With the results presented in this paper it is therefore possible t o investigate the modulational stability of circularly polarised waves of arbitrary polarisation in the manner of Mj$lhus [ 71 forIn this paper we present the solution to the two component non-linear derivative Schr6dinger equation enables modulational stability of circularly polarised long Alfven waves of arbitrary polarisation to be investigated. The covariant formalism used is easily adapted to solve the n-component non-linear derivative Schrodinger equation.the single component derivative nonlinear Schrodinger equation although we d o not pursue this here.

The prolongation structure approach of Wahlquist and Estabrook is used to determine an inverse scattering formulation for a generalization of the nonlinear Schrödinger equation to two spatial dimensions.

The prolongation structure approach of Wahlquist and Estabrook is used to determine nonlinear evolution equations in two spatial dimensions for which an inverse scattering formulation exists. The equations of nonlinear wave–envelope interactions and the Kadomtsev–Petviashvilli–Dryuma equation are considered in detail.

The models presented by Lu and Taur, [1], for lightly doped double gate and surround gate MOSFETs each require numerical solution of a transcendental equation. In this paper we present compact solutions for the equations based on the Lambert function, [2]. These solutions are shown to be accurate compared with exact numerical solutions.

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