NDLI: Solutions of the three-dimensional sine-Gordon equation

Content Provider	Springer Nature Link
Author	Aero, E. L. Bulygin, A. N. Pavlov, Yu. V.
Copyright Year	2009
Abstract	We obtain exact solutions U(x, y, z, t) of the three-dimensional sine-Gordon equation in a form that Lamb previously proposed for integrating the two-dimensional sine-Gordon equation. The three-dimensional solutions depend on arbitrary functions F(α) and ϕ(α,β), whose arguments are some functions α(x, y, z, t) and β(x, y, z, t). The ansatzes must satisfy certain equations. These are an algebraic system of equations in the case of one ansatz. In the case of two ansatzes, the system of algebraic equations is supplemented by first-order ordinary differential equations. The resulting solutions U(x, y, z, t) have an important property, namely, the superposition principle holds for the function tan(U/4). The suggested approach can be used to solve the generalized sine-Gordon equation, which, in contrast to the classical equation, additionally involves first-order partial derivatives with respect to the variables x, y, z, and t, and also to integrate the sinh-Gordon equation. This approach admits a natural generalization to the case of integration of the abovementioned types of equations in a space with any number of dimensions.
Starting Page	313
Ending Page	319
Page Count	7
File Format	PDF
ISSN	00405779
Journal	Theoretical and Mathematical Physics
Volume Number	158
Issue Number	3
e-ISSN	15739333
Language	English
Publisher	Springer US
Publisher Date	2009-04-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	sine-Gordon equation wave equation Hamilton-Jacobi equation superposition principle Applications of Mathematics Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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

Solutions of the sine-Gordon equation with a variable amplitude

Bound state solutions of the elliptic sine-Gordon equation

Superposition principle and exact solutions of a nonlinear diffusion equation

Application of Exp-function method to wave solutions of the Sine-Gordon and Ostrovsky equations

Complex Sine-Gordon-2: A New Algorithm for Multivortex Solutions on the Plane

Sine-Gordon equation on the semi-axis

Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

Noncommuting integrals of motion for the quantum sine-gordon equation

Nonlinear dynamics of a quasi-one-dimensional helicoidal structure

Solutions of the three-dimensional sine-Gordon equation

Similar Documents

Solutions of the sine-Gordon equation with a variable amplitude

Bound state solutions of the elliptic sine-Gordon equation

Superposition principle and exact solutions of a nonlinear diffusion equation

Application of Exp-function method to wave solutions of the Sine-Gordon and Ostrovsky equations

Complex Sine-Gordon-2: A New Algorithm for Multivortex Solutions on the Plane

Sine-Gordon equation on the semi-axis

Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

Noncommuting integrals of motion for the quantum sine-gordon equation

Nonlinear dynamics of a quasi-one-dimensional helicoidal structure

Solutions of the three-dimensional sine-Gordon equation