%0 Journal Article %1 WOS:000524281800001 %A Haas, Tobias %A Schneider, Guido %C POSTFACH 101161, 69451 WEINHEIM, GERMANY %D 2020 %I WILEY-V C H VERLAG GMBH %J ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK %K imported from:brittalenz %N 6 %R 10.1002/zamm.201900230 %T Failure of the N-wave interaction approximation without imposing periodic boundary conditions %V 100 %X The N-wave interaction (NWI) system appears as an amplitude system in the description of N nonlinearly interacting and linearly transported wave packets in dispersive wave systems such as the water wave problem or problems in nonlinear optics. The purpose of this paper is twofold. First we give a new simplified proof for the failure of the NWI approximation in case of resonances which are located at integer multiples of a basic wave number k(0) in the original 2 pi/k0-spatially periodic dispersive wave system. Secondly, we give a first rigorous proof that an amplitude system fails in the description of an original system, without imposing periodic boundary conditions on the original system.

@article{WOS:000524281800001, abstract = {The N-wave interaction (NWI) system appears as an amplitude system in the description of N nonlinearly interacting and linearly transported wave packets in dispersive wave systems such as the water wave problem or problems in nonlinear optics. The purpose of this paper is twofold. First we give a new simplified proof for the failure of the NWI approximation in case of resonances which are located at integer multiples of a basic wave number k(0) in the original 2 pi/k0-spatially periodic dispersive wave system. Secondly, we give a first rigorous proof that an amplitude system fails in the description of an original system, without imposing periodic boundary conditions on the original system.}, added-at = {2021-09-13T10:24:35.000+0200}, address = {POSTFACH 101161, 69451 WEINHEIM, GERMANY}, affiliation = {Schneider, G (Corresponding Author), Univ Stuttgart, Inst Anal Dynam \& Modellierung, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Haas, Tobias; Schneider, Guido, Univ Stuttgart, Inst Anal Dynam \& Modellierung, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.}, author = {Haas, Tobias and Schneider, Guido}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/237e1aec66c945f901b62009398df4ecf/mathematik}, doi = {10.1002/zamm.201900230}, interhash = {f9711cbfc6eee1ea73831f27c43aa0ec}, intrahash = {37e1aec66c945f901b62009398df4ecf}, journal = {ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK}, keywords = {imported from:brittalenz}, language = {English}, month = jun, number = 6, publisher = {WILEY-V C H VERLAG GMBH}, timestamp = {2021-09-13T08:24:35.000+0200}, title = {Failure of the N-wave interaction approximation without imposing periodic boundary conditions}, type = {Article}, volume = 100, year = 2020 }