A Higher-Order Septic Nonlinear Model for Transverse Waves in a Generalized Elastic Medium

The nonlinear Schrödinger equation (NLSE) describes the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear dispersive media such as elastic, acoustic, fluid, and fiber under different physical phenomena. It is clear that NLSEs are excellent examples of infinite-dimensional dynamical systems involving various and interesting scenarios; including soliton and wave packets; the existence of the homoclinic structure of solutions; so on. This study explores the contributions of the septic nonlinear and third-order dispersive effects in the nonlinear modulation of two transverse waves propagating in a generalized elastic medium. Using the reductive perturbation method, a pair of coupled quintic-septic NLSEs with a third-order dispersion term is obtained. Exact solutions and bifurcations of the new coupled system are also discussed.