Consider in polar coordinates an equation of the form f_ {r} = sigma (re ^ {ia}}) | | f _ {theta} | ^ {m}, f _ {theta}. If m = 0, then we arrive at the well-known Beltrami equation.
Please advise the literature on nonlinear equations.
[1] A. C. Newell, “Perturbative theory of solitons,” Solitons in Mathematics and Physics (Society for Industrial and Applied Mathematics, Philadelphia, PA, 1985).
[2] M. Lakshamanan and S. Rajasekhar: Nonlinear Dynamics: Integrability, Chaos, and Patterns (Springer, New York, 2002).
[3] H. Berestycki and Y. Porneau (eds), Nonlinear PDE's in Condensed Matter and Reactive Flows (Springer, New York, 2002).