Nonlinear Partial Differential Equations: Exact Solutions, Symmetries, Methods, and Applications

• Other Authors: Kudryashov, Nikolai (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2023
• Subjects: Research & information: general; Mathematics & science; stochastic Kuramoto-Sivashinsky; fractional Kuramoto-Sivashinsky; exact stochastic-fractional solutions; \({(\frac{G^{\prime }}{G})}\)-expansion method; dynamics; hydraulic drive; similarity; multicriteria optimization; generalized Schrödinger equation; solitary wave; exact solution; implicit function; spiking neural networks; synaptic plasticity; spike-timing-dependent plasticity; memristor; solitons; refractive index; Kudryashov; generalized 2D equal-width equation; Weierstrass elliptic functions; Kudryashov's method; conservation laws; Noether's theorem; improved adomian decomposition method; optical soliton; Fokas-Lenells equations; cubic-quartic optical solitons; multiwave; periodic cross-kink solutions; rational and interaction solutions; time-fractional ion sound and Langmuir waves system; generalized SIdV equation; auxiliary equation method; exact traveling waves; solitary waves-kink and bell types; periodic waves; peakon; Cardano; semi-inverse; perturbation; polynomial law; Laplace-Adomian decomposition; birefringence; NLSE; lump solitons; breathers; a (2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation; Lie point symmetries; optimal system of Lie subalgebras; bifurcation theory; exact solitary wave solutions; Bragg gratings; porous media; stability; pore-scale network model; drainage; generalized nonlinear Schrödinger equation; Kerr nonlinearity; simplest equation method; dispersion of unrestricted order; nonlinear partial differential equations; differential constraints; gas hydrates; multi-component fluid dynamic; permafrost formation; self-gravitation; magnetohydrodynamic forces; support operator method; mathematical modeling; COVID-19 pandemic; inverse problems; time-dependent SEIR model
• Online Access: DOAB: download the publication; DOAB: description of the publication

This reprint contains the 19 articles accepted and published in the Special Issue "Nonlinear Partial Differential Equations: Exact Solutions, Symmetries, Methods and Applications, 2023" of the MDPI "Mathematics" journal. This publication covers a wide range of topics pertaining to the theory and applications of Nonlinear Partial Differential Equations and its generalizations. These journal covers special methods for constructing solutions to nonlinear nonintegrable partial differential equations and application of differential equations to describe physical, technological and environmental processes, among other topics. The main focus of this Special Issue is the use of computer mathematics methods to obtain the results of the presented works. We hope that the reprint will be an interesting and useful resource for those working in the area of Nonlinear Partial Differential Equations: Exact Solutions, Symmetries, Methods and Applications, as well as those with the proper mathematical background and willingness to familiarize themselves with recent advances in nonlinear mathematical models. Nowadays, these influence almost all aspects of human life.