Commutation Methods Applied to the mKdV-Equation

COMMUTATION METHODS APPLIED TO THE mKdV-EQUATION

An explicit construction of solutions of the modified Korteweg-de Vries equation given a solution of the (ordinary) Korteweg-de Vries equation is provided. Our theory is based on commutation methods (i.e., N = 1 supersymmetry) underlying Miura's transformation that links solutions of the two evolution equations. In connection with the extensively studied Korteweg-de Vries (KdV-) equation its co...

Convergence of iterative methods applied to Burgers-Huxley equation

on the status of mixed methods research in applied linguistics

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convergence of iterative methods applied to burgers-huxley equation

The mKdV equation on a finite interval

We analyse an initial-boundary value problem for the mKdV equation on a finite interval by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex k-plane. This Riemann-Hilbert problem has explicit (x, t)-dependence and it involves certain functions of k referred to as “spectral functions”. Some of these functions are defined in terms of t...