Hw. Schurmann, TRAVELING-WAVE SOLUTIONS OF THE CUBIC-QUINTIC NONLINEAR SCHRODINGER-EQUATION, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 54(4), 1996, pp. 4312-4320
A subset of the exact analytical traveling-wave solutions of the equat
ion i Psi(t) + Psi(zz) = a(1) Psi\Psi\(2) + a(2) Psi\Psi\(4) is presen
ted in compact form. The solutions are expressed in terms of Weierstra
ss's elliptic function p and include periodic and solitary-wave-like s
olutions. The algebraic conditions for both cases are given. Examples
are presented for simple cases.