Asymptotics of the Solution of the Cauchy Problem for a Singularly Perturbed System of Oscillation Equations with a Weak Nonlinearity

An asymptotic expansion with respect to a small parameter of a singularly perturbed system of hyperbolic equations, describing vibrations of two rigidly connected strings is constructed. Under certain conditions imposed on these problems, the principal term of the asymptotic expansion of the solution is described by the generalized Korteweg–de Vries equation.