Whitham modulation theory for the defocusing nonlinear Schrödinger equation in two and three spatial dimensions

Abstract The Whitham modulation equations for the defocusing nonlinear Schrödinger (NLS) equation in two, three and higher spatial dimensions are derived using a two-phase ansatz periodic traveling wave solutions by period-averaging conservation laws of NLS equation. resulting written vector form, which allows one to show that they preserve rotational invariance equation, as well with respect scaling Galilean transformations, immediately generalize calculations from two three. transformation Riemann-type variables is described detail; harmonic soliton limits explicitly down; reduction those radial carried out. Finally, extension theory briefly outlined. multidimensional NLS-Whitham obtained here may be used study large amplitude wavetrains variety applications including photonics matter waves.