Wave propagating on cord in static viscous fluid under non-gravitational field

In this paper, a two-dimensional wave equation for a cord (thin rope) that describes waves propagating on a cord in static viscous fluid under the non-gravitational field is derived. There, the viscous drag force is assumed to be proportional to the reverse velocity of motion. To solve this equation for a particular solution, micro-amplitude approximation is also assumed. As a result, unimodal and kink solitary wave solutions with damped velocities for this equation are found. It is denoted that progressive waves in the present system stop in nearly finite time. In appendix, the reason why the phase shifts between incident and reflective waves on connected two cords are inverse to the case of light waves is explained.