NDLI: Spectral stability of one-dimensional reaction–diffusion equation with symmetric and asymmetric potential

Content Provider	Springer Nature Link
Author	Varatharajan, N. DasGupta, Anirvan
Copyright Year	2015
Abstract	In this work, the spectral stability of a class of solutions of the one-dimensional nonlinear reaction–diffusion equation with spatial symmetry and asymmetry is studied. The solutions are first obtained using the $$G'/G$$ -expansion method, and it is shown that this technique generates only kink and antikink type solutions. The essential spectra of the perturbed differential operator at the equilibrium states are obtained. The Evans function is used to determine the point spectrum using Lie midpoint method and Magnus method over a large range of spatial distance. It is shown that for a symmetric potential well, the stationary kink and antikink solutions connecting the stable equilibrium (vacuum) states of the system are stable. Interestingly, it is found that for a potential with broken symmetry, the stable stationary kink/antikink solutions transform into stable traveling kink/antikink solutions. This partially answers the question (Alfimov and Medvedeva in Phys Rev E 84:056606, 2011) on the qualitative features of the potential that are decisive for the existence/nonexistence of traveling kink/antikink solutions. The region of stability of the traveling kink/antikink solutions in the parameter space of the potential is identified. An interesting exchange of wave speeds between the kink and antikink solutions through the stationary solution state corresponding to the symmetric potential is brought out.
Starting Page	1257
Ending Page	1269
Page Count	13
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	80
Issue Number	3
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-02-11
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Reaction–diffusion equation Symmetric and asymmetric potential $$G'/G$$ -expansion method Spectral stability 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

Stability and bifurcation analysis of a reaction–diffusion equation with distributed delay

Spectral method for solving the equal width equation based on Chebyshev polynomials

A new method for finding special solutions of nonlinear diffusion equation

Some discussions about variable separation of nonlinear models using Riccati equation expansion method

Soliton solutions of nonlinear diffusion–reaction-type equations with time-dependent coefficients accounting for long-range diffusion

Turing instability and pattern formation of neural networks with reaction–diffusion terms

Light bullet in parity-time symmetric potential

New solitary wave solutions of time-fractional coupled Jaulent–Miodek equation by using two reliable methods

Forced dissipative Boussinesq equation for solitary waves excited by unstable topography

Spectral stability of one-dimensional reaction–diffusion equation with symmetric and asymmetric potential

Similar Documents

Stability and bifurcation analysis of a reaction–diffusion equation with distributed delay

Spectral method for solving the equal width equation based on Chebyshev polynomials

A new method for finding special solutions of nonlinear diffusion equation

Some discussions about variable separation of nonlinear models using Riccati equation expansion method

Soliton solutions of nonlinear diffusion–reaction-type equations with time-dependent coefficients accounting for long-range diffusion

Turing instability and pattern formation of neural networks with reaction–diffusion terms

Light bullet in parity-time symmetric potential

New solitary wave solutions of time-fractional coupled Jaulent–Miodek equation by using two reliable methods

Forced dissipative Boussinesq equation for solitary waves excited by unstable topography

Spectral stability of one-dimensional reaction–diffusion equation with symmetric and asymmetric potential