Application of Argument Principle for Study a Structure of Roots of Transcendental Equations - Khabeev, Nail Suleiman (Journal of Vibration Testing and System Dynamics, 2026)
In study of the structure of shock waves in bubbly liquids we need to find integral curve connecting two singular points of the system of differential equations. We linearized the system of basic equations around equilibrium state. The condition of existence of nontrivial solution of the linear equations leads to the characteristic transcendental equation with respect to exponential index. The structure of roots of such equation is studied by using argument principle [1]. It is shown that for compression waves such equation has one real root.