Modulation Theory for Self-Focusing in the Nonlinear Schrödinger–Helmholtz Equation
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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.