Multi-soliton solutions for the supercritical gKdV equations

Vianney Combet

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arXiv · 1002.2354

Multi-soliton solutions for the supercritical gKdV equations

Vianney Combet

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Abstract

For the L^2 subcritical and critical (gKdV) equations, Martel proved the existence and uniqueness of multi-solitons. Recall that for any N given solitons, we call multi-soliton a solution of (gKdV) which behaves as the sum of these N solitons asymptotically as time goes to infinity. More recently, for the L^2 supercritical case, Cote, Martel and Merle proved the existence of at least one multi-soliton. In the present paper, as suggested by a previous work concerning the one soliton case, we first construct an N-parameter family of multi-solitons for the supercritical (gKdV) equation, for N arbitrarily given solitons, and then prove that any multi-soliton belongs to this family. In other words, we obtain a complete classification of multi-solitons for (gKdV).

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Vianney Combet. 2010-02-12. Multi-soliton solutions for the supercritical gKdV equations. https://arxiv.org/abs/1002.2354

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