TY - JOUR
T1 - Stability and grain boundaries in the dispersive Newell-whitehead-segel equation
AU - Malomed, Boris A.
PY - 1998
Y1 - 1998
N2 - An equation to describe nearly ID traveling-waves patterns, obtained first by Brand, Lomdahl and Newell, is revisited. In addition to the previously known transverse Benjamin-Feir condition, necessary for stability of plane waves, it is demonstrated that, if this condition is met, a quarter of the plane-wave existence band is unstable against transverse perturbations, while three quarters are stable. Most essential results 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.
AB - An equation to describe nearly ID traveling-waves patterns, obtained first by Brand, Lomdahl and Newell, is revisited. In addition to the previously known transverse Benjamin-Feir condition, necessary for stability of plane waves, it is demonstrated that, if this condition is met, a quarter of the plane-wave existence band is unstable against transverse perturbations, while three quarters are stable. Most essential results 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.
UR - http://www.scopus.com/inward/record.url?scp=19044364860&partnerID=8YFLogxK
U2 - 10.1088/0031-8949/57/1/011
DO - 10.1088/0031-8949/57/1/011
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:19044364860
SN - 0031-8949
VL - 57
SP - 115
EP - 117
JO - Physica Scripta
JF - Physica Scripta
IS - 1
ER -