Persistence of counterflow-driven instability in non-integrable two-component systems

Determine to what extent the counterflow-driven modulational-instability mechanism identified for the integrable defocusing Manakov system persists in related non-integrable two-component nonlinear Schrödinger systems.

Background

The paper identifies relative counterflow between the two components as the mechanism driving the instability of defocusing Manakov plane waves. It contrasts this with a recent related non-integrable two-component system in which counterpropagation was not permitted, so the same mechanism could not operate.

The authors leave unresolved whether the instability mechanism survives when integrability and the miscibility-threshold coupling structure are lost. This is a concrete extension question concerning the robustness of the paper’s stability conclusions outside the Manakov setting.

References

Finally, we note that in the recent experimental and theoretical study of a related, non-integrable two-component system, the two components were not permitted to counterpropagate, so the mechanism described above could not operate; understanding to what extent it survives away from the integrable, miscibility-threshold point is an interesting open question.

— On the dispersionless limit of the Manakov system, its Riemann invariants, and the modulational stability of its counterpropagating plane waves  (2609.26669 - Adriazola et al., 22 Sep 2026) in Section 5, Modulational stability and instability of plane wave solutions