Outputs (6)

Interconnections among nonlinear field equations (2020)
Journal Article
Fairlie, D. B. (2020). Interconnections among nonlinear field equations. Journal of Physics A: Mathematical and Theoretical, 53(10), Article 104001. https://doi.org/10.1088/1751-8121/ab6f17

Galileons are related to other implicitly integrable equations such as the first order nonlinear wave equation and the universal field equation, which is a Lagrangian for the Galileon.

An atavistic Lie algebra (2006)
Journal Article
Fairlie, D. B., & Zachos, C. K. (2006). An atavistic Lie algebra. Physics Letters B, 637(1-2), 123-127. https://doi.org/10.1016/j.physletb.2006.04.013

An infinite-dimensional Lie Algebra is proposed which includes, in its subalgebra and limits, most Lie Algebras routinely utilised in physics. It relies on the finite oscillator Lie group and appears applicable to twisted noncommutative QFT and CFT.

Implicit solutions to some Lorentz invariant non-linear equations revisited (2005)
Journal Article
Fairlie, D. B. (2005). Implicit solutions to some Lorentz invariant non-linear equations revisited. Journal of Nonlinear Mathematical Physics, 12(3), 449-456. https://doi.org/10.2991/jnmp.2005.12.3.8

An implicit solution to the vanishing of the so-called Universal Field Equation, or Bordered Hessian, which dates at least as far back as 1935 \cite{chaundy} is revived, and derived from a much later form of the solution. A linear ansatz for an impli... Read More about Implicit solutions to some Lorentz invariant non-linear equations revisited.

Vertex Ring-Indexed Lie Algebras (2005)
Journal Article
Fairlie, D., & Zachos, C. (2005). Vertex Ring-Indexed Lie Algebras. Physics Letters B, 620(3-4), 195-199. https://doi.org/10.1016/j.physletb.2005.06.033

Infinite dimensional Lie algebras are introduced, which are only partially graded, and are specified by indices lying on cyclotomic rings. They may be thought of as generalisations of the Onsager algebra, but unlike it or its sl(n) generalisations, t... Read More about Vertex Ring-Indexed Lie Algebras.

Extra dimensions and nonlinear equations (2003)
Journal Article
Curtright, T., & Fairlie, D. (2003). Extra dimensions and nonlinear equations. Journal of Mathematical Physics, 44(6), 2692-2703. https://doi.org/10.1063/1.1543227

Solutions of nonlinear multi-component Euler–Monge partial differential equations are constructed in n spatial dimensions by dimension-doubling, a method that completely linearizes the problem. Nonlocal structures are an essential feature of the meth... Read More about Extra dimensions and nonlinear equations.

The complex Bateman equation (1999)
Journal Article
Fairlie, D., & Leznov, A. (1999). The complex Bateman equation. Letters in Mathematical Physics, 49(3), 213-216. https://doi.org/10.1023/a%3A1007619823018

The general solution to the complex Bateman equation is constructed. It is given in implicit form in terms of a functional relationship for the unknown function. The known solution of the usual Bateman equation is recovered as a special case.