Modulation Theory for Self-Focusing in the Nonlinear Schrödinger–Helmholtz Equation Academic Article uri icon

abstract

  • The nonlinear Schrodinger-Helmholtz (SH) equation in N space dimensions with 2 nonlinear power was proposed as a regularization of the classic nonlinear Schrodinger (NLS) equation. It was shown that the SH equation has a larger regime [image omitted] of global existence and uniqueness of solutions compared with that of the classic NLS [image omitted]. In the limiting case where the Schrodinger-Helmholtz equation is viewed as a perturbed system of the classic NLS equation, we apply modulation theory to the classic critical case (=1, N=2) and show that the regularization prevents the formation of singularities of the NLS equation. Our theoretical results are supported by numerical simulations.

author list (cited authors)

  • Cao, Y., Musslimani, Z. H., & Titi, E. S.

citation count

  • 4

publication date

  • February 2009