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

In this paper we construct a new kind of positive solutions of $$\text{De}u-u+u^p=0\text{on}{\mathbb{R}}^2$$ when $p>2.$ These solutions $\displaystyle{u(x,z)\sim \om(x-f(z))+ \sum_{i=1}^{\infty}\om_{0}((x, z)-\xi_i\vec{e}_{1})}$as$L\rightarrow +\infty$where$\om$ is a unique positive homoclinic solution of $\text{om}\mathrm{"}-\text{om}+{\text{om}}^p=0$ in $\mathbb{R}$ ; ${\text{om}}_0$ is the two dimensional positive solution and ${\vec{e}}_1=(1,0)$ and ${\xi }_j$ are points such that ${\xi }_j=jL+\mathcal{O}(1)$ for all $j\ge 1.$ This represents a first result on the {\em coexistence} of fronts and bumps. Geometrically, our new solutions correspond to {\em triunduloid} in the theory of CMC surface.