Abstract
The nonlinear Schrodinger equation formally describes slow modulations in time and space of an underlying spatially and temporarily oscillating wave packet. It is the purpose of this paper to prove estimates between the formal approximation, obtained via the nonlinear Schrodinger equation, and true solutions of the original system. The method developed in an earlier paper in case of non-trivial quadratic resonances is improved to cover also the additional problem of a trivial resonance at the wavenumber k = 0 as it occurs for the water wave problem. For a Boussinesq equation, a formal and phenomenological model for surface water waves subject to gravity and surface tension, we establish the approximation property in case the formal NLS approximation is stable in the system for the three wave interaction associated to the resonance. Although we restrict ourselves to a Boussinesq equation we believe that the result is also true for the full water wave problem.
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.
