A uniform train of periodic waves may be unstable to large scale variations so that some incoherence can develop. The analysis is presented for the case of gravity waves, and for a class of interaction problems typical of many physical systems.

Nonlinear multiphase wavetrains on deep water are described using a nonlinear Schrödinger equation system. Instability and multiphase solitary envelope waves are considered in special cases.

The propagation of multiphase modes is considered for the case when group‐velocity projections overlap. Criteria are developed for wave instabilities and for the existence of multiphase solitary envelope solutions.

The equations of motion for three-dimensional long waves on a liquid film are formulated, and the equation for the surface height is derived. The interaction between two- and three-dimensional waves is considered.

Articles you may be interested inFourth-order coupled nonlinear Schrödinger equations for gravity waves on deep water Phys. Fluids 23, 062102 (2011); 10.1063/1.3598316 Fourth-order nonlinear evolution equations for a capillary-gravity wave packet in the presence of another wave packet in deep water Phys. Fluids 19, 097101 (2007); 10.1063/1.2772252Fourth-order nonlinear evolution equations for counterpropagating capillary-gravity wave packets on the surface of water of infinite depth A fourthorder evolution equation for deep water surface gravity waves in the presence of wind blowing over water Phys. Fluids A 2, 778 (1990);