Potential theory (Green's formulas, Green's function etc.) was discovered by George Green who was doing physics. His work was called "An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism".
Laplace equation was first written in a paper on Saturn rings.
Eigenvalues, eigenvectors and adjoint operators were discovered by mathematicians who
were doing physics (namely celestial mechanics). Fourier transform was
discovered by Fourier who was doing physics (in his studies of heat flow).
Same applies to Bessel functions and theta functions which appear for the first time
in Fourier's book on heat. Fourier series were discovered by Daniel Bernoulli who was doing physics (oscillations of a string).
Vector analysis was invented by physicists Herz and Gibbs.
Maxwell's book on electromagneitsm is literally packed with mathematical discoveries.
Calculus of operators (a.k.a. operational calculus) was discovered
by physicist/electrical engineer Oliver Heaviside, who was studying the
The theories of unbounded operators, operator algebras and quantum logic were developed by von Neumann to give mathematical foundations of quantum mechanics.
Lee and Yang Theorem was discovered by two physicists who studied phase transitions.
Yang-Mills equations were discovered by physicists Yang and Mills working on quantum field theory.
The list can be made almost infinite.