Mathematical Research Letters
Volume 5 (1998)
A unified approach to vortex motion laws of complex scalar field equations
Pages: 455 – 460
In this short note, we give a unified rigorous derivation of vortex motion laws of nonlinear wave (NLW) and nonlinear heat (NLH) equations based on the fluid dynamic approach the authors recently developed in solving the nonlinear Schrödinger (NLS) equation. Hence in all three complex scalar field equations, the motion laws follow from the Euler-type equations, and the knowledge of the finite mass Radon defect measure.