Holomorphic extension of solutions of semilinear elliptic equations

We prove sharp analytic estimates and holomorphic extensions in sectors of Cd for the solutions of a wide class of semilinear elliptic differential and pseudodifferential equations in Rd, improving earlier results where the extension was shown for a strip. Moreover, we derive exponential decay estimates for such extended solutions. The results presented apply in particular to solitary wave solutions of many classical nonlinear evolution equations as KdV-type, long-wave-type and Schrödinger equations.