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Travelling waves arise in several areas of science, hence modification of travelling wave properties is of great interest. While many studies have demonstrated how to control the form or shape of a solitary travelling wave by employing soliton or dispersion management, far less is known about controlling the motion of a travelling wave while keeping its form unchanged. We present a technique for control of travelling wave motion using time-varying coefficients, which we refer to as wave management. The technique allows one to alter the trajectory of a travelling wave, slowing, stopping, or reversing the direction of the wave, all while ensuring that the wave form is unchanged, and we illustrate this through multiple examples. Our results suggest that wave management is a promising tool for applications where one needs to modify the motion of a wave while preserving its form, and we highlight several potential applications.
We analyse the stability of periodic, travelling-wave solutions to the Kawahara equation and some of its generalizations. We determine the parameter regime for which these solutions can exhibit resonance. By examining perturbations of small-amplitude
We consider a two-level atomic system, interacting with an electromagnetic field controlled in amplitude and frequency by a high intensity laser. We show that the amplitude of the induced electric field, admits an envelope profile corresponding to a
The generalized perturbative reduction method is used to find the two-component vector breather solution of the Born-Infeld equation $ U_{tt} -C U_{zz} = - A U_{t}^{2} U_{zz} - sigma U_{z}^{ 2} U_{tt} + B U_{z} U_{t} U_{zt} $. It is shown that the so
In order to later find explicit analytic solutions, we investigate the singularity structure of a fundamental model of nonlinear optics, the four-wave mixing model in one space variable z. This structure is quite similar, and this is not a surprise,
The motion of metastable helium atoms travelling through a standing light wave is investigated with a semi-classical numerical model. The results of a calculation including the velocity dependence of the dipole force are compared with those of the co