Lin–Tsien equation explained

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

2 u _{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. ^[1]

References

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

Notes and References

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