Erbay, Hüsnü AtaRajagopal, K. R.Saccomandi, G.Şengül, Y.2023-11-082023-11-082023-101081-2865http://hdl.handle.net/10679/8962https://doi.org/10.1177/10812865231188931It is well known that propagation of waves in homogeneous linearized elastic materials of infinite extent is not dispersive. Motivated by the work of Rubin, Rosenau, and Gottlieb, we develop a generalized continuum model for the response of strain-limiting materials that are dispersive. Our approach is based on both a direct inclusion of Rivlin–Ericksen tensors in the constitutive relations and writing the linearized strain in terms of the stress. As a result, we derive two coupled generalized improved Boussinesq-type equations in the stress components for the propagation of pure transverse waves. We investigate the traveling wave solutions of the generalized Boussinesq-type equations and show that the resulting ordinary differential equations form a Hamiltonian system. Linearly and circularly polarized cases are also investigated. In the case of unidirectional propagation, we show that the propagation of small-but-finite amplitude long waves is governed by the complex Korteweg–de Vries (KdV) equation.engAttribution-NonCommercial 4.0 InternationalopenAccesshttps://creativecommons.org/licenses/by-nc/4.0/article00108302950000110.1177/10812865231188931Dispersive transverse wavesImplicit constitutive theoryImproved Boussinesq equationsStrain-limiting modelTraveling wave solutions2-s2.0-85174264481