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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.
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Raphaël Côte, Yvan Martel, Frank Merle. Construction of multi-soliton solutions for the L2-supercritical gKdV and NLS equations. Revista Matemática Iberoamericana, European Mathematical Society, 2011, 27 (1), pp.273-302. ⟨10.4171/RMI/636⟩. ⟨hal-00385072⟩

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