Generalized nonlinear Schrodinger equation: Conservation of energy and solitary-wave solutions

We show the conservation of momentum and energy of a generalized nonlinear Schrodinger equation. Moreover, we obtain a new traveling-wave solution of this equation with an additional term of the form Gamma(psi (x, t)) = lambda (1)psi (x, t) + lambda (2)psi (x,t)(q) + lambda (3)psi (x,t)(2-2q). We present two cases where the density of energy of the system, for the traveling-wave solution, has a solitary-wave behavior.