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In this paper we investigate via the shooting method the existence of homoclinic solutions of a fourth-order differential equation arising in the theory of water waves.
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Gheorghe Moroșanu, Diko Souroujon, Stepan Tersian, Homoclinic solutions of a fourth-order travelling wave ODE. Port. Math. 64 (2007), no. 3, pp. 281–301DOI 10.4171/PM/1787