Abstract
Two approaches to solution of the two-dimensional Helmholtz equation with a wave number are proposed. The results can be applied both in numerical areas of physics and in the theory of nonlinear equations. The first approach is based on the requirement of the covariance of equation under the generalized Darboux transformation (Moutard transformation). It allows to construct a new solution of equation, using a given initial solution of the equation. Simultaneously we obtain the dressing relation for the wave number. The simplest examples of the approach are considered in detail. In the second approach the Green-Oauchy formula (the /spl part/~ -method) is applied to reduce the solution of the equation to the solution of a system of singular integral equations.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
