Long-time behaviour of soliton ensembles. Part I––Emergence of ensembles

This paper is focused on the emergence of the KdV solitons from an initial harmonic excitation. In the long run this process is characterized not so much by regular soliton trains but rather by soliton ensembles. It has been shown explicitly that under indicated initial conditions the width of emerging solitons are mostly larger than the distance between maxima of wave profiles. Consequently, visible are the ensembles formed by several simultaneously interacting solitons including also hidden (virtual) solitons. The conditions for emerging such ensembles are studied over the wide range of amplitude ratios for typical dispersion parameters. Based on that analysis, it is possible to cast more light to the recurrence and periodicity in the long run (see Part II).