  We consider an integrable generalization of the nonlinear Schr\"odinger (NLS)
equation that was recently derived by one of the authors using bi-Hamiltonian
methods. This equation is related to the NLS equation in the same way that the
Camassa Holm equation is related to the KdV equation. In this paper we: (a) Use
the bi-Hamiltonian structure to write down the first few conservation laws. (b)
Derive a Lax pair. (c) Use the Lax pair to solve the initial value problem. (d)
Analyze solitons.
