  Using an effective Hamiltonian with d-wave superconductivity (dSC) and
competing antiferromagnetic (AF) interactions, we show that weak and
one-dimensionally modulated dSC, spin density wave (SDW) and charge density
wave (CDW) could coexist in the ground state configuration. With proper
parameters, the SDW order exhibits a period of 8a, while for dSC and CDW orders
the period is 4a. The local density of states (LDOS), which probing the
behavior of quasiparticle excitations, is found to have the identical
stripe-like structure as those in dSC and CDW orders. We point out that any
energy dependent modulations should come from the scatterings of the
quasiparticles from weak defects. The LDOS as a function of the bias voltage
are showing two small bumps within the superconducting coherence peaks, a
signature of presence of the stripes. When a strong impurity like Zn is placed
in such a system, the LDOS at its nearest neighboring sites are suppressed at
the zero bias by the local AF order and show a double-peak structure.
