Peregrine soliton and Akhmediev Breather in superthermal multi-ion plasmas and their role in ion-induced nanostructuring

The nonlinear Schrödinger equation (NLSE) is used to study the dynamics of electrostatic wave envelopes in a multi-ion, superthermal plasma. The plasma contains Sr²⁺, Ti⁴⁺, and O²⁻ ions with a κ-distribution of electrons. We use weakly nonlinear analysis to develop analytical formulas for the dispersion (P) and nonlinear (Q) coefficients, methodically investigating their effect on the superthermality index κ and ion concentration ratio β=n_T0/n_s0 We found that reducing κ (stronger suprathermal effects) increases anomalous dispersion (P<0) and self-focusing nonlinearity (Q<0), whereas increasing β increases modulational instability (PQ>0) via increasing ion inertia and charge density. Localized wave structures are predicted universally by PQ. The Peregrine soliton (transient rogue wave) and Akhmediev breather (periodic modulation) show remarkable spatiotemporal localization in NLSE numerical solutions. Plasma density variations cause mechanical strains beyond material cohesion limitations, causing nanoscale surface deformation under ion irradiation. Our results provide a plasma parameter-based paradigm for nanostructure morphology control in plasma-assisted nanofabrication and space plasma settings.