NDLI: Convergent analytic solutions for homoclinic orbits in reversible and non-reversible systems

Content Provider	Springer Nature Link
Author	Roy Choudhury, S. Gambi, G.
Copyright Year	2013
Abstract	In this paper, convergent, multi-infinite, series solutions are derived for the homoclinic orbits of a canonical fourth-order ODE system, in both reversible and non-reversible cases. This ODE includes traveling-wave reductions of many important non-linear PDEs or PDE systems, for which these analytical solutions would correspond to regular or localized pulses of the PDE. As such, the homoclinic solutions derived here are clearly topical, and they are shown to match closely to earlier results obtained by homoclinic numerical shooting. In addition, the results for the non-reversible case go beyond those that have been typically considered in analyses conducted within bifurcation-theoretic settings.We also comment on generalizing the treatment here to parameter regimes where solutions homoclinic to exponentially small periodic orbits are known to exist, as well as another possible extension placing the solutions derived here within the framework of a comprehensive categorization of ALL possible traveling-wave solutions, both smooth and non-smooth, for our governing ODE.
Starting Page	1769
Ending Page	1782
Page Count	14
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	73
Issue Number	3
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2013-04-20
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Homoclinic orbits Shil’nikov analysis Reversible and non-reversible systems Traveling wave solution Vibration, Dynamical Systems, Control Mechanics Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

3-periodic traveling wave solutions for a dynamical coupled map lattice

Exact traveling wave solutions and bifurcations of the Biswas–Milovic equation

Numerical Continuation of Homoclinic Orbits to Non-Hyperbolic Equilibria in Planar Systems

Exact traveling wave solutions and bifurcations of the generalized derivative nonlinear Schrödinger equation

Detecting stable–unstable nonlinear invariant manifold and homoclinic orbits in mechanical systems

Different wave solutions associated with singular lines on phase plane

Exact traveling wave solutions and bifurcations of a further modified Zakharov–Kuznetsov equation

Traveling wave solutions for nonlinear dispersive water-wave systems with time-dependent coefficients

New no-traveling wave solutions for the Liouville equation by Bäcklund transformation method

Convergent analytic solutions for homoclinic orbits in reversible and non-reversible systems

Similar Documents

3-periodic traveling wave solutions for a dynamical coupled map lattice

Exact traveling wave solutions and bifurcations of the Biswas–Milovic equation

Numerical Continuation of Homoclinic Orbits to Non-Hyperbolic Equilibria in Planar Systems

Exact traveling wave solutions and bifurcations of the generalized derivative nonlinear Schrödinger equation

Detecting stable–unstable nonlinear invariant manifold and homoclinic orbits in mechanical systems

Different wave solutions associated with singular lines on phase plane

Exact traveling wave solutions and bifurcations of a further modified Zakharov–Kuznetsov equation

Traveling wave solutions for nonlinear dispersive water-wave systems with time-dependent coefficients

New no-traveling wave solutions for the Liouville equation by Bäcklund transformation method

Convergent analytic solutions for homoclinic orbits in reversible and non-reversible systems