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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

4 votes

Book about fluid dynamics

Perhaps this CFD crash course and also A crash course in fluid mechanics could help a bit.
just-learning's user avatar
1 vote

Lax pairs for linear PDEs

The term Lax pair is fairly often used in a broader sense as a pair of linear equations (not necessarily of the form you mention, i.e., $L\phi=\lambda\phi$ and $\dot{\phi}=B\phi$) whose compatibility …
just-learning's user avatar
0 votes

Non-linear Basis for PDE's

In the spirit close to Ben's answer there also is nonlinear superposition coming from the Backlund transformations for systems that are integrable in the sense of soliton theory, see e.g. this introdu …
just-learning's user avatar