Methods of Theoretical Physics

JETP Letters

, Volume 95, Issue 9, pp 486-491

First online:

On the nonlinear Schrödinger equation for waves on a nonuniform current

  • V. P. RubanAffiliated withLandau Institute for Theoretical Physics, Russian Academy of Sciences Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


A nonlinear Schrödinger equation with variable coefficients for surface waves on a large-scale steady nonuniform current has been derived without the assumption of a relative smallness of the velocity of the current. This equation can describe with good accuracy the loss of modulation stability of a wave coming to a counter current, leading to the formation of so-called rogue waves. Some theoretical estimates are compared to the numerical simulation with the exact equations for a two-dimensional potential motion of an ideal fluid with a free boundary over a nonuniform bottom at a nonzero average horizontal velocity.