Traveling-wave solutions of the cubic-quintic nonlinear Schrödinger equation

Abstract

A subset of the exact analytical traveling-wave solutions of the equation i${\mathrm{\ensuremath{\Psi}}}_{\mathit{t}}$+${\mathrm{\ensuremath{\Psi}}}_{\mathit{zz}}$=${\mathit{a}}_{1}$\ensuremath{\Psi}|\ensuremath{\Psi}${\mathrm{|}}^{2}$+${\mathit{a}}_{2}$\ensuremath{\Psi}|\ensuremath{\Psi}${\mathrm{|}}^{4}$ is presented in compact form. The solutions are expressed in terms of Weierstrass's elliptic function \ensuremath{\wp} and include periodic and solitary-wave-like solutions. The algebraic conditions for both cases are given. Examples are presented for simple cases. \textcopyright{} 1996 The American Physical Society.