Non-linear wave modulation in a prestressed fluid field thin elastic tube

In the present work, employing the non-linear equations of an incompressible, isotropic and elastic thin tube and the approximate equations of an incompressible inviscid fluid, the amplitude modulation of weakly non-linear waves is examined. Assuming the weakness of dispersive effects and utilizing the reductive perturbation technique, it is shown that the amplitude modulation of these waves is governed by a non-linear Schrödinger (NLS) equation. Some special solutions of the NLS equation are given and the modulational instability of the plane wave solution is discussed for some elastic materials and initial deformations.