The height of an $n$th-order fundamental rogue wave for the nonlinear Schrödinger equation

Abstract

The height of an $n$th-order fundamental rogue wave $q_{\mathrm{rw}}^{[n]}$ for the nonlinear Schrödinger equation, namely $(2n+1)c$, is proved directly by a series of row operations on matrices appeared in the $n$-fold Darboux transformation. Here the positive constant $c$ denotes the height of the asymptotical plane of the rogue wave.

arXiv comment5 pages, 56 conferences

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• The solutions of classical and nonlocal nonlinear Schrödinger equations with nonzero backgrounds: Bilinearisation and reduction approach