The generalized Schrödinger equation with the
power-law of nonlinearity, which describes propagation
pulses in optical fibers, is analyzed. The well-known unified auxiliary equation approach is used to study the solitary
wave solutions of the proposed equation. The solutions of
solitary waves and periodic waves at zero or unity modulus
of ellipticity are obtained by employing Jacobi elliptic function solutions. The obtained novel solutions which come in
a variety of forms, including kink, periodic, dark, bright,
W-shaped, singular, and singular periodic are extracted by
the hyperbolic, trigonometric, and exponential functions. In
addition, the impact of the degree of nonlinearity on the
periodic and solitary wave structures is examined. Furthermore, a comprehensive bifurcation analysis is performed to
explore the structural transitions and qualitative behaviors of
the solutions. Phase portraits are constructed to visualize the
dynamical nature of the equilibrium points and to elucidate
the global behavior of the system in the phase space
See More
See Less