Multi-Soliton Solutions for the Supercritical gKdV Equations

By Vianney Combet. 2010

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For the L 2 subcritical and critical (gKdV) equations, Martel [11] 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 t → + ∞. More recently, for the L 2 supercritical case, C te et al. [4] proved the existence of at least one multi-soliton. In the present paper, as suggested by a previous work concerning the one soliton case [3], 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).

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9d9b720a5a01fbec141e3f7ede5e73b1f8dd1112