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 $t\to +\infty$, were constructed in previous works for the L2 critical and subcritical (NLS) and (gKdV) equations. 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.

References in corpus (1)

• Threshold solutions for the focusing 3d cubic Schroedinger equation

Cited by in corpus (2)

• Smooth type II blow up solutions to the four dimensional energy critical wave equation
• Blow up for the critical gKdV equation I: dynamics near the soliton