Magnetization dynamics in uniformly magnetized ferromagnetic media is studied by using Landau-Lifshitz-Gilbert equation. The nonlinear evolution equation is integrable with site-dependent and biquadratic exchange interaction by means of Landau-Lifshitz (LL) equation which is well understood. In the present work, we construct the exact solitary solutions of the nonlinear evolution equation, particularly, we employ the modified extended tangent hyperbolic function method. We show the shape changing property of solitons for the given integrable system in the presence of damping as well as inhomogeneities.

We report the modulational instability (MI) analysis for the modulation equations governing the propagation of coherent polarized light through a nematic liquid crystal (NLC) slab, in the limit of low light intensity and local material response. The linear stability analysis of the nonlinear plane wave solutions is performed by considering both the wave vectors (k,l) of the basic states and wave vectors (K,L) of the perturbations as free parameters. We compute the MI gain, and the MI gain peak is reduced and the stable bandwidth is widened with the increase of the strength of the applied electric field. Further, we invoke the extended homogeneous balance method and Exp-function method aided with symbolic computation and obtain a series of periodic solitonic humps of nematicon profiles admitting the propagation of laser light in the NLC medium.

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Among many types of proteinaceous filaments, microtubules (MTs) constitute the most rigid components of the cellular cytoskeleton. Microtubule dynamics is essential for many vital cellular processes such as intracellular transport, metabolism, and cell division. We investigate the nonlinear dynamics of inhomogeneous microtubulin systems and the MT dynamics is found to be governed by a perturbed sine-Gordon equation. In the presence of various competing nonlinear inhomogeneities, it is shown that this nonlinear model can lead to the existence of kink and antikink solitons moving along MTs. We demonstrate kink-antikink pair collision in the framework of Hirota's bilinearization method. We conjecture that the collisions of the quanta of energy propagating in the form of kinks and antikinks may offer a new view of the mechanism of the retrograde and anterograde transport direction regulation of motor proteins in microtubulin systems.