I'm searching for *throughout* references that -- in the long term -- can help me *gradually* gain a *solid background* and firm foundations to understand the *main methods and theorems* to deal with **nonlinear problems** (in particular, *wave equations, solitary wave solutions (solitons) , nonlinear elliptic and hyperbolic PDEs, periodic solutions of Lagrangian and Hamiltonian Systems*, **etc**.) that arise in science (specifically, *mathematical* and *theoretical physics*). 

The following textbooks caught my attention:

* Zdzislaw Denkowski, Stanislaw Migórski, and Nikolaos S. Papageorgiou, *An
Introduction to Nonlinear Analysis: Theory*;
* Antonio Ambrosetti and Giovanni Prodi, *A Primer of Nonlinear Analysis*;
* Antonio Ambrosetti and David Arcoya, *An Introduction to Nonlinear Functional Analysis and Elliptic Problems*;
* Abdul-Majid Wazwaz, *Partial differential equations and solitary waves theory*;
* Herbert Koch, Daniel Tataru, and Monica Vişan, *Dispersive Equations and Nonlinear Waves*;
* Kung Ching Chang, *Methods in Nonlinear Analysis*.

I would like to receive some advice from the experienced researchers in nonlinear analysis and mathematical physics of *Mathematics Stack Exchange*:

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> > ***Question:*** How should I go about learning nonlinear analysis? That is, assuming knowledge of real analysis, what resources and what kind of approach (and order) to read through them would you
> >  recommend to build a solid knowledge of nonlinear analysis? 
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