A Study on the Methodology of Dispersive Partial Differential Equation

Abstract

Nonlinear dispersive and wave equations are fundamental models to various regions of material science and building like plasma physical science, nonlinear optics, Bose-Einstein condensates, water waves, and general relativity. Delineations fuse the nonlinear Schrodinger, wave, Klein-Gordon, water wave, and Einstein's equations of general relativity. This field of PDE has seen an impact in development in the past twenty, most of the way by virtue of a couple of viable cross-treatments with various zones of science; mainly symphonious investigation, dynamical frameworks, and probability. It furthermore continues being a champion among the most powerful regions of investigation, rich with issues and open to various intriguing heading. The current paper highlights the methodology of dispersive partial differential equations.