TY - JOUR

T1 - New conservation forms and lie algebras of ermakov-pinney equation

AU - Orhan, Ozlem

AU - Ozer, Teoman

PY - 2018/8

Y1 - 2018/8

N2 - In this study, we investigate first integrals and exact solutions of the Ermakov-Pinney equation. Firstly, the Lagrangian for the equation is constructed and then the determining equations are obtained based on the Lagrangian approach. Noether symmetry classification is implemented, the first integrals, conservation laws are obtained and classified. This classification includes Noether symmetries and first integrals with respect to different choices of external potential function. Furthermore, the time independent integrals and analytical solutions are obtained by using the modified Prelle-Singer procedure as a different approach. Additionally, for the investigation of conservation laws of the equation, we present the mathematical connections between the λ-symmetries, Lie point symmetries and the modified Prelle-Singer procedure. Finally, new Lagrangian and Hamiltonian forms of the equation are determined.

AB - In this study, we investigate first integrals and exact solutions of the Ermakov-Pinney equation. Firstly, the Lagrangian for the equation is constructed and then the determining equations are obtained based on the Lagrangian approach. Noether symmetry classification is implemented, the first integrals, conservation laws are obtained and classified. This classification includes Noether symmetries and first integrals with respect to different choices of external potential function. Furthermore, the time independent integrals and analytical solutions are obtained by using the modified Prelle-Singer procedure as a different approach. Additionally, for the investigation of conservation laws of the equation, we present the mathematical connections between the λ-symmetries, Lie point symmetries and the modified Prelle-Singer procedure. Finally, new Lagrangian and Hamiltonian forms of the equation are determined.

KW - Classification

KW - First integral

KW - Invariant solution

KW - Lagrangian and Hamiltonian description

KW - Noether theory

KW - Prelle-Singer method

KW - λ-symmetry.

UR - http://www.scopus.com/inward/record.url?scp=85032951032&partnerID=8YFLogxK

U2 - 10.3934/dcdss.2018046

DO - 10.3934/dcdss.2018046

M3 - Article

AN - SCOPUS:85032951032

SN - 1937-1632

VL - 11

SP - 753

EP - 764

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

IS - 4

ER -