NLS equation with variable coefficient in a stenosed elastic tube filled with an averaged inviscid fluid - Yaan, Yee Choy; Kim, Gaik Tay; Chee, Tiong Ong (IDOSI Publications, 2012)
Wave modulation in an elastic tube had been studied by researchers since year 1979. However there is no wave modulation work in a stenosed elastic tube yet. Hence, in the present work, by considering the artery as a prestressed thin elastic tube with a symmetrical stenosis and the blood as an incompressible averaged inviscid fluid, we have studied the amplitude modulation of non-linear waves in such a composite medium by using the reductive perturbation method [10]. The governing equations can be reduced to the non-linear Schrodinger (NLS) equation with variable coefficient. The progressive wave solution to the above non-linear evolution equation is then sought. The non-linear Schrodinger (NLS) equation with variable coefficient shows increasing shock wave propagates to the right as real time passed.