Analytical solution of the damped Helmholtz-Duffing equation
Consider the differential equation \[ \ddot x+ Ax+ 2\nu\dot x+ Bx^2+\varepsilon x^3= 0.\tag{\(*\)} \] Under the assumption \(A= {3B^2+ 8\varepsilon\nu\over 9\varepsilon}\), the author derives an analytic solution of equation \((*)\) by using Jacobian elliptic functions.
scientific article; zbMATH DE number 6092822