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Special Issue "Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models, II"
A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics and Symmetry/Asymmetry".
Deadline for manuscript submissions: closed (30 April 2018) | Viewed by 20343
Special Issue Editors
Interests: symmetry analysis of nonlinear differential equations (both ODEs and PDEs) and techniques for the construction of exact solutions of PDEs; In particular, physically important equations, such as nonlinear heat equations and governing equations modeling of granular materials and nonlinear elasticity
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, Collections and Topics in MDPI journals
Special Issue in Symmetry: Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models
Special Issue in Entropy: Applications of Nonlinear Diffusion Equations
Special Issue in Symmetry: Symmetry and Biomathematics: Recent Developments and Challenges
Special Issue Information
This Special Issue is a natural continuation of the previous one, “ Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models ”, which was very successful https://www.mdpi.com/journal/symmetry/special_issues/Lie_Conditional_Symmetries
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 50 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.
Last but not the least, submissions devoted to different aspects of relations of symmetry with integrability and conservation laws of a given nonlinear PDE are encouraged.
Prof. Dr. Danny Arrigo
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 submissions that pass pre-check are 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 2000 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.