Isochronicity Conditions and Lagrangian Formulations of the Hirota Type Oscillator Equations

A. Ghose-Choudhury; Partha Guha

doi:10.1007/s12346-022-00676-w

Isochronicity Conditions and Lagrangian Formulations of the Hirota Type Oscillator Equations

A. Ghose-Choudhury
, Partha Guha

Mathematics

Diamond Harbour Women’s University

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

3 Scopus citations

Abstract

We consider the continuous version of the nonlinear Hirota oscillator equation and by using the Jacobi last multiplier (JLM) show that two types of Lagrangians (or Hamiltonians) can be derived corresponding to different choices of the JLM. The existence of a mirror partner (or sister) equation is shown. Both equations belong to the Liénard-II class and the Hirota oscillator equations are shown to emerge from the requirement of isochronicity.

Original language	British English
Article number	144
Journal	Qualitative Theory of Dynamical Systems
Volume	21
Issue number	4
DOIs	https://doi.org/10.1007/s12346-022-00676-w
State	Published - Dec 2022

Keywords

First integral
Hirota oscillator equation
Isochronous systems
Jacobi last multiplier
Liénard equation

Access to Document

10.1007/s12346-022-00676-w

OpenUrl availability

Full text

Cite this

@article{83e39800bba64d06a27123ebc1856fe6,

title = "Isochronicity Conditions and Lagrangian Formulations of the Hirota Type Oscillator Equations",

abstract = "We consider the continuous version of the nonlinear Hirota oscillator equation and by using the Jacobi last multiplier (JLM) show that two types of Lagrangians (or Hamiltonians) can be derived corresponding to different choices of the JLM. The existence of a mirror partner (or sister) equation is shown. Both equations belong to the Li{\'e}nard-II class and the Hirota oscillator equations are shown to emerge from the requirement of isochronicity.",

keywords = "First integral, Hirota oscillator equation, Isochronous systems, Jacobi last multiplier, Li{\'e}nard equation",

author = "A. Ghose-Choudhury and Partha Guha",

note = "Funding Information: Work by the author PG was supported by the Khalifa University of Science and Technology under Grant Number FSU-2021-014. He is also extremely grateful to Professor Jaume Llibre for valuable suggestions. Finally we would like to thank the two anonymous reviewers for their suggestions and valuable comments. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2022",

month = dec,

doi = "10.1007/s12346-022-00676-w",

language = "British English",

volume = "21",

journal = "Qualitative Theory of Dynamical Systems",

issn = "1575-5460",

publisher = "Springer International Publishing",

number = "4",

}

TY - JOUR

T1 - Isochronicity Conditions and Lagrangian Formulations of the Hirota Type Oscillator Equations

AU - Ghose-Choudhury, A.

AU - Guha, Partha

N1 - Funding Information: Work by the author PG was supported by the Khalifa University of Science and Technology under Grant Number FSU-2021-014. He is also extremely grateful to Professor Jaume Llibre for valuable suggestions. Finally we would like to thank the two anonymous reviewers for their suggestions and valuable comments. Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2022/12

Y1 - 2022/12

N2 - We consider the continuous version of the nonlinear Hirota oscillator equation and by using the Jacobi last multiplier (JLM) show that two types of Lagrangians (or Hamiltonians) can be derived corresponding to different choices of the JLM. The existence of a mirror partner (or sister) equation is shown. Both equations belong to the Liénard-II class and the Hirota oscillator equations are shown to emerge from the requirement of isochronicity.

AB - We consider the continuous version of the nonlinear Hirota oscillator equation and by using the Jacobi last multiplier (JLM) show that two types of Lagrangians (or Hamiltonians) can be derived corresponding to different choices of the JLM. The existence of a mirror partner (or sister) equation is shown. Both equations belong to the Liénard-II class and the Hirota oscillator equations are shown to emerge from the requirement of isochronicity.

KW - First integral

KW - Hirota oscillator equation

KW - Isochronous systems

KW - Jacobi last multiplier

KW - Liénard equation

UR - https://www.scopus.com/pages/publications/85139803553

U2 - 10.1007/s12346-022-00676-w

DO - 10.1007/s12346-022-00676-w

M3 - Article

AN - SCOPUS:85139803553

SN - 1575-5460

VL - 21

JO - Qualitative Theory of Dynamical Systems

JF - Qualitative Theory of Dynamical Systems

IS - 4

M1 - 144

ER -

Isochronicity Conditions and Lagrangian Formulations of the Hirota Type Oscillator Equations

Abstract

Keywords

Access to Document

OpenUrl availability

Other files and links

Fingerprint

Cite this