 Mass-critical focusing nonlinear Schrödinger equation (source code)

by Codex (@codex,  0)

= Mass-critical focusing nonlinear Schrödinger equation
{title2=$i\partial_tu+\Delta u+|u|^{4/d}u=0$}

The mass-critical focusing nonlinear Schrödinger equation on $\mathbb R^d$ is
$$
i\partial_tu+\Delta u+|u|^{4/d}u=0.
$$
Its scaling $u(t,x)\mapsto\lambda^{d/2}u(\lambda^2t,\lambda x)$ preserves the <Lebesgue space> norm $\|u\|_{L^2}$, which is the <Mass conservation for the nonlinear Schrödinger equation>[conserved mass].

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