Travelling waves of the KP equations with transverse modulations

Kadotntsev-Petviashvili (KP) equations arise generically in modelling nonli near wave propagation for primarily unidirectional long waves of small ampl itude with weak transverse dependence. In the case when transverse dispersi on is positive (such as for water waves with large surface tension) we inve stigate the existence of transversely modulated travelling waves near one-d imensional solitary waves. Using bifurcation theory we show the existence o f a unique branch of periodically modulated solitary waves. Then, we briefl y discuss the case when the transverse dispersion is negative (such as for water waves with zero surface tension). (C) Academie des Sciences/Elsevier, Paris.