A Model Describing the Propagation of a Femtosecond Pulse in a Kerr Nonlinear Medium

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We consider a model of nonlinear interaction of femtosecond pulses with a Kerr nonlinear medium, allowing for first and second order dispersion, nonlinear response dispersion, and mixed time and space derivatives. The invariants are constructed by a transformation of the generalized nonlinear Schrodinger equation that involves changing to new functions and reduces the original equation to a form without the nonlinear response derivatives and the mixed derivatives. Appropriate conservation laws are established for the transformed equation. The invariants derived in this article lead to conservative difference schemes and allow control of computer simulation results.