article published yes Rowan Killip author Jason Murphy author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca We construct solutions with prescribed scattering state to the cubic-quintic NLS (mathematical formular)in three spatial dimensions in the class of solutions with (mathematical formular). This models disturbances in an infinite expanse of (quantum) fluid in its quiescent state— the limiting modulus c corresponds to a local minimum in the energy density. Our arguments build on work of Gustafson, Nakanishi, and Tsai on the (defocusing) Gross–Pitaevskii equation. The presence of an energy-critical nonlinearity and changes in the geometry of the energy functional add several new complexities. One new ingredient in our argument is a demonstration that solutions of such (perturbed) energy-critical equations exhibit continuous dependence on the initial data with respect to the weak topology on H1/x. Mathematical Sciences Publishers2016 eng final-state problemwave operatorscubic-quintic NLSnonvanishing boundary conditions 2157-5045 1948-206X 1506.0615110.2140/apde.2016.9.1523 971523-1574 yes Killip R, Murphy J, Vişan M. The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions. <i>Analysis &#38; PDE</i>. 2016;9(7):1523-1574. doi:<a href="https://doi.org/10.2140/apde.2016.9.1523">10.2140/apde.2016.9.1523</a> R. Killip, J. Murphy, and M. Vişan, “The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions,” <i>Analysis &#38; PDE</i>, vol. 9, no. 7. Mathematical Sciences Publishers, pp. 1523–1574, 2016. Killip, Rowan, et al. “The Final-State Problem for the Cubic-Quintic NLS with Nonvanishing Boundary Conditions.” <i>Analysis &#38; PDE</i>, vol. 9, no. 7, Mathematical Sciences Publishers, 2016, pp. 1523–74, doi:<a href="https://doi.org/10.2140/apde.2016.9.1523">10.2140/apde.2016.9.1523</a>. Killip, R., Murphy, J., &#38; Vişan, M. (2016). The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions. <i>Analysis &#38; PDE</i>. Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/apde.2016.9.1523">https://doi.org/10.2140/apde.2016.9.1523</a> Killip, Rowan, Jason Murphy, and Monica Vişan. “The Final-State Problem for the Cubic-Quintic NLS with Nonvanishing Boundary Conditions.” <i>Analysis &#38; PDE</i>. Mathematical Sciences Publishers, 2016. <a href="https://doi.org/10.2140/apde.2016.9.1523">https://doi.org/10.2140/apde.2016.9.1523</a>. R. Killip, J. Murphy, M. Vişan, Analysis &#38; PDE 9 (2016) 1523–1574. Killip R, Murphy J, Vişan M. 2016. The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions. Analysis &#38; PDE. 9(7), 1523–1574. 220512026-06-19T07:54:01Z2026-06-25T08:23:10Z