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Orbital Stability of Double Solitons for the Benjamin-Ono Equation

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In this paper we prove the orbital stability of double solitons for the Benjamin-Ono equation. In the case of the KdV equation, this stability has been proved in [17]. Parts of the proof given there rely on the fact that the Euler-Lagrange equations for the conserved quantities of the KdV equation are ordinary differential equations. Since this is not the case for the Benjamin-Ono equation, new methods are required. Our approach consists in using a new invariant for multi-solitons, and certain new identities motivated by the Sylvester Law of Inertia.

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  1. Departamento de Matematica, IMECC-UNICAMP, C.P. 6065, Campinas, SP-Brasil, CEP, 13083-970, Brasil

    Aloisio Neves & Orlando Lopes

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  1. Aloisio Neves
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  2. Orlando Lopes
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Correspondence to Orlando Lopes.

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Communicated by P. Constantin

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Neves, A., Lopes, O. Orbital Stability of Double Solitons for the Benjamin-Ono Equation. Commun. Math. Phys. 262, 757–791 (2006). https://doi.org/10.1007/s00220-005-1484-5

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  • DOI: https://doi.org/10.1007/s00220-005-1484-5

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