Differential-Invariant Solutions
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-018-3736-x
Abstract: We construct differential-invariant solutions to automorphic systems and propose a method for classifying differential-invariant submodels. read more here.
Keywords: invariant solutions; differential invariant;
Optimal system, group invariant solutions and conservation laws of the CGKP equation
Sign Up to like & getrecommendations! Published in 2017 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-017-3392-6
Abstract: In this paper, the (2 + 1)-dimensional cubic generalized Kadomtsev–Petviashvili (CGKP) equation that is derived from the Maxwell–Bloch equations is investigated. By means of Lie symmetry analysis method, we obtain the Lie point symmetries for the equation… read more here.
Keywords: group invariant; invariant solutions; system; optimal system ... See more keywords
Symmetry reductions, group-invariant solutions and conservation laws of a three-coupled Korteweg-de Vries system
Sign Up to like & getrecommendations! Published in 2019 at "Chinese Journal of Physics"
DOI: 10.1016/j.cjph.2019.06.004
Abstract: Abstract The Korteweg-de Vries (KdV)-type equations appear during the studies on the cosmic plasmas, planetary atmospheres and oceans. In this paper, via the Lie symmetry method, we investigate a three-coupled KdV system. Lie point symmetry… read more here.
Keywords: system; korteweg vries; three coupled; symmetry ... See more keywords
Optimal system and classification of invariant solutions of nonlinear class of wave equations and their conservation laws
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125615
Abstract: Abstract We study the classification of invariant solutions of a class of nonlinear wave equations using Lie symmetry analysis and the underlying optimal systems of subalgebras. We propose a classification of Lie generators via optimal… read more here.
Keywords: class; classification invariant; optimal systems; classification ... See more keywords
Invariant solutions of the Eckhaus-Kundu model with nonlinear dispersion and non-Kerr nonlinearities
Sign Up to like & getrecommendations! Published in 2019 at "Waves in Random and Complex Media"
DOI: 10.1080/17455030.2019.1587210
Abstract: This paper will study Eckhaus-Kundu equation from the perspective of Lie symmetry analysis. We will systematically construct similarity reductions in order to perform the explicit invariant solutions of this version of the nonlinear Schrödinger equation… read more here.
Keywords: eckhaus kundu; invariant solutions; solutions eckhaus; nonlinear dispersion ... See more keywords
Twistor structures and boost-invariant solutions to field equations
Sign Up to like & getrecommendations! Published in 2017 at "Gravitation and Cosmology"
DOI: 10.1134/s0202289317040119
Abstract: We start with a brief overview of a non-Lagrangian approach to field theory based on a generalization of the Kerr-Penrose theorem and algebraic twistor equations. Explicit algorithms for obtaining the set of fundamental (Maxwell, SL(2,ℂ)-Yang-Mills,… read more here.
Keywords: invariant solutions; structures boost; field; twistor structures ... See more keywords
Symmetry analysis and invariant solutions of (3 + 1)-dimensional Kadomtsev–Petviashvili equation
Sign Up to like & getrecommendations! Published in 2018 at "International Journal of Geometric Methods in Modern Physics"
DOI: 10.1142/s0219887818501256
Abstract: Based on Lie symmetry analysis, we study nonlinear waves in fluid mechanics with strong spatial dispersion. The similarity reductions and exact solutions are obtained based on the optimal system an... read more here.
Keywords: invariant solutions; symmetry analysis; analysis invariant; symmetry ... See more keywords
Invariant Solutions of Black-Scholes Equation with Ornstein-Uhlenbeck Process
Sign Up to like & getrecommendations! Published in 2021 at "Symmetry"
DOI: 10.3390/sym13050847
Abstract: This paper analyses the model of Black–Scholes option pricing from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the Black–Scholes equation. Furthermore,… read more here.
Keywords: invariant solutions; black scholes; ornstein uhlenbeck; process ... See more keywords