Geodesic
Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg–de Vries equation
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 2, pp. 283-326
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In this article, we prove the existence of a non-scattering solution, which is minimal in some sense, to the mass-subcritical generalized Korteweg–de Vries (gKdV) equation in the scale critical Lˆr space where Lˆr={f∈S′(R)|‖f‖Lˆr=‖fˆ‖Lr′<∞}. We construct this solution by a concentration compactness argument. Then, key ingredients are a linear profile decomposition result adopted to Lˆr-framework and approximation of solutions to the gKdV equation which involves rapid linear oscillation by means of solutions to the nonlinear Schrödinger equation.

DOI : 10.1016/j.anihpc.2017.04.003
Classification : 35Q53, 35B40, 35B30
Keywords: Generalized Korteweg–de Vries equation, Scattering problem, Threshold solution 
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     author = {Masaki, Satoshi and Segata, Jun-ichi},
     title = {Existence of a minimal non-scattering solution to the mass-subcritical generalized {Korteweg{\textendash}de} {Vries} equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {283--326},
     year = {2018},
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Masaki, Satoshi; Segata, Jun-ichi. Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg–de Vries equation. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 2, pp. 283-326. doi: 10.1016/j.anihpc.2017.04.003

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