He’s variational iteration method [1, 2], which is a modified general Lagrange multiplier method [3], has been shown to solve effectively, easily and accurately a large class of nonlinear problems with approximations which converge quickly to accurate solutions. It was successfully applied to autonomous ordinary differential equations [4], nonlinear partial differential equations with variable ...

The Cauchy problem for Helmholtz equation arises from inverse scattering problems. Specific backgrounds can be seen in the existing literature; we can refer to 1–6 and so forth. A number of numerical methods for stabilizing this problem are developed. Several boundary element methods combined with iterative, conjugate gradient, Tikhonov regularization, and singular value decomposition methods a...

In this study, we obtained some exact solutions of the coupled non-linear Helmholtz equation through sub-equation method. The were hyperbolic and trigonometric. We observed MATHEMATICA 11.2 that these provided equations, presented graphs in last section.

In this paper, we present an analytical expression for the resonance frequency of Helmholtz attenuators with air cavity and membrane. We derive the characteristic equations based on one-dimensional isentropic acoustic models and illustrate the eeects on the resonance frequency of certain design variations. 1 INTRODUCTION The development of high speed paper machines requires a better control of ...

We study some hybrid inverse problems associated to BVP’s for Schrödinger and Helmholtz type equations. The we consider consist in the determination of coefficients from knowledge internal energy densities. establish local Lipschitz stability inequalities as well Hölder inequalities.

The propagation of transverse magnetic (TM) and electric (TE) electromagnetic waves in a regular ideal waveguide arbitrary cross section is considered. It assumed that the permittivity permeability magnetodielectric filling are functions depend on coordinate time. Analytical expressions for components vectors TM- TE-fields obtained from system Maxwell equations. They expressed terms longitudina...

The nonlocal Darboux transformation for the stationary axially symmetric Schr\"odinger and Helmholtz equations is considered. Formulae are obtained its relation to generalized Moutard established. New examples of two - dimensional potencials exact solutions as an application transformation.