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

• Format: eBook
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2023
• Subjects: ({(\frac{G^{\prime }}{G})}\)-expansion method; a (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation; auxiliary equation method; bifurcation theory; birefringence; Bragg gratings; breathers; Cardano; conservation laws; COVID-19 pandemic; cubic-quartic optical solitons; differential constraints; dispersion of unrestricted order; drainage; dynamics; exact solitary wave solutions; exact solution; exact stochastic-fractional solutions; exact traveling waves; Fokas–Lenells equations; fractional Kuramoto–Sivashinsky; gas hydrates; generalized 2D equal-width equation; generalized nonlinear Schrödinger equation; generalized Schrödinger equation; generalized SIdV equation; hydraulic drive; implicit function; improved adomian decomposition method; inverse problems; Kerr nonlinearity; Kudryashov; Kudryashov’s method; Laplace–Adomian decomposition; Lie point symmetries; lump solitons; magnetohydrodynamic forces; mathematical modeling; Mathematics and Science; memristor; multi-component fluid dynamic; multicriteria optimization; multiwave; NLSE; Noether’s theorem; nonlinear partial differential equations; optical soliton; optimal system of Lie subalgebras; peakon; periodic cross-kink solutions; periodic waves; permafrost formation; perturbation; polynomial law; pore-scale network model; porous media; rational and interaction solutions; Reference, Information and Interdisciplinary subjects; refractive index; Research and information: general; self-gravitation; semi-inverse; similarity; simplest equation method; solitary wave; solitary waves—kink and bell types; solitons; spike-timing-dependent plasticity; spiking neural networks; stability; stochastic Kuramoto–Sivashinsky; support operator method; synaptic plasticity; time-dependent SEIR model; time-fractional ion sound and Langmuir waves system; Weierstrass elliptic functions
• DOI: 10.3390/books978-3-0365-8097-5
• ISBN: 3036580972; 9783036580975; 9783036580968; 3036580964

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.