ON THE NUMBER OF SOLITONS FOR THE INTERMEDIATE LONG-WAVE EQUATION

In this work we use an extension of the WKB method to nonlocal problem s to count the number of solitons produced by an arbitrary slowly vary ing initial disturbance in the ILW (Intermediate Long Wave) evolution equation. The results give the complete description for the range of p arameters. In the course of the analysis we also recover the results f or the Benjamin-One equation, recently obtained by dimensional argumen ts and verified by numerical simulations by Miloh et al. [5] and ingen iously by Matsuno [3],under a specific and still unproved assumption r egarding the additive behavior of the conservation laws for the Benjam in-One equation.