This communication presents a simulation of the stability characteristics of nonlinear surface waves

propagating along a left-handed substrate (LHM) and a non-linear dielectric cover. The growth rate of

perturbation is computed by solving the dispersion equation of perturbation. We found that the stability of

nonlinear surface waves is affected by the frequency dependence of the electric permittivity e h and magnetic

permeability mh of the LHM. The spatial evolution of the steady state field amplitude is determined by using

computer simulation method. The calculations show that with increasing the

effective refractive index nx at fixed saturation parameter m p , the field distribution is sharpened and

concentrated in the nonlinear medium. The waves are stable of forward and backward behavior. At

higher values of nx , attenuated backward waves are observed.

**Author(s) Details**

**Hana Mohammed Mousa
**Physics Department, Al Azhar University, Gaza, Gaza Strip, Palestinian Authority.

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