Dimensionless dynamics: Multipeak and envelope solitons in perturbed nonlinear Schrödinger equation with Kerr law nonlinearity

In this work, the dimensionless form of the improved perturbed nonlinear Schrödinger equation with Kerr law of fiber nonlinearity is solved for distinct exact soliton solutions. We examined the multi-wave solitons and rational solitons of the governing equation using the logarithmic transformation and symbolic computation using an ansatz functions approach. Multi-wave solitons in fluid dynamics describe the situation in which a fluid flow shows several different regions (or peaks) of high concentration or intensity of a particular variable (e.g., velocity, pressure, or vorticity). Multi-wave solitons in turbulent flows might indicate the existence of several coherent structures, like eddies or vortices. These formations are areas of concentrated energy or vorticity in the turbulent flow. Understanding how these peaks interact and change is essential to comprehending the energy cascade and dissipation in turbulent systems. Furthermore, a sub-ordinary differential equation approach is used to create solutions for the Weierstrass elliptic function, periodic function, hyperbolic function, Chirped free, dark-bright (envelope solitons), and rational solitons, as well as the Jacobian elliptic function, periodic function, and rational solitons. Also, as the Jacobian elliptic function's' modulus m approaches values of 1 and 0, we find trigonometric function solutions, solitons-like solutions, and computed chirp free-solitons. Envelope solitons can arise in stratified fluids and spread over the interface between layers, such as layers in the ocean with varying densities. Their research aids in the management and prediction of wave events in artificial and natural fluid settings. In fluids, periodic solitons are persistent, confined wave structures that repeat on a regular basis, retaining their form and velocity over extended distances. These structures occur in a variety of settings, including internal waves in stratified fluids, shallow water waves, and even plasma physics.