Physical Meaning
The independent coordinate has sense of time. Indeed, it may be proportional to time with some relation like, where is constant.
The derivative may have sense of velocity of particle with coordinate ; then can be interpreted as acceleration; and the mass of such a particle is equal to unity.
The dissipative function may have sense of coefficient of the speed-proportional friction.
Usually, both parameters and are supposed to be positive; then this speed-proportional friction coefficient grows exponentially at large positive values of coordinate .
The potential is a fixed function, which also shows exponential growth at large positive values of coordinate .
In the application in laser physics, may have a sense of logarithm of number of photons in the laser cavity, related to its steady-state value. Then, the output power of such a laser is proportional to and may show pulsation at oscillation of .
Both analogies, with a unity mass particle and logarithm of number of photons, are useful in the analysis of behavior of the Toda oscillator.
Read more about this topic: Toda Oscillator
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