Global Analytic Solutions and Symmetric Waves of the 0-Equation

In this work we consider a nonlocal evolution equation with quadratic nonlinearities from the point of view of existence of solutions. Given the lack of conservation laws, we first discuss the conditions for obtaining a unique global solution for initial data in Sobolev spaces. Then we restrict the space for the initial data to improve the regularity of the solution. Finally, we conclude with the characterization of symmetric solutions as traveling waves.