Construction of multi-soliton solutions for the L2-supercritical gKdV and NLS equations

Abstract

Multi-soliton solutions, i.e. solutions behaving as the sum of N given solitons as t → +∞, were constructed for the L2 critical and subcritical (NLS) and (gKdV) equations in previous works (see [23], [16] and [20]). In this paper, we extend the construction of multi-soliton solutions to the L2 supercritical case both for (gKdV) and (NLS) equations, using a topological argument to control the direction of instability.