Modulation Theory for Self-Focusing in the Nonlinear Schrodinger-Helmholtz Equation

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.

authors

• Titi, Edriss

published proceedings

• NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION

author list (cited authors)

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

citation count

• 6

complete list of authors

• Cao, Yanping||Musslimani, Ziad H||Titi, Edriss S

publication date

• February 2009

publisher

• Taylor & Francis  Publisher

published in

• Numerical Functional Analysis and Optimization  Journal

keywords

• Hamiltonian
• Modulation Theory
• Perturbed Critical Nonlinear Schrodinger Equation
• Regularization Of The Nonlinear Schrodinger Equation
• Schrodinger-helmholtz Equation
• Schrodinger-newton Equation

Digital Object Identifier (DOI)

• 10.1080/01630560802679398

start page

• 46

end page

• 69

volume

• 30

issue

• 1-2

URL

• http%3A%2F%2Fdx.doi.org%2F10.1080%2F01630560802679398