New Conservation Laws, Lagrangian Forms, and Exact Solutions of Modified Emden Equation

Gülden Gün Polat; Teoman Özer

doi:10.1115/1.4035408

New Conservation Laws, Lagrangian Forms, and Exact Solutions of Modified Emden Equation

Gülden Gün Polat, Teoman Özer^*

^*Corresponding author for this work

Department of Civil Engineering

Istanbul Technical University

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

This study deals with the determination of Lagrangians, first integrals, and integrating factors of the modified Emden equation by using Jacobi and Prelle-Singer methods based on the Lie symmetries and λ -symmetries. It is shown that the Jacobi method enables us to obtain Jacobi last multipliers by means of the Lie symmetries of the equation. Additionally, via the Lie symmetries of modified Emden equation, we analyze some mathematical connections between λ -symmetries and Prelle-Singer method. New and nontrivial Lagrangian forms, conservation laws, and exact solutions of the equation are presented and discussed.

Original language	English
Article number	041001
Journal	Journal of Computational and Nonlinear Dynamics
Volume	12
Issue number	4
DOIs	https://doi.org/10.1115/1.4035408
Publication status	Published - 1 Jul 2017

Bibliographical note

Publisher Copyright:
Copyright © 2017 by ASME.

Keywords

first integrals
Jacobi last multipliers
Lagrangians
modified Emden equation
Prelle-Singer method
λ-symmetries

Access to Document

10.1115/1.4035408

Cite this

@article{010158b8a4884fe19369b248c7dcbdd8,

title = "New Conservation Laws, Lagrangian Forms, and Exact Solutions of Modified Emden Equation",

abstract = "This study deals with the determination of Lagrangians, first integrals, and integrating factors of the modified Emden equation by using Jacobi and Prelle-Singer methods based on the Lie symmetries and λ -symmetries. It is shown that the Jacobi method enables us to obtain Jacobi last multipliers by means of the Lie symmetries of the equation. Additionally, via the Lie symmetries of modified Emden equation, we analyze some mathematical connections between λ -symmetries and Prelle-Singer method. New and nontrivial Lagrangian forms, conservation laws, and exact solutions of the equation are presented and discussed.",

keywords = "first integrals, Jacobi last multipliers, Lagrangians, modified Emden equation, Prelle-Singer method, λ-symmetries",

author = "{G{\"u}n Polat}, G{\"u}lden and Teoman {\"O}zer",

note = "Publisher Copyright: Copyright {\textcopyright} 2017 by ASME.",

year = "2017",

month = jul,

day = "1",

doi = "10.1115/1.4035408",

language = "English",

volume = "12",

journal = "Journal of Computational and Nonlinear Dynamics",

issn = "1555-1423",

publisher = "The American Society of Mechanical Engineers(ASME)",

number = "4",

}

TY - JOUR

T1 - New Conservation Laws, Lagrangian Forms, and Exact Solutions of Modified Emden Equation

AU - Gün Polat, Gülden

AU - Özer, Teoman

PY - 2017/7/1

Y1 - 2017/7/1

N2 - This study deals with the determination of Lagrangians, first integrals, and integrating factors of the modified Emden equation by using Jacobi and Prelle-Singer methods based on the Lie symmetries and λ -symmetries. It is shown that the Jacobi method enables us to obtain Jacobi last multipliers by means of the Lie symmetries of the equation. Additionally, via the Lie symmetries of modified Emden equation, we analyze some mathematical connections between λ -symmetries and Prelle-Singer method. New and nontrivial Lagrangian forms, conservation laws, and exact solutions of the equation are presented and discussed.

AB - This study deals with the determination of Lagrangians, first integrals, and integrating factors of the modified Emden equation by using Jacobi and Prelle-Singer methods based on the Lie symmetries and λ -symmetries. It is shown that the Jacobi method enables us to obtain Jacobi last multipliers by means of the Lie symmetries of the equation. Additionally, via the Lie symmetries of modified Emden equation, we analyze some mathematical connections between λ -symmetries and Prelle-Singer method. New and nontrivial Lagrangian forms, conservation laws, and exact solutions of the equation are presented and discussed.

KW - first integrals

KW - Jacobi last multipliers

KW - Lagrangians

KW - modified Emden equation

KW - Prelle-Singer method

KW - λ-symmetries

UR - http://www.scopus.com/inward/record.url?scp=85009967856&partnerID=8YFLogxK

U2 - 10.1115/1.4035408

DO - 10.1115/1.4035408

M3 - Article

AN - SCOPUS:85009967856

SN - 1555-1423

VL - 12

JO - Journal of Computational and Nonlinear Dynamics

JF - Journal of Computational and Nonlinear Dynamics

IS - 4

M1 - 041001

ER -

New Conservation Laws, Lagrangian Forms, and Exact Solutions of Modified Emden Equation

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this