First integrals for time-dependent higher-order Riccati equations by nonholonomic transformation
type: Item
instance of: scholarly article
title: First integrals for time-dependent higher-order Riccati equations by nonholonomic transformation
zbMATH Open document ID: 1223.65053
author: Partha Guha
author: Barun Khanra
author: A. Ghose Choudhury
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2011-07-13T00:00:00Z
review text: The authors study the first integrals for time-dependent higher-order Riccati equations by nonholonomic transformations. They first introduce the nonholonomic transformation method and use it to compute the first integrals of the time dependent second-order Riccati equation. Then they apply the transformation to compute the first integrals of a class of third-order ordinary differential equations. The authors illustrate the method by several examples.
reviewed by: Seenith Sivasundaram
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 5920357
zbMATH Keywords: nonholonomic transformation
zbMATH Keywords: first integrals
zbMATH Keywords: second-order Riccati equation
zbMATH Keywords: Gambier equation
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.cnsns.2010.12.012
OpenAlex ID: W2066130314
cites work: General technique to produce isochronous Hamiltonians
cites work: Examples of isochronous Hamiltonians: classical and quantal treatments
cites work: On the general solution for the modified Emden-type equation
cites work: A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators
cites work: Lagrangian formalism for nonlinear second-order Riccati systems: One-dimensional integrability and two-dimensional superintegrability
cites work: Linearization under nonpoint transformations
cites work: Sundman Symmetries of Nonlinear Second-Order and Third-Order Ordinary Differential Equations
cites work: Linearisable third-order ordinary differential equations and generalised sundman transformations: the case \(X'''=0\)
cites work: ON PLANAR AND NON-PLANAR ISOCHRONOUS SYSTEMS AND POISSON STRUCTURES
cites work: Dynamics of a completely integrableN-coupled Liénard-type nonlinear oscillator
cites work: The Gambier mapping, revisited
cites work: Q5676532
cites work: Q3603819
cites work: Perturbation theory of Kepler motion based on spinor regularization.
cites work: THE LINEAR SYMTRIES OF A NONLINEAR DIFFERENTIAL EQUATION
cites work: Functional differential equations for the free energy and the effective energy in the broken-symmetry phase of \(\phi^4\)-theory and their recursive graphical solution
cites work: First integrals for one-dimensional particle motion in a non-linear, time-dependent potential field
cites work: Riccati's Nonlinear Differential Equation
DOI: 10.1016/J.CNSNS.2010.12.012
description: scientific article; zbMATH DE number 5920357