Special Issue "Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models"
A special issue of Symmetry (ISSN 2073-8994).
Deadline for manuscript submissions: closed (31 October 2016).
Interests: Non-linear PDEs: Lie and conditional symmetries, exact solutions and their properties; Application of symmetry-based methods for analytical solving nonlinear initial and boundary value problems arising in mathematical physics and mathematical biology
Special Issues and Collections in MDPI journals
Special Issue in Symmetry: Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models, II
Special Issue in Entropy: Applications of Nonlinear Diffusion Equations
This Special Issue is a natural continuation of the previous one, “Lie Theory and Its Applications”, which was very successful https://www.mdpi.com/journal/symmetry/special_issues/lie_theory.
Nowadays, the most powerful methods for construction of exact solutions of nonlinear partial differential equations (PDEs) are symmetry based methods. These methods originated from the Lie method, which was created by the prominent Norwegian mathematician Sophus Lie in the 19th century. The method was essentially developed using modern mathematical language in the 1960s and 1970s. Although the technique of the Lie method is well-known, the method still attracts the attention of many researchers, and new results are published on a regular basis.
However, it is well-known that the Lie method is not efficient for solving PDEs with a “poor” Lie symmetry (i.e., their maximal algebra of invariance is trivial). Thus, other symmetry-based methods (conditional symmetry, weak symmetry, generalized conditional symmetry etc.) were developed during the last few decades. The best known among them is the method of nonclassical symmetries, proposed by G. Bluman and J. Cole in 1969. Nevertheless, this approach was suggested almost 60 years ago, its successful applications for solving nonlinear equations were accomplished only in the 1990s. Moreover, one may say that progress is still modest in applications of non-Lie methods to systems of PDEs and integro-differential equations, especially those arising in real world applications. Thus, this Special Issue welcomes articles devoted to these topics. Articles and reviews devoted to the theoretical foundations of symmetry based methods and their applications for solving other nonlinear equations (especially reaction-diffusion-convection equations and higher-order PDEs) and nonlinear models (especially for biomedical applications) are also welcome.
Prof. Dr. Roman M. Cherniha
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
- Lie symmetry
- nonclassical symmetry
- Q-conditional symmetry
- (generalized) conditional symmetry
- invariance algebra of nonlinear PDE
- symmetry of (initial) boundary-value problem
- exact solution
- invariant solution
- non-Lie solution