Variational method and nonlinear oscillations and waves

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Abstract
A direct variational method is developed for studying the asymptotic behavior of a wide class of nonlinear oscillation and wave problems. From some judiciously chosen trial solutions with adjustable parameters, equations governing the change of amplitudes and phases are derived and solved. The method is simple in concept and straightforward in application. Different aspects of the method are illustrated by applications to various examples: the oscillation of a pendulum with changing length; the motion of a charged particle in a strong magnetic field; the linear and nonlinear Klein–Gordon equations; and the linear and nonlinear Korteweg–de Vries equations.

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