NUMERICAL MODELING OF INTERACTION BIFURCATION WITH NONLINEAR EQUATION

Abstract

From the type of bifurcation, we studied the bifurcation diagram and its stability. The stability of the soliton is proved for fourth order dispersion using the sign definiteness of the operator and integral estimates of the sobolev type. This proof is based on the boundedness of the Hamilitonian for a fixed value of the pulse energy. Using methods for determining explicit solutions given certain conditions and assumptions, we find and explore solutions to the one-dimensional nonlinear Schrödinger problem. Specifically, semi-trivial solutions, then find the explicit solutions with the methods derived from solving the semi-trivial solutions. We use ode45 matlab software to numerical bifurcation diagrams. Various bifurcation diagrams of coupled Schrödinger equations from nonlinear physics are obtained, which suggests the uniqueness of the ground state solution.