About this Research Topic
Nonlinear problems, originating from applied science that is closely related to practices, contain rich and extensive content. It makes the corresponding nonlinear models also complex and diverse. Due to the intricacy and contingency of nonlinear problems, unified mathematical methods still remain far and few between. In this regard, the comprehensive use of symmetric methods, along with other mathematical methods, becomes an effective option to solve nonlinear problems.
Symmetry plays a vital role in numerous fields, particularly for solving various types of algebraic, differential, integrable, and geometrical equations. Since many natural phenomena as well as physical and engineering applications can be portrayed and modeled by series of equations, it is of pivotality to solve these equations for enabling researchers to interpret their results precisely. Certainly, these equations include algebraic equations, differential equations, integral equations, difference equations, differential-difference equations, discrete, semi-discrete differential equations, and fractional equations.
Symmetries and group theory have critical importance for studies of complex nonlinear systems. They have provided the science foundations in the past. They serve for development of modern science and mathematics, including mathematical physics, nonlinear systems, and nonlinear differential equations.
In this Research Topic, we aim to bring together latest studies underscoring advances and applications of symmetry in nonlinear mathematical physics equations (NMPEs). We welcome Original Research and Review articles to bridge knowledge gaps on aforementioned issues in NMPEs and promote the development of symmetry and its applications. Key themes include, but not limited to:
• Symmetry of NMPEs and its applications
• Exact solutions to NMPEs and their physical applications
• Semi-analytical solutions to NMPEs and their physical applications
• Analytical and numerical approximations to NMPEs
• Conservation laws of NMPEs
Symmetry plays a vital role in numerous fields, particularly for solving various types of algebraic, differential, integrable, and geometrical equations. Since many natural phenomena as well as physical and engineering applications can be portrayed and modeled by series of equations, it is of pivotality to solve these equations for enabling researchers to interpret their results precisely. Certainly, these equations include algebraic equations, differential equations, integral equations, difference equations, differential-difference equations, discrete, semi-discrete differential equations, and fractional equations.
Symmetries and group theory have critical importance for studies of complex nonlinear systems. They have provided the science foundations in the past. They serve for development of modern science and mathematics, including mathematical physics, nonlinear systems, and nonlinear differential equations.
In this Research Topic, we aim to bring together latest studies underscoring advances and applications of symmetry in nonlinear mathematical physics equations (NMPEs). We welcome Original Research and Review articles to bridge knowledge gaps on aforementioned issues in NMPEs and promote the development of symmetry and its applications. Key themes include, but not limited to:
• Symmetry of NMPEs and its applications
• Exact solutions to NMPEs and their physical applications
• Semi-analytical solutions to NMPEs and their physical applications
• Analytical and numerical approximations to NMPEs
• Conservation laws of NMPEs
Keywords: symmetry, conservation laws, exact solutions, nonlinear differential equation, fractional differential equation, nonlinear waves
Important Note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.
