Solution of nonlinear wave equations of the complex quintic Ginzburg-Landau and nonlinear Schrodinger type

In this letter, we present a new method to solve the nonlinear wave equations of the complex quintic Ginzburg-Landau and nonlinear Schrodinger type for arbitrarily large coefficients. The key point is to take the features of each term and to separate the equation into two parts, a linear part and a nonlinear one. The former is analyzed by means of the Fourier transform in the complex field. The latter is solved by modulus-phase formulation leading to an hyperbolic system highly connected to the nonlinear systems treated in fluid dynamics. This will allow the analysis of the difficult cases that appear when the nonlinear higher order terms (that give rise to phenomena such as shock formation) are considered.