Abstract
The stability of spatiotemporal waves will be analysed for four conservative systems: a pair of coupled nonlinear Schrodinger equations, the system with cubic nonlinearity (a popular optics model), the semilinear wave equation (a prototype nonlinear wave model), and the water-wave model based on irrotational flow. In particular, two-wave interactions will be investigated for the first and third models; resonant wave mixing between waves and wavelength doubled waves will be considered for the second model; two-wave interactions and three-wave interactions will be investigated for the fourth model. Moreover, since each of these models can be reformulated as a Hamiltonian system on a multisymplectic structure, the stability analyses will be performed within a multisymplectic framework.