Lin–Tsien equation
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The Lin–Tsien equation (named after C. C. Lin and H. S. Tsien) is an integrable partial differential equation
- [math]\displaystyle{ 2u_{tx}+u_xu_{xx}-u_{yy} = 0. }[/math]
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 [math]\displaystyle{ u }[/math] satisfies the Lin–Tsien equation, then [math]\displaystyle{ v=u_x }[/math] 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. doi:10.1007/s11005-017-1013-4. Bibcode: 2018LMaPh.108..359S.
- 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. https://books.google.com/books?id=xwaZP3fxAzIC.
- Rogers, C.; Ames, William F. (1989). Nonlinear boundary value problems in science and engineering. Academic Press. p. 373. ISBN 9780080958705. https://books.google.com/books?id=qyDE9V3AIn8C.
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