Lin–Tsien equation

The Lin–Tsien equation (named after C. C. Lin and H. S. Tsien) is an integrable partial differential equation


 * $$2u_{tx}+u_xu_{xx}-u_{yy} = 0. $$

Integrability of this equation follows from its being, modulo an appropriate linear change of dependent and independent variables, a potential form of the dispersionless KP equation. Namely, if $$u$$ satisfies the Lin–Tsien equation, then $$v=u_x$$ satisfies, modulo the said change of variables, the dispersionless KP equation. The Lin-Tsien equation admits a (3+1)-dimensional integrable generalization, see.