STABILITY AND GRAIN-BOUNDARIES IN THE DISPERSIVE NEWELL-WHITEHEAD-SEGEL EQUATION

An equation to describe nearly Ip traveling-waves patterns, obtained f irst by Brand, Lomdahl and Newell, is revisited. In addition to the pr eviously known transverse Benjamin-Feir condition, necessary for stabi lity of plane waves, it is demonstrated that, if this condition is met , a quarter of the plane-wave existence band is unstable against trans verse perturbations, white three quarters are stable. Most essential r esults are obtained for linear defects in the form of grain boundaries (GB's). An effective Burgers equation is derived, in the framework of which a GB is tantamount to a shock wave. Asymmetric GB's are moving at a constant velocity.