Solutions of Nonlinear Polyharmonic Equation with Periodic Potential

Abstract

Quasi-periodic solutions of a nonlinear periodic polyharmonic equation in ${\mathbb{R}}^n$, $n>1$, are studied. It is proven that there is an extensive "non-resonant" set $\mathcal{G}\subset {\mathbb{R}}^n$ such that for every $\vec{k}\in \mathcal{G}$ there is a solution asymptotically close to a plane wave $A{e}^{i⟨\vec{k},\vec{x}⟩}$ as $|\vec{k}|\to \infty$.

References in corpus (1)

• Superfluidity breakdown of periodic matter waves in quasi one-dimensional annular traps via resonant scattering with moving defects