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

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

2009-05-04

arxiv.org/abs/0905.0470v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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