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The paper addresses the thermophoretic motion (TM) equation, which is serviced to describe soliton-like thermophoresis of wrinkles in graphene sheet based on Korteweg-de Vries (KdV) equation. The generalized unified method is capitalized to construct wrinkle-like multiple soliton solutions. Graphical analysis of one, two, and three-soliton solutions is carried out to depict certain properties like width, amplitude, shape, and open direction are adjustable through various parameters.

In this work, dark and singular soliton solutions of the (1[Formula: see text]+[Formula: see text]2)-dimensional chiral nonlinear Schrödinger’s equation are obtained and analyzed dynamically along with graphical depictions. The extraction of these chiral solitons is carried out using two integration tools such as the modified simple equation method and the [Formula: see text]-expansion method. The validity conditions for the existence of these solitons are also retrieved. It is highlighted that the solitons retrieved here are of chiral nature.

In this paper, the generalized second-order nonlinear Schrödinger equation with light-wave promulgation in an optical fiber, is studied for optical soliton solutions. Three analytical methods such as the $\mathrm{exp}\left(-\phi \left(\chi \right)\right)$-expansion method, the G′/G2-expansion method and the first integral methods are used to extract dark, singular, periodic, dark-singular combo optical solitons for the proposed model. These solitons appear with constraint conditions on their parameters and they are also presented. These three strategic schemes have made this retrieval successful. The given model is also studied for modulation instability on the basis of linear stability analysis. A dispersion relation is obtained between wave number and frequency.

An efficient method of isolation from high-frequency vibrations is the use of periodically layered composites acting as a mechanical filter. This device is a periodically layered stack of alternating materials with widely different densities and stiffnesses. The working principle of the device is wave reflection, and the device becomes increasingly effective when there is a large impedance mismatch which leads to rapid attenuation of an input wave for certain frequency ranges. This filter acts only in specific frequency bands. At other frequencies, it will transmit the vibratory energy unmodified, thus acting as a mechanical notch filter. The theoretical development of the mechanical notch filter is based on the theory of waves in periodically layered media. Floquet theory is used to solve the equations for the propagation of plane waves through a laminated system of parallel plates of different materials when the direction of propagation is normal to the plates. Several experiments were conducted to prove the validity of the mechanical notch filter concept. These experiments demonstrated that the theory is correct and that the results have practical application.