Oscillator Toda
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High Quality Content by WIKIPEDIA articles! Oscillator Toda is special kind of nonlinear oscillator; it is vulgarization of the Toda field theory, which refers to a continuous limit of Toda's chain, of chain of particles, with exponential potential of interaction between neighbors. The oscillator Toda is used as simple model to understand the phenomenon of self-pulsation, which is quasi-periodic pulsation of the output intensity of a solid-state laser in the transient regime. At small (but still positive) values of ~u~ and ~v~, the pulsation decays slowly, and this decay can be described…mehr

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High Quality Content by WIKIPEDIA articles! Oscillator Toda is special kind of nonlinear oscillator; it is vulgarization of the Toda field theory, which refers to a continuous limit of Toda's chain, of chain of particles, with exponential potential of interaction between neighbors. The oscillator Toda is used as simple model to understand the phenomenon of self-pulsation, which is quasi-periodic pulsation of the output intensity of a solid-state laser in the transient regime. At small (but still positive) values of ~u~ and ~v~, the pulsation decays slowly, and this decay can be described analytically. In the first approximation parameters ~u~ and ~v~ give additive contributions to the decay; the decay rate, as well as the amplitude and phase of the nonlinear oscillation can be approximated with elementary functions in the similar manner, as the period above. This allows to approximate the solution of the initial equation.