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arXiv · 2105.04498

Reduction of nonlinear field theory equations to envelope models: towards a universal understanding of analogues of relativistic systems

Charles W. Robson·Fabio Biancalana
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Abstract

We investigate a novel mapping between solutions to several members of the Klein-Gordon family of equations and solutions to equations describing their reductions via the slowly varying envelope approximation. This mapping creates a link between the study of interacting relativistic fields and that of systems more amenable to laboratory-based analogue research, the latter described by nonlinear Schr\"odinger equations. A new evolution equation is also derived, emerging naturally from the sine-Gordon formula, possessing a Bessel-function nonlinearity; numerical investigations show that solutions to this novel equation include quasi-solitary waves, breather solutions, along with pulse splittings and recombinations.

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Charles W. Robson, Fabio Biancalana. 2021-05-10. Reduction of nonlinear field theory equations to envelope models: towards a universal understanding of analogues of relativistic systems. https://arxiv.org/abs/2105.04498

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