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This paper mainly concentrates on obtaining solutions and other exact traveling wave solutions using the generalized G-expansion method. Some new exact solutions of the coupled nonlinear Schrödinger system using the mentioned method are extracted. This method is based on the general properties of the nonlinear model of expansion method with the support of the complete discrimination system for polynomial method and computer algebraic system (AS) such as Maple or Mathematica. The nonparaxial solitons with the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide is studied. To attain this, an illustrative case of the coupled nonlinear Helmholtz (CNLH) system is given to illustrate the possibility and unwavering quality of the strategy utilized in this research. These solutions can be significant in the use of understanding the behavior of wave guides when studying Kerr medium, optical computing and optical beams in Kerr like nonlinear media. Physical meanings of solutions are simulated by various Figures in 2D and 3D along with density graphs. The constraint conditions of the existence of solutions are also reported in detail. Finally, the modulation instability analysis of the CNLH equation is presented in detail. [ABSTRACT FROM AUTHOR]

This manuscript introduces a novel bidirectional wave dynamics to the q-deformed Sinh-Gordon model. The main objective of this study is to investigate the simultaneous motion of two symmetrical waves. The ϕ 6 -model expansion technique is used for achieving the required objective. The ϕ 6 -model expansion technique extracts new solitary wave solutions for the proposed model. Moreover, we delve into the mathematical aspects and explore the physical characteristics of the q-deformed Sinh-Gordon equation in its bidirectional form. The study provides intricate derivations of the innovative solutions, accompanied by visual representations that offer insights into their physical structures. The findings of this investigation significantly contribute to our comprehension of this model. Finally, fascinating three-dimensional plots and two-dimensional line plots are displayed. [ABSTRACT FROM AUTHOR]