Abstract:In this paper we show that solutions of the cubic nonlinear Schrödinger equation are asymptotic limit of solutions to the Benney system. Due to the special characteristic of the one-dimensional transport equation same result is obtained for solutions of the onedimensional Zakharov and 1d-Zakharov-Rubenchik systems. Convergence is reached in the topology L 2 (R) × L 2 (R) and with an approximation in the energy space H 1 (R) × L 2 (R). In the case of the Zakharov system this is achieved without the condition ∂t… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.