Strongly interacting multi-solitons with logarithmic relative distance for the gKdV equation

Abstract

We consider the following class of equations of (gKdV) typewith mass sub-critical () and mass super-critical nonlinearities (). We prove the existence of two-solitary wave solutions with logarithmic relative distance, i.e. solutions satisfyingwhere is a fixed constant, in sub-critical cases and in super-critical cases. This regime corresponds to strong attractive interactions. For sub-critical p, it was known that opposite-sign traveling waves are attractive. For super-critical p, we derive from our computations that same-sign traveling waves are attractive.