Abstract The thermal response of nematicons in a parabolic potential has been
numerically studied. Single-peak nematicons exist only in the absence of thermal
response coefficients. Because focusing reorientational nonlinearity is dominant in
this case. In the presence of thermal response, the competition between focusing
reorientational and defocusing thermal nonlinearities leads to the transformation of
single-peak to double-peak nematicons. In this domain, the defocusing thermal
nonlinearity is greater than the focusing reorientational nonlinearity, resulting in
double-peak nematicons. The energy landscape experienced by the light beam within
the medium is modified by the competing nonlinearities. The presence of both
focusing reorientational and defocusing thermal nonlinearities creates multiple maxima
in the energy landscape, allowing for the stabilization of double-peak nematicons as
equilibrium states. When a parabolic potential is present, periodic oscillations can
be obtained in nematicon. For small values of thermal response coefficients, doublepeak
nematicons having periodic oscillations are obtained. The thermal response
coefficients have significant impacts on the wavelength of the oscillations of doublepeak
nematicon. The wavelength has been found to increase with increasing thermal
response coefficients. Large values of the thermal response coefficients result in a
double-peak nematicon with no oscillations. The linear stability analysis shows that
single-peak nematicons and double-peak nematicons having periodic oscillations are
stable, while double-peak nematicon with a non-oscillatory nature is unstable.