Asymptotic stability of solitons of the subcritical gKdV equations revisited

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Asymptotic stability of solitons of the gKdV equations with general nonlinearity (2007, methodology): “These results have been improved and simplified in [15] in the subcritical power case.”
Stability of cnoidal waves (2006, background): “For solitary waves, stability theory was begun by Benjamin [5] and has since been refined and improved in several ways (see, for example, [4], [8], [11], [22], [25], [26], [37], [38], [39], [40], [43], [49], [50]).”
Multi-Soliton Solutions for the Supercritical gKdV Equations (2010, methodology): “[14] Y. Martel and F. Merle.”
Asymptotic stability of solitons for mKdV (2015, unknown): “The proof that we give below combines the virial approach of MartelMerle [37] and the weighted estimates of Pego-Weinstein [48], in the spirit of the recent work of Mizumachi-Tzvetkov [47] on the L2 stability of solitons for KdV. 1.2.”
Global well-posedness of the KP-I initial-value problem in the energy space (2007, background): “Moreover, the more subtle question of asymptotic stability, as in [21, 22 , 18], can also be naturally posed in the energy space.”
Asymptotic stability of solitons for the Benjamin-Ono equation (2008, methodology): “See also [17] for similar use of monotonicity arguments.”