Existence of Ground States for a 1D Rtivistic Schrödinger Equation

J.P. BORGNA; D. RIAL

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Lugar: New York; Año: 2011

0022-2488

Relativistic Schr¨dinger equation with a non linear potential interaction describes the dynamics of a particle, with rest mass m, travelling to a  fraction |v| < 1 of the light speed c = 1. At first, we deal with the local and global existence of solutions of the flux, and in the second term, and according to the relativistic nature of the problem, we look for boosted solitons as a minimizer of a suitable variational problem. Our proof uses a concentration-compactness type argument. Stability results for boosted solitons are established.