in its own right.
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