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.