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Korteweg- de Vries equation --- Schröginger equations

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Mathematical physics --- Solitons --- Korteweg-de Vries equation --- Solitons. --- Korteweg-de Vries, Équation de. --- Pulses, Solitary wave --- Solitary wave pulses --- Wave pulses, Solitary --- Connections (Mathematics) --- Nonlinear theories --- Wave-motion, Theory of --- KdV equation --- Differential equations, Nonlinear

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Differential equations, Partial --- Hamiltonian systems --- Mathematical physics --- Solitons --- Equations aux dérivées partielles --- Systèmes hamiltoniens --- Physique mathématique --- Equations aux dérivées partielles --- Systèmes hamiltoniens --- Physique mathématique --- Solitons. --- Korteweg-de Vries equation --- Korteweg-de Vries, Équation de --- Differential equations, Nonlinear --- Équations différentielles non linéaires --- Lie groups --- Lie, Groupes de --- Lie algebras --- Lie, Algèbres de

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Mathematical physics --- Differential equations, Partial --- Solitons --- Scattering (Mathematics) --- Equations aux dérivées partielles --- Dispersion (Mathématiques) --- Numerical solutions --- Solutions numériques --- 517.93 --- -Scattering (Mathematics) --- Pulses, Solitary wave --- Solitary wave pulses --- Wave pulses, Solitary --- Connections (Mathematics) --- Nonlinear theories --- Wave-motion, Theory of --- Scattering theory (Mathematics) --- Boundary value problems --- Scattering operator --- Partial differential equations --- Special differential equations. Systems of analytic mechanics, automatic control, operators. Dynamic systems --- Solitons. --- Numerical solutions. --- Scattering (Mathematics). --- 517.93 Special differential equations. Systems of analytic mechanics, automatic control, operators. Dynamic systems --- Equations aux dérivées partielles --- Dispersion (Mathématiques) --- Solutions numériques --- Numerical analysis --- Korteweg-de Vries equation --- Korteweg-de Vries, Équation de --- Korteweg-de Vries equation. --- Korteweg-de Vries, Équation de --- Dynamique différentiable --- Differential equations, Partial - Numerical solutions --- Equations aux derivees partielles --- Scattering

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Symmetry and complexity are the focus of a selection of outstanding papers, ranging from pure Mathematics and Physics to Computer Science and Engineering applications. This collection is based around fundamental problems arising from different fields, but all of them have the same task, i.e. breaking the complexity by the symmetry. In particular, in this Issue, there is an interesting paper dealing with circular multilevel systems in the frequency domain, where the analysis in the frequency domain gives a simple view of the system. Searching for symmetry in fractional oscillators or the analysis of symmetrical nanotubes are also some important contributions to this Special Issue. More papers, dealing with intelligent prognostics of degradation trajectories for rotating machinery in engineering applications or the analysis of Laplacian spectra for categorical product networks, show how this subject is interdisciplinary, i.e. ranging from theory to applications. In particular, the papers by Lee, based on the dynamics of trapped solitary waves for special differential equations, demonstrate how theory can help us to handle a practical problem. In this collection of papers, although encompassing various different fields, particular attention has been paid to the common task wherein the complexity is being broken by the search for symmetry.

fractional differential equations --- fractional oscillations (vibrations) --- fractional dynamical systems --- nonlinear dynamical systems --- harmonic wavelet --- filtering --- multilevel system --- forced Korteweg-de Vries equation --- trapped solitary wave solutions --- numerical stability --- two bumps or holes --- finite difference method --- Laplacian spectra --- categorical product --- Kirchhoff index --- global mean-first passage time --- spanning tree --- degradation trajectories prognostic --- asymmetric penalty sparse decomposition (APSD) --- rolling bearings --- wavelet neural network (WNN) --- recursive least squares (RLS) --- health indicators --- first multiple Zagreb index --- second multiple Zagreb index, hyper-Zagreb index --- Zagreb polynomials --- Nanotubes