Abstract. We consider the following class of equations of (gKdV) typewith mass sub-critical (2 < p < 5) and mass super-critical nonlinearities (p > 5). We prove the existence of 2-solitary wave solutions with logarithmic relative distance, i.e. solutions u(t) satisfyingwhere c = c(p) > 0 is a fixed constant, σ = −1 in sub-critical cases and σ = 1 in supercritical cases. For the integrable case (p = 3), such solution was known by integrability theory. 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.
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