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This nonexistence result is in contrast to the one obtained by Martel-Merle-Rapha\\\"el [17] for the mass-critical generalized Korteweg-de Vries (gKdV) equation. 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This nonexistence result is in contrast to the one obtained by Martel-Merle-Rapha\\\"el [17] for the mass-critical generalized Korteweg-de Vries (gKdV) equation. 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