Equivalent linearization of systems with distributed parameters (Q1826035)

The author applies the method of equivalent linearization for ODES (that is, a nonlinear equation, such as \(m\ddot x+kx=\epsilon f(x,\dot x)\) is replaced by the corresponding equivalent linearized equation \(m\ddot x+\lambda_ e(a)\dot x+K_ e(a)x=0\) to investigate some one-dimensional systems with distributed parameter which describe weakly nonlinear stationary waves in an unbounded string, a viscoelastic bar, and electric cable, free and forced vibrations of a bounded string and a bounded bar, and propagation of electromagnetic waves in ferromagnetic half space and plate. These problems reduce to integration of one-dimensional quasilinear hyperbolic equations of the form \[ \rho u_{tt}-b(u_ x)u_{xx}=0\quad (\rho b(u_ x)>0). \]