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...

We present the Girsanov theorem for a non linear Itô equation in an infinite dimensional Hilbert space with a non linearity of polynomial growth and an infinite dimensional additive noise. We assume a condition weaker than Novikov one, as done by Mikulevicius and Rozovskii in the study of more general stochastic PDE’s. The equivalence of the laws of the linear equation and of the non linear equ...