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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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This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.

heteroclinic solutions --- non-instantaneous impulses --- Schauder’s fixed point theory --- dichotomy --- second-order differential/difference/q-difference equation of hypergeometric type --- differential equations --- a priori estimates --- global solutions --- generalized Liouville equation --- Hilbert space --- dissipation --- collocation method --- exponential dichotomy --- Sumudu decomposition method --- three-step Taylor method --- dynamical system --- lower and upper solutions --- problems in the real line --- Nagumo condition on the real line --- SIRS epidemic model --- first order periodic systems --- regular solutions --- Clairin’s method --- coupled nonlinear systems --- Navier–Stokes equations --- Bäcklund transformation --- asymptotic stability --- Caputo fractional derivative --- exponential stability --- difference equations --- lipschitz stability --- strong nonlinearities --- polynomial solution --- integro-differentials --- kinetic energy --- Legendre wavelets --- weak solutions --- discrete Lyapunov equation --- population dynamics --- non-uniform lattices --- Korteweg-de Vries equation --- time-dependent partial differential equations --- mean curvature operator --- functional boundary conditions --- mathematical modelling --- fixed point theory --- limit-periodic solutions --- Arzèla Ascoli theorem --- Miura transformation --- state dependent delays --- ?-Laplacian operator --- divided-difference equations --- effective existence criteria