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This manuscript concentrates the behaviour of nematic liquid crystals (NLC) incorporating cubic-septic law property. The resulting solutions of the model play a significant role in the energy transport of soliton molecules in liquid crystals. In this study, the Jacobi elliptic (JE) function technique, which is one of the efficient integration procedure, is used to investigate chirped elliptic and solitary wave solitons like bright, dark, kink, singular, hyperbolic with some constraint conditions while the hyperbolic type traveling wave solutions of the equation defining the NLC incorporating cubic-septic law property is also represented as dark and singular solitons. The linear section of the obtained pulse chirp has two intensity-dependent chirping components that change the chirp. The results of this work could help us understand how chirped solitary waves (CSW) propagate in a weakly nonlocal cubic-septic law medium. This study improves the understanding of nonlinear light-matter interactions in liquid crystals by providing new insights into the role of chirped pulses in forming and modulating spatial optical solitons. Furthermore, we provide successful results in 3D, 2D, and contour forms. It is emphasized that the constrained technique is more effective and powerful than other ways, and the conclusions drawn in this work can contribute in understanding of the soliton molecules found in liquid crystals. • Nematic liquid crystals (NLC) incorporating cubic-septic law nonlinearity is discussed. • Jacobi elliptic (JE) function technique, is used to find different solitary wave solutions. • Several chirped soliton solutions including bright, dark, singular, periodic, hyperbolic, and other solitons a re obtained successfully. • The suitable chirp for each of these optical solitons is likewise produced. [ABSTRACT FROM AUTHOR]

This article analyses the influence of psychological and social addictions such as drug and tobacco consumption problems on humans by using an appropriate nonlinear computational formulation. We propose a mathematical model to simulate the multiple stages and behaviors of the smoking addiction process. Firstly, we present the dynamics of the local and global stability of the tobacco smoking model at existing equilibrium points and discuss the Hopf-Bifurcation analysis of the delayed model by regarding the time delay as a bifurcation parameter and derive specific formulas for the stability and direction of the Hopf bifurcation employing the normal form theory and centre manifold theorem. Then, we enhance our delayed model by considering the effects of the social environment. Precisely, we incorporate additive white noises into our delayed system to simulate the stochastic factors. Then, we analytically present some statistical properties of the perturbed system. Finally, we performed the sensitivity analysis and some numerical examples to discuss the feasibility of our theoretical findings. • This article analyzes the influence of psychological and social addictions. • Simulate the multiple stages and behaviors of smoking addiction process. • Present the Hopf-Bifurcation analysis of the delayed model. • Effects of social environment on proposed model. • Incorporate additive white noises in delayed system. • Sensitivity analysis and numerical examples are given. [ABSTRACT FROM AUTHOR]