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.
