Ya-Jie Liu, Hui Alan Wang, Xing-Biao Hu, Ying-Nan Zhang
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引用次数: 0
Abstract
The Hirota–Miwa equation is one of the most celebrated fully discrete integrable systems. By introducing bilinear operators of trigonometric-type, we propose a novel variant of the Hirota–Miwa equation, which can be regarded as an integrable discretization of the Kadomtsev–Petviashvili-I (KPI) equation. It turns out that this new equation admits a number of physically significant solutions, including solitons, lumps, breathers, and periodic wave solutions. As far as we know, it is the first time that lump solutions have been reported in the context of fully discrete integrable systems. In addition, the numerical periodic wave solutions are computed by employing deep learning techniques. Finally, the reduction procedure is considered, which yields a trigonometric-type discrete Korteweg–de Vries (KdV) equation and a trigonometric-type discrete Boussinesq equation.
期刊介绍：
MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas.
The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process.
The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed.
The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.
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