  Antikink dispersion of the asymmetric $J_1$-$J_2$ sawtooth spin-1/2
anisotropic Heisenberg antiferromagnetic chain has been derived. Value of
spin-gap is obtained by estimating the minimum of dispersion relation
variationally. The exact doubly-degenerate ground state energy has been derived
at the symmetric point, $J_1=J_2$, for the whole anisotropic regime. Analytic
form of dispersion relations of three different antikink states is obtained and
their validity in the parameter space is discussed. The value of spin-gap,
specific heat and susceptibility are estimated numerically by diagonalizing the
Hamiltonian for chains of finite length. The inherent frustration of this
antiferromagnetic model leads to the appearance of additional peak at
low-temperatures in the specific heat.
