A Classical field models with infinite conserved quantities

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1. Dec 5, 2017

Othin

Couldn't really fit the precise question in the title due to the character limit. I want to know what are some sufficient conditions for a model in classical field theory to possess infinitely many conserved quantities. The sine-Gordon and KdV equations are examples of such systems. Now, intuitely I believe that a system which allows Bäcklund transformations should fit the bill, for we can generate an infinite number of solitons. But I don't know if that's actually right and, if it is, I can't understand the reason as precisely as I would like. Is it? What are [other, if that is indeed one] sufficient conditions for a system to possess infinitely many conserved quantities?

2. Dec 10, 2017

PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.