Selected volumes from the Interdisciplinary Mathematics series. written and published by Robert Hermann (1931 - 2020).  Good starting points:

**Geometric Theory of Non-Linear Differential Equations, Backlund Transformations and Solitons** (XII part A and XIV part B)

**Toda Lattices, Cosymplectic Manifolds, Bäcklund Transformations, and Kinks** (XV part A,  XVIII part B)

**Cartanian Geometry, Nonlinear Waves, and Control Theory** (XX part A, XXI part B)

Interesting ideas, some of which remain to be explored.  Being privately published and decades old, the books are hard to obtain, too.