TY - JOUR A1 - Anco, Stephen A1 - Mohiuddin, Mohammad A1 - Wolf, Thomas T1 - Traveling waves and conservation laws for complex mKdV-type equations Y1 - 2012 U6 - https://doi.org/10.1016/j.amc.2012.06.061 VL - 219 IS - 2 SP - 679 EP - 698 ER - TY - GEN A1 - Anco, Stephen A1 - Mohiuddin, Mohammad A1 - Wolf, Thomas T1 - Travelling waves and conservation laws for complex mKdV-type equations N2 - Travelling waves and conservation laws are studied for a wide class of $U(1)$-invariant complex mKdV equations containing the two known integrable generalizations of the ordinary (real) mKdV equation. The main results on travelling waves include deriving new complex solitary waves and kinks that generalize the well-known mKdV $\sech$ and $\tanh$ solutions. The main results on conservation laws consist of explicitly finding all 1st order conserved densities that yield phase-invariant counterparts of the well-known mKdV conserved densities for momentum, energy, and Galilean energy, and a new conserved density describing the angular twist of complex kink solutions. T3 - ZIB-Report - 12-34 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16124 SN - 1438-0064 ER -