American Journal of Optics and Photonics 2020; 8(3): 61-73 http://www.sciencepublishinggroup.com/j/ajop doi: 10.11648/j.ajop.20200803.12 ISSN: 2330-8486 (Print); ISSN: 2330-8494 (Online) Triangular Rogue Waves and Multi- Wave Trains Generation in a Chameleon Electrical Transmission Line Bedel Giscard Onana Essama 1, * , Salome Ndjakomo Essiane 1 , Frederic Biya – Motto 2 , Mohammed Shabat 3 , Jacques Atangana 4 1 Higher Technical Teachers Training College (HTTTC) of Ebolowa, University of Yaoundé I, Ebolowa, Cameroon 2 Department of Physics, Faculty of Science, University of Yaounde I, Yaounde, Cameroon 3 Department of Physics, Islamic University of Gaza, Gaza City, Palestine 4 Higher Teacher Training College of Yaoundé, University of Yaoundé I, Yaoundé, Cameroon Email address: * Corresponding author To cite this article: Bedel Giscard Onana Essama, Salome Ndjakomo Essiane, Frederic Biya – Motto, Mohammed Shabat, Jacques Atangana. Triangular Rogue Waves and Multi- Wave Trains Generation in a Chameleon Electrical Transmission Line. American Journal of Optics and Photonics. Vol. 8, No. 3, 2020, pp. 61-73. doi: 10.11648/j.ajop.20200803.12 Received: August 9, 2020; Accepted: August 26, 2020; Published: November 23, 2020 Abstract: In this work, we present a particular nonlinear transmission line called chameleon nonlinear transmission line. In fact, the chameleon’s behavior is related to the fact that without changing its appearance, the line can exhibit alternatively purely right - or left - handed behavior. This transmission line is different to the composite one. So, the goal of this work is to demonstrate that this special line can support the propagation of soliton light pulse subjected to quintic – phase modulation, improve the freak wave’s mechanism of generation and verify the chameleon’s behavior of the line. Consequently, we employ collective coordinate’s theory in order to give a great characterization of the light pulse. Then, we introduce an upgraded function called “type II Ansatz function” with eight collective coordinates compared to the conventional Gaussian Ansatz with six collective coordinates. We show that the two additional coordinates will allow us to improve the technique of measurement of internal excitation leading to the generation of rogue events. Moreover, these coordinates will give supplemental details on frequency shift and chirp distortions during the generation of specific rogue events such as “wall of waves”, tree structures, multi - wave trains, Kuznetsov - Ma breathers, Akhmediev breathers, Peregrine solitons and triangular rogue waves. The stability of the soliton light pulse will be also investigated at specific frequency ranges. Keywords: Triangular Rogue Waves, Chameleon Transmission Line, Multi - Wave Trains, Tree Structures, Collective Coordinates 1. Introduction Metamaterials are materials which present a negative refraction index compared to ordinary materials with positive one [1, 2]. Consequently, this type of materials which is not found in nature is named negative index, double - negative or left - handed metamaterials [1, 2]. Further, transmission lines are found at microwave frequencies zone [3, 4]. This discovery leads to left - handed transmission line capable to support soliton light pulses propagation [5 - 11]. Thereafter, composite right/left - handed transmission lines are also found where left - handed behavior is presented at low frequencies and right - handed behavior at high frequencies [12 - 18]. Recently, a new field of investigation has emerged where extreme events lead to many physical applications [19 - 21]. Furthermore, extreme events are found in several domains such as nonlinear optics [22], lasers [23], and plasmas [24]. In addition, some interesting extreme events have been studied such as Peregrine solitons [25], Kuznetsov - Ma breathers [26 - 28], Akhmediev breathers [26, 29 - 31] in the nonlinear Schrödinger equation [32]. The most important freak wave’s mechanism of generation is modulation instability which fundamentally acts on nonlinear dispersive systems [33]. In optics, modulation instability originates