Existence of Non-Periodic Real-Valued and Complex-Valued Solutions of Mathews-Lakshmanan Oscillator Equation

We show in this paper the existence of non-periodic real-valued and complex-valued solutions of the Mathews-Lakshmanan oscillator equation. The theory allows also to find the sinusoidal periodic solution given by the authors. As an oscillator can only have periodic solutions for the same model parameters, we conclude that the Mathews-Lakshmanan equation is a pseudo-oscillator.