On a coupled system of a Ginzburg-Landau equation with a quasilinear conservation law

João-Paulo Dias, Filipe Oliveira, Hugo Tavares

We study the Cauchy problem for a coupled system of a complex Ginzburg-Landau equation with a quasilinear conservation law $$ \left\{\begin{array}{rlll} e^{-iθ}u_t&=&u_{xx}-|u|^2u-…