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. ^[1]

References

^ Sergyeyev, A. (2018). "New integrable (3+1)-dimensional systems and contact geometry". Letters in Mathematical Physics. 108 (2): 359–376. arXiv:1401.2122. Bibcode:2018LMaPh.108..359S. doi:10.1007/s11005-017-1013-4. S2CID 119159629.

D. Zwillinger. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 138, 1997.
Ames, William F. (1965). Nonlinear partial differential equations in engineering, Vol. 18. Academic Press. p. 173. ISBN 9780080955247.
Rogers, C.; Ames, William F. (1989). Nonlinear boundary value problems in science and engineering. Academic Press. p. 373. ISBN 9780080958705.

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[AS-1] Sergyeyev, A. (2018). "New integrable (3+1)-dimensional systems and contact geometry". Letters in Mathematical Physics. 108 (2): 359–376. arXiv:1401.2122. Bibcode:2018LMaPh.108..359S. doi:10.1007/s11005-017-1013-4. S2CID 119159629.

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