The Landau-Lifshitz-Gilbert (LLG) equation is a fascinating nonlinear evolution equation both from mathematical and physical points of view. It is related to the dynamics of several important physical systems such as ferromagnets, vortex filaments, moving space curves, etc. and has intimate connections with many of the well-known integrable soliton equations, including nonlinear Schrödinger and...

Abstract On the basis of two sets Lenard recursion sequences and zero-curvature equation associated with a matrix spectral problem, we derive entire sine-Gordon hierarchy, which is composed all positive negative flows. Using theory hyperelliptic curves, Abel-Jacobi coordinates are introduced, from corresponding flows linearized. The algebro-geometric solutions hierarchy constructed by using asy...

In this work, we use two different analytic schemes which are the Sine-Gordon expansion technique and modified exp -expansion function to construct novel exact solutions of non-linear Schrödinger equation, describing gravity waves in infinite deep water, sense conformable derivative. After getting various travelling wave solutions, plot 3D, 2D contour surfaces present behaviours obtained soluti...