New entire positive solution for the nonlinear Schrodinger equation: Coexistence of fronts and bumps

Sanjiban Santra, Juncheng Wei

In this paper we construct a new kind of positive solutions of $$\De u-u+u^{p}=0 \text{on} \R^2$$ when $p>2.$ These solutions $\displaystyle{u(x,z)\sim \om(x-f(z))+ \sum_{i=1}^{\i…