Scattering operator for the one-dimensional Dirac equation with power nonlinearity

作者：Hayashi Nakao^*; Sasaki Hironobu

来源：Journal of Hyperbolic Differential Equations, 2016, 13(4): 821-832.

DOI：10.1142/S0219891616500223

• Nonlinear Dirac equation
• power nonlinearity
• scattering operator

We consider the nonlinear Dirac equation with a power nonlinearity
(partial derivative(t) + alpha partial derivative(x) + i beta)Phi = lambda vertical bar Phi vertical bar(p-1 Phi),
where 3 < p < 5, lambda is an element of C. We prove the existence of the scattering operator in the neighborhood of the origin of the weighted Sobolev space H-1,H-1 boolean AND H-s,H-0, where 4/(p-1) < s < p.

• 出版日期2016-12