Lin–Tsien equation

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

$2u_{tx}+u_x{u}_{xx}-u_{yy}=0.$

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.

References

• D. Zwillinger. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 138, 1997.
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