Modulational instability in a coupled nonlocal media with cubic, quintic and septimal nonlinearities

In this paper, the modulational instability of the one-dimensional optical soliton has been studied in the presence of Gaussian and sine oscillatory nonlocal response functions. By properly managing the sign as well as the magnitude of cubic, quintic and septimal nonlinearities and the strength of nonlocal response functions, a remarkable impact on the dynamics of modulational instability has been observed. We have investigated both the symmetric (equal power values for pump and probe beams) and asymmetric (unequal power values for pump and probe beams) cases, in which the asymmetric case shows a reduced bandwidth of MI compared to the symmetric case. Furthermore, our study has revealed the emergence of both type A and type B Akhmediev breathers under specific combinations of higher-order nonlinearities and nonlocal response functions. Specifically, the Gaussian nonlocal response function leads to the formation of type A Akhmediev breathers, while the sine oscillatory nonlocal response function can give rise to both type A and type B Akhmediev breathers, which depends upon the strength of the nonlocal response function.