In this paper the existence of weak solutions of the nonlinear generalized KdV equation is shown and conditions for which weak solutions decay to zero at large times are obtained.
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Nikolayev A. A. Ubyvanie resheniy obobshchennogo uravneniya Kortevega–de Friza pri bol’shih vremenakh [Decay of the solutions of the generalized Korteweg–de Vries equation at large times]. Vestnik Tambovskogo universiteta. Seriya: estestvennye i tekhnicheskie nauki – Tambov University Reports. Series: Natural and Technical Sciences, 2019, vol. 24, no. 125, pp. 99–111.