I Are non-perturbative methods in physics limited to quantum physics?

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Non-perturbative methods are critical is some parts of quantum physics, but it isn't clear to me if they are ever present in classical physics.
Non-perturbative methods are critical in parts of quantum field theory, such as QCD, and have at least some applications in quantum electrodynamics. You can also have mathematical problems that don't have perturbative solutions.

But, it isn't clear to me if classical physics can ever have non-perturbative solutions, and I'm not sure how to find an answer.

In particular, I'm interested in whether non-perturbative effects can be present in general relativity, or if, in the area of gravity, that are necessarily confined to quantum gravity theories.
 
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ohwilleke said:
But, it isn't clear to me if classical physics can ever have non-perturbative solutions, and I'm not sure how to find an answer.
Of course. For example, many QFT books have chapters on topological solutions such as solitons, instantons and magnetic monopoles, which are classical non-perturbative solutions.
ohwilleke said:
In particular, I'm interested in whether non-perturbative effects can be present in general relativity
Of course. The classic examples are Schwarzschild, Reissner-Nordstrom and Kerr solution.
 
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ohwilleke said:
it isn't clear to me if classical physics can ever have non-perturbative solutions
There is a huge amount of work on completely integrable systems. Many of them are related to problems of physics.
 
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