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The dynamics of the modulation instability induced by cross phase modulationis studied by considering the influence of the walk-off and noninstantaneousresponse effects for two copropagating optical fields travelling in theanomalous regime of dispersion. To do so, we make use of extensions of thenonlinear Schr\"odinger equation jointly with the Debye model for polarization,which is shown to be effective and simplified when compared to theimplementation of other methods for the noninstantaneous nonlinear response. Inanalyzing the sideband formation, two bands are observed with differentbehaviors with respect to the way the maximum gain and the respective frequencyvary with increasing phase mismatch. Further, we also show that the manner inwhich the maximum gain as well as its corresponding frequency scale with thedelay parameter $\tau$ is substantially different from the cases of both fieldsexperiencing the normal group-velocity dispersion regime and the case of mixedregimes. These facts may give rise to many new possibilities for the evolutionof the modulated wave when compared to the nonanomalous cases studied in theliterature.

Modulation instability in noninstantaneous Kerr media with walk-off  effects and cross-phase modulation for two copropagating beams experiencing  anomalous GVD regime