Exact Solitonic Solutions in New Hamiltonian Amplitude Equation using Riccati-Bernoulli Method

The propagation of optical pulses in nonlinear media is a complex phenomenon that requires accurate modeling and analysis. The New Hamiltonian Amplitude Equation (HNLS) is a fundamental model that describes this phenomenon, but solving it exactly is a challenging task. We employ the Riccati-Bernoulli Sub ODE method to derive exact soliton solutions to the HNLS. This research contributes to the understanding of optical soliton dynamics in various nonlinear regimes, providing a foundation for the development of novel optical communication systems and devices. We use the Riccati-Bernoulli Sub ODE method to derive exact soliton solutions to the HNLS. The method is applied to various nonlinear regimes, including Kerr law, Quadratic Cubic, and Parabolic law nonlinearities. Additionally, we obtain particular solutions using the power series method. The resulting optical soliton solutions are expressed in terms of various mathematical functions, including trigonometric functions, hyperbolic functions, exponential functions, and rational functions. These solutions describe the oscillatory behavior, exponential growth or decay, rapid growth or decay, and algebraic decay or growth of optical pulses in various nonlinear regimes. The solutions obtained using the power series method provide further insight into the behavior of optical pulses in these regimes. Our results provide a comprehensive understanding of optical soliton dynamics in nonlinear media.