Variational Principles for Two Kinds of Coupled Nonlinear Equations in Shallow Water
| Autor: | Kecheng Peng, Xiao-Qun Cao, Ya-Nan Guo, Shi-Cheng Hou, Cheng-Zhuo Zhang |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics and Astronomy (miscellaneous)
020209 energy General Mathematics 02 engineering and technology (2+1)-dimensional dispersive long-wave equations Space (mathematics) 01 natural sciences 010305 fluids & plasmas Variational principle 0103 physical sciences 0202 electrical engineering electronic engineering information engineering Computer Science (miscellaneous) Applied mathematics Mathematics variational principle Computer simulation lcsh:Mathematics calculus of variations Broer-Kaup equations lcsh:QA1-939 Conserved quantity Nonlinear system Chemistry (miscellaneous) Homogeneous space Calculus of variations Soliton |
| Zdroj: | Symmetry Volume 12 Issue 5 Symmetry, Vol 12, Iss 850, p 850 (2020) |
| ISSN: | 2073-8994 |
| DOI: | 10.3390/sym12050850 |
| Popis: | It is a very important but difficult task to seek explicit variational formulations for nonlinear and complex models because variational principles are theoretical bases for many methods to solve or analyze the nonlinear problem. By designing skillfully the trial-Lagrange functional, different groups of variational principles are successfully constructed for two kinds of coupled nonlinear equations in shallow water, i.e., the Broer-Kaup equations and the (2+1)-dimensional dispersive long-wave equations, respectively. Both of them contain many kinds of soliton solutions, which are always symmetric or anti-symmetric in space. Subsequently, the obtained variational principles are proved to be correct by minimizing the functionals with the calculus of variations. The established variational principles are firstly discovered, which can help to study the symmetries and find conserved quantities for the equations considered, and might find lots of applications in numerical simulation. |
| Databáze: | OpenAIRE |
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