The Hydrodynamic Nonlinear Schrödinger Equation: Space and Time
AbstractThe nonlinear Schrödinger equation (NLS) is a canonical evolution equation, which describes the dynamics of weakly nonlinear wave packets in time and space in a wide range of physical media, such as nonlinear optics, cold gases, plasmas and hydrodynamics. Due to its integrability, the NLS provides families of exact solutions describing the dynamics of localised structures which can be observed experimentally in applicable nonlinear and dispersive media of interest. Depending on the co-ordinate of wave propagation, it is known that the NLS can be either expressed as a space- or time-evolution equation. Here, we discuss and examine in detail the limitation of the first-order asymptotic equivalence between these forms of the water wave NLS. In particular, we show that the the equivalence fails for specific periodic solutions. We will also emphasise the impact of the studies on application in geophysics and ocean engineering. We expect the results to stimulate similar studies for higher-order weakly nonlinear evolution equations and motivate numerical as well as experimental studies in nonlinear dispersive media. View Full-Text
Share & Cite This Article
Chabchoub, A.; Grimshaw, R.H.J. The Hydrodynamic Nonlinear Schrödinger Equation: Space and Time. Fluids 2016, 1, 23.
Chabchoub A, Grimshaw RHJ. The Hydrodynamic Nonlinear Schrödinger Equation: Space and Time. Fluids. 2016; 1(3):23.Chicago/Turabian Style
Chabchoub, Amin; Grimshaw, Roger H.J. 2016. "The Hydrodynamic Nonlinear Schrödinger Equation: Space and Time." Fluids 1, no. 3: 23.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.