In this study, we obtained some exact solutions of the coupled non-linear Helmholtz equation through sub-equation method. The were hyperbolic and trigonometric. We observed MATHEMATICA 11.2 that these provided equations, presented graphs in last section.

Abstract We study the generalized hydrodynamics of one-dimensional classical non linear Schrӧdinger equation in attractive phase. thereby show that thermodynamic limit is entirely captured by solitonic modes and radiation absent. Our results are derived considering semiclassical quantum Bose gas, where Planck constant has a key role as regulator soliton gas. use our result to adiabatic interact...

In this paper, closed-form analytical equations for the time-domain amplitude of the MOS cross-coupled oscillators are derived. The procedure of the paper is based on estimating an accurate equation for describing the behavior of the cross-coupled MOS configurations and finding a reasonable solution for the nonlinear differential equation governing the circuit. The solution method is presented ...

This paper demonstrates an equivalence between rotating magnetized shear flows and a stressed elastic beam. This results from finding the same form of dynamical equations after an asymptotic reduction of the axis-symmetric magnetorotational instability (MRI) under the assumption of almost-critical driving. The analysis considers the MRI dynamics in a non-dissipative near-equilibrium regime. Bot...

A single bunch of charged particles in a storage ring is a system of 10-10 coupled non-linear oscillators with radiative energy loss and compensated by the accelerating cavity. A stable collective mode in such system was induced and observed in the SPEAR storage ring using a turn-by-turn phase space monitor. New possibilities of using this mode as a tool to experimentally study non-linear dynam...