paper

Linear Superposition for a Large Number of Nonlinear Equations

arXiv:1302.5767 · doi:10.1016/j.physleta.2013.08.015

Abstract

We demonstrate a kind of linear superposition for a large number of nonlinear equations, both continuum and discrete. In particular, we show that whenever a nonlinear equation admits solutions in terms of Jacobi elliptic functions $\cn(x,m)$ and $\dn(x,m)$, then it also admits solutions in terms of their sum as well as difference, i.e. $\dn(x,m) \pm \sqrt{m}\, \cn(x,m)$. Further, we also show that whenever a nonlinear equation admits a solution in terms of $\dn^2(x,m)$, it also has solutions in terms of $\dn^2(x,m) \pm \sqrt{m}\, \cn(x,m)\, \dn(x,m)$ even though $\cn(x,m)\, \dn(x,m)$ is not a solution of that nonlinear equation. Finally, we obtain similar superposed solutions in coupled theories.

11 pages, no figures

References in corpus (1)

Cited by in corpus (19)