Figure 1.
A simple case of the two particles interactions
-
Previous Article
Dynamics of solitary waves and periodic waves for a generalized KP-MEW-Burgers equation with damping
- CPAA Home
- This Issue
-
Next Article
Analysis of COVID-19 epidemic transmission trend based on a time-delayed dynamic model
doi: 10.3934/cpaa.2021075
Online First
Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.
Readers can access Online First articles via the “Online First” tab for the selected journal.
On the even solutions of the Toda system: a degree argument approach
| 1. | Department of Mathematics, University of Science and Technology of China, Hefei 230027, China |
| 2. | Department of Mathematics, Towson University, Towson, MD 21252, USA |
| 3. | School of Mathematical Sciences and Physics, North China Electric Power University, Beijing 102206, China |
In this paper, we show the existence of even solutions with prescribed asymptotic behavior at infinity. Instead of using the integrability of the Toda system, the novel idea here is a degree argument approach. Perturbation theory has also been used in our study. Our method can be generalized to explore non-integrable systems with exponential type nonlinearities.
Keywords:
Even solutions,
Toda system,
degree argument approach,
perturbation theory,
non-integrable system.
Mathematics Subject Classification:
Primary: 34B30, 34D10, 34E99.
Citation:
Yong Liu, Jing Tian, Xuelin Yong.
On the even solutions of the Toda system: a degree argument approach. Communications on Pure & Applied Analysis, doi: 10.3934/cpaa.2021075
![]()
Figure 2.
A simple case of the three particles interactions
| [1] |
Yong Liu. Even solutions of the Toda system with prescribed asymptotic behavior. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1779-1790. doi: 10.3934/cpaa.2011.10.1779 |
| [2] |
Weiwei Ao. Sharp estimates for fully bubbling solutions of $B_2$ Toda system. Discrete & Continuous Dynamical Systems, 2016, 36 (4) : 1759-1788. doi: 10.3934/dcds.2016.36.1759 |
| [3] |
Manuel del Pino, Michal Kowalczyk, Juncheng Wei. The Jacobi-Toda system and foliated interfaces. Discrete & Continuous Dynamical Systems, 2010, 28 (3) : 975-1006. doi: 10.3934/dcds.2010.28.975 |
| [4] |
Chunyan Ji, Daqing Jiang. Persistence and non-persistence of a mutualism system with stochastic perturbation. Discrete & Continuous Dynamical Systems, 2012, 32 (3) : 867-889. doi: 10.3934/dcds.2012.32.867 |
| [5] |
Jann-Long Chern, Sze-Guang Yang, Zhi-You Chen, Chih-Her Chen. On the family of non-topological solutions for the elliptic system arising from a product Abelian gauge field theory. Discrete & Continuous Dynamical Systems, 2020, 40 (6) : 3291-3304. doi: 10.3934/dcds.2020127 |
| [6] |
Jérôme Coville, Juan Dávila. Existence of radial stationary solutions for a system in combustion theory. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 739-766. doi: 10.3934/dcdsb.2011.16.739 |
| [7] |
Yongsheng Mi, Boling Guo, Chunlai Mu. Well-posedness and blow-up scenario for a new integrable four-component system with peakon solutions. Discrete & Continuous Dynamical Systems, 2016, 36 (4) : 2171-2191. doi: 10.3934/dcds.2016.36.2171 |
| [8] |
Dmitry Treschev. A locally integrable multi-dimensional billiard system. Discrete & Continuous Dynamical Systems, 2017, 37 (10) : 5271-5284. doi: 10.3934/dcds.2017228 |
| [9] |
Xiaoyue Li, Xuerong Mao. Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation. Discrete & Continuous Dynamical Systems, 2009, 24 (2) : 523-545. doi: 10.3934/dcds.2009.24.523 |
| [10] |
Johan Matheus Tuwankotta, Eric Harjanto. Strange attractors in a predator–prey system with non-monotonic response function and periodic perturbation. Journal of Computational Dynamics, 2019, 6 (2) : 469-483. doi: 10.3934/jcd.2019024 |
| [11] |
Yingshu Lü. Symmetry and non-existence of solutions to an integral system. Communications on Pure & Applied Analysis, 2018, 17 (3) : 807-821. doi: 10.3934/cpaa.2018041 |
| [12] |
Wai-Ki Ching, Sin-Man Choi, Min Huang. Optimal service capacity in a multiple-server queueing system: A game theory approach. Journal of Industrial & Management Optimization, 2010, 6 (1) : 73-102. doi: 10.3934/jimo.2010.6.73 |
| [13] |
Francesco Paparella, Alessandro Portaluri. Geometry of stationary solutions for a system of vortex filaments: A dynamical approach. Discrete & Continuous Dynamical Systems, 2013, 33 (7) : 3011-3042. doi: 10.3934/dcds.2013.33.3011 |
| [14] |
Zuowei Cai, Jianhua Huang, Liu Yang, Lihong Huang. Periodicity and stabilization control of the delayed Filippov system with perturbation. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1439-1467. doi: 10.3934/dcdsb.2019235 |
| [15] |
Juncheng Wei, Jun Yang. Toda system and interior clustering line concentration for a singularly perturbed Neumann problem in two dimensional domain. Discrete & Continuous Dynamical Systems, 2008, 22 (3) : 465-508. doi: 10.3934/dcds.2008.22.465 |
| [16] |
E. Norman Dancer. On a degree associated with the Gross-Pitaevskii system with a large parameter. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 1835-1839. doi: 10.3934/dcdss.2019120 |
| [17] |
Gerald Teschl. On the spatial asymptotics of solutions of the Toda lattice. Discrete & Continuous Dynamical Systems, 2010, 27 (3) : 1233-1239. doi: 10.3934/dcds.2010.27.1233 |
| [18] |
Ran Zhuo, Wenxiong Chen, Xuewei Cui, Zixia Yuan. Symmetry and non-existence of solutions for a nonlinear system involving the fractional Laplacian. Discrete & Continuous Dynamical Systems, 2016, 36 (2) : 1125-1141. doi: 10.3934/dcds.2016.36.1125 |
| [19] |
Peter Markowich, Jesús Sierra. Non-uniqueness of weak solutions of the Quantum-Hydrodynamic system. Kinetic & Related Models, 2019, 12 (2) : 347-356. doi: 10.3934/krm.2019015 |
| [20] |
Stig-Olof Londen, Hana Petzeltová. Convergence of solutions of a non-local phase-field system. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 653-670. doi: 10.3934/dcdss.2011.4.653 |
2020 Impact Factor: 1.916
Tools
Metrics
Other articles
by authors
[Back to Top]