Erbay, Hüsnü AtaErbay, Saadet2014-06-262014-06-262012-120893-9659http://hdl.handle.net/10679/383https://doi.org/10.1016/j.aml.2012.07.012In this paper, we investigate the transverse linear instability of one-dimensional solitary wave solutions of the coupled system of two-dimensional long-wave–short-wave interaction equations. We show that the one-dimensional solitary waves are linearly unstable to perturbations in the transverse direction if the coefficient of the term associated with transverse effects is negative. This transverse instability condition coincides with the non-existence condition identified in the literature for two-dimensional localized solitary wave solutions of the coupled system.enginfo:eu-repo/semantics/restrictedAccessArticle25122402240600030903320007310.1016/j.aml.2012.07.012Long wave–short wave equationsTransverse instabilitySolitary waves2-s2.0-84865461136