Multiscale expansion of the lattice sine--Gordon equation
Xiaoda Ji, Decio Levi, Matteo Petrera
TL;DR
This paper develops a multiscale expansion method for the lattice sine-Gordon equation, deriving a new discrete nonlinear Schrödinger type equation that describes its asymptotic behavior.
Contribution
It introduces a novel multiscale expansion approach to lattice equations, leading to a new discrete NLS-type equation for the sine-Gordon model.
Findings
Derived a partial difference equation governing far-field behavior.
Established a new discrete nonlinear Schrödinger type equation.
Provided insights into the asymptotic dynamics of lattice sine-Gordon systems.
Abstract
We expand a discrete--time lattice sine--Gordon equation on multiple lattices and obtain the partial difference equation which governs its far field behaviour. Such reduction allow us to obtain a new completely discrete nonlinear Schr\"oedinger (NLS) type equation.
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Taxonomy
TopicsNonlinear Photonic Systems · Nonlinear Waves and Solitons · Numerical methods for differential equations