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Coupled system description of perturbed KdV equation
Yair Zarmi
In the multiple-soliton case, the freedom in the expansion of the solution of the perturbed KdV equation is exploited so as to transform the equation into a system of two equations…
Spontaneously generated waves and obstacles to integrability in perturbed evolution equations
Alex Vekser, Yair Zarmi
The perturbed Burgers and KdV equations are considered. Often, the perturbation excites waves that are different from the solution one is seeking. In the case of the Burgers equati…
Overcoming Obstacles to Integrability in Perturbed Nonlinear Evolution Equations
Alex Veksler, yair zarmi
Obstacles to integrability in perturbed evolution equations are overcome by allowing higher-order terms in the expansion of the solution to depend explicitly on time and position.…
Travelling Wave Solutions of a Simple Non-Local Burgers-Like Equation
Alex Veksler, Yair Zarmi
A Lax pair consisting of the Forsyth-Hopf-Cole transformation and a linear differential (in time) - difference (in continuous space) equation generates the whole hierarchy of the B…
Limitations of the Method of Multiple-Time-Scales
Peter B. Kahn, Yair Zarmi
In the Method of Multiple-Time-Scales (MMTS), the introduction of independent time scales and the elimination of secular terms in the fast time variable, T0 = t, lead to the well-k…