The nonlinear Schrödinger-Helmholtz (SH) equation in N space dimensions with 2σ nonlinear power was proposed as a regularization of the classical nonlinear Schrödinger (NLS) equation. It was shown that the SH equation has a larger regime (1 ≤ σ < 4 N ) of global existence and uniqueness of solutions compared to that of the classical NLS (0 < σ < 2 N ). In the limiting case where the Schrödinger...

A method for explicitly solving the exterior Dirichlet problem for the threedimensional Helmholtz equation in terms of the Dirichlet Green's function for Laplace's equation has recently been found [6]. The present work shows how a similar technique may be used to solve the exterior Neumann problem in terms of the corresponding Neumann-Green function for Laplace's equation. The existence of the ...

This project’s aim seeks to study the acceleration of numerical algorithms used to solve the Helmholtz equation with Dirichlet boundary conditions. The Helmholtz equation arises naturally in physical problems modeled by partial differential equations in space and time as a time-independent wave equation when applying the technique of separation of variables. Using Dirichlet boundary conditions ...

Providing an illustration of sound propagation in the Hormoz Strait ,this paper is about acoustic wave propagation in shallow water for a harmonic point source with low frequency, less than 1000 and solution of a homogenous Helmholtz equation using parabolic equation. C++ programming is used to solve Helmholtz equation [9] and MATLAB software is used to illustrate figures and animate them [6], ...

We consider three problems for the Helmholtz equation in interior and exterior domains in R, (d = 2, 3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions to these problems that, in combination, give bounds on the inverses of the combined-field boundary integral operators for ex...