Hey I wanna start studying nonlinear physics, and to be honest I don't know from where to start, I need books for beginners that explains things in general about the nonlinear science branches, so please if anyone knows can you recommend good books
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2$\begingroup$ What is your background in physics? $\endgroup$Marius Ladegård Meyer– Marius Ladegård Meyer2024-09-10 11:15:21 +00:00Commented Sep 10, 2024 at 11:15
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1$\begingroup$ This is an immense field, and analytical results are few and far between. How much computing power can you access? $\endgroup$ZeroTheHero– ZeroTheHero2024-09-10 11:44:39 +00:00Commented Sep 10, 2024 at 11:44
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5$\begingroup$ Classification of mathematical problems as linear and nonlinear is like classification of the Universe as bananas and non-bananas. (Network Humor, source unknown). -- math.utah.edu/~alfeld/quotes.html $\endgroup$Andrew– Andrew2024-09-10 11:57:07 +00:00Commented Sep 10, 2024 at 11:57
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4$\begingroup$ @Andrew This is hilarious. And the point is valid. But on a second look one realizes that physics overwhelmingly deals with linear or near-linear problems. We just have very little idea of what to do when things are not linear. Sidney Coleman put it most candidly: "Theoretical physics is defined as a set of courses each of which discusses harmonic oscillator" (yes, precisely this way. No specific mentions of young physicists, nor their careers: youtu.be/PN46bztKuPs?si=sqSArU-mn-Wq2f4k&t=2164). So bananas or not, that's what we do in physics. $\endgroup$John– John2024-09-10 12:22:07 +00:00Commented Sep 10, 2024 at 12:22
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2$\begingroup$ Study kinematics at first, there will be your first non-linear experience as per non-linear $x(t)$ definition : $x=x_0+v_0t+at^2/2$. As in a general sense, system where output variable responds not proportionally to some input variable change (in this case change of time $\Delta t$) is a non-linear one. Secondly,- for fully understanding non-linear systems,- you must at first get a very good grasp on linear ones. No pun intended. $\endgroup$Agnius Vasiliauskas– Agnius Vasiliauskas2024-09-10 13:10:06 +00:00Commented Sep 10, 2024 at 13:10
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1 Answer
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A reasonable place to start could be
Strogatz, Steven H. "Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering", (Studies in Nonlinearity) (2001).
It covers the required theory and does contain some exercises, but it's already 20+ years old so obviously the numerical exercises require only minimum computing power.