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. {{cite journal |doi=10.1007/s11005-017-1013-4 |arxiv=1401.2122 |title=New integrable (3+1)-dimensional systems and contact geometry |year=2018 |last1=Sergyeyev |first1=A. |s2cid=119159629 |journal=Letters in Mathematical Physics |volume=108 |issue=2 |pages=359–376 |bibcode=2018LMaPh.108..359S }}