# The Initial-Value Problem for the Cubic-Quintic NLS with Nonvanishing Boundary Conditions

@article{Killip2018TheIP, title={The Initial-Value Problem for the Cubic-Quintic NLS with Nonvanishing Boundary Conditions}, author={Rowan Killip and Jason Murphy and Monica Visan}, journal={SIAM J. Math. Analysis}, year={2018}, volume={50}, pages={2681-2739} }

We consider the initial-value problem for the cubic-quintic nonlinear Schrodinger equation $ (i\partial_t+\Delta)\psi=\alpha_1 \psi-\alpha_{3}\vert \psi\vert^2 \psi+\alpha_5\vert \psi\vert^4 \psi $ in three spatial dimensions in the class of solutions with $|\psi(x)|\to c >0$ as $|x|\to\infty$. Here $\alpha_1$, $\alpha_3$, $\alpha_5$, and $c$ are such that $\psi(x)\equiv c$ is an energetically stable equilibrium solution to this equation. Normalizing the boundary condition to $\psi(x)\to 1$ as… CONTINUE READING

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