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Yomba, E. (2008) A Generalized Auxiliary Equation Method and Its Application to Nonlinear Klein-Gordon and Generalized Nonlinear Camassa-Holm Equations. Physics Letters A, 372, 1048-1060.
https://doi.org/10.1016/j.physleta.2007.09.003

has been cited by the following article:

• TITLE: Embedded and Standard Bright Solitons, Kinks, and Standard and Asymmetric Dark Solitons, in a Generalized Nonlinear Schrödinger Equation with Fourth-Order Diffraction, Weak Nonlocality and a Quintic Nonlinearity

  AUTHORS: Jorge Fujioka, Áurea Espinosa-Cerón, Juan Adrián Reyes

  KEYWORDS: Nonlinear Schrödinger Equation, Weak Nonlocality, Bright and Dark Solitons, Fourth-Order Diffraction, Vakhitov-Kolokolov Stability Criterion

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.7, July 31, 2026

  ABSTRACT: In this article, we study a generalized nonlinear Schrödinger equation with second- and fourth-order diffraction, a weak nonlocality, and cubic and quintic nonlinearities. We show that this equation possesses several exact analytical solutions. In particular, it has embedded and standard bright solitons, kinks, and standard and asymmetric dark solitons. The Vakhitov-Kolokolov stability criterion shows that the embedded solitons may be VK-stable or VK-unstable, the standard solitons are VK-unstable, and the dark solitons are VK-stable. It is shown that if the embedded solitons are perturbed, they emit monochromatic radiation.