32 citations · 93 across the 12 of their papers we have counts for
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On the Whitham system for the (2+1)-dimensional nonlinear Schrödinger equation
Mark J. Ablowitz, Justin T. Cole, Igor Rumanov
We derive the Whitham modulation equations for the nonlinear Schrödinger equation in the plane (2d NLS) with small dispersion. The modulation equations are derived in terms of both…
Whitham equations and phase shifts for the Korteweg-deVries equation
Mark J. Ablowitz, Justin T. Cole, Igor Rumanov
The semi-classical Korteweg-deVries equation for step-like data is considered with a small parameter in front of the highest derivative. Using perturbation analysis Whitham theory…
On the Whitham system for the radial nonlinear Schrödinger equation
Mark J. Ablowitz, Justin T. Cole, Igor Rumanov
Dispersive shock waves (DSWs) of the defocusing radial nonlinear Schrödinger (rNLS) equation in two spatial dimensions are studied. This equation arises naturally in Bose-Einstein…
Whitham modulation theory for (2+1)-dimensional equations of Kadomtsev-Petviashvili type
Mark J. Ablowitz, Gino Biondini, Igor Rumanov
Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev-Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP…
A universal asymptotic regime in the hyperbolic nonlinear Schrödinger equation
Mark J. Ablowitz, Yi-Ping Ma, Igor Rumanov
The appearance of a fundamental long-time asymptotic regime in the two space one time dimensional hyperbolic nonlinear Schrödinger (HNLS) equation is discussed. Based on analytical…