Open Access
Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Reviews in mathematical modelling
|
|
---|---|---|
Article Number | 67 | |
Number of page(s) | 14 | |
DOI | https://doi.org/10.1051/mmnp/2020029 | |
Published online | 03 December 2020 |
- H. Bateman, Some recent researches on the motion of fluids. Mon. Weather Rev. 43 (1915) 163–170. [CrossRef] [Google Scholar]
- J.M. Burgers, A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech. 1 (1948) 171–199. [CrossRef] [MathSciNet] [Google Scholar]
- F. Calogero and A. Degasperis, Spectral transform and solitons. North-Holland, Amsterdam (1982). [Google Scholar]
- J.C. Chen, Y. Chen, B.F. Feng and K.I. Maruno, Multi-dark soliton solutions of the twodimensional multi-component yajima-oikawa systems. J. Phys. Soc. Jpn. 84 (2015) 034002. [CrossRef] [Google Scholar]
- S.-S. Chen, B. Tian, Y. Sun and C.-R. Zhang, Generalized Darboux Transformations, Rogue Waves, and Modulation Instability for the Coherently Coupled Nonlinear Schródinger Equations in Nonlinear Optics. Ann. Phys. 531 (2019) 1900011. [CrossRef] [Google Scholar]
- Z. Du, B. Tian, H.-P. Chai and X.-H. Zhao, Dark-bright semi-rational solitons and breathers for a higher-order coupled nonlinear Schródinger system in an optical fiber. Appl. Math. Lett. 102 (2020) 106110. [CrossRef] [Google Scholar]
- X.-X. Du, B. Tian, Q.-X. Qu, Y.-Q. Yuan and X.-H. Zhao, Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma. Chaos Solitons Fract. 134 (2020) 109709. [CrossRef] [Google Scholar]
- P.G. Estëvez and J. Prada, Lump solutions for PDEs: algorithmic construction and classification. J. Nonlinear Math. Phys. 15 (2008) 166–75. [CrossRef] [Google Scholar]
- X.-Y. Gao, Mathematical view with observational/experimental consideration on certain (2+1)-dimensional waves in the cosmic/laboratory dusty plasmas. Appl. Math. Lett. 91 (2019) 165–172. [CrossRef] [Google Scholar]
- C. Garrett and J. Gemmrich, Rogue waves. Physics Today 62 (2009) 62–63. [CrossRef] [Google Scholar]
- X.-Y. Gao, Y.-J. Guo and W.-R. Shan, Water-wave symbolic computation for the Earth, Enceladus and Titan: The higher-order Boussinesq-Burgers system, auto- and non-auto-Bácklund transformations. Appl. Math. Lett. 104 (2020) 106170. [CrossRef] [Google Scholar]
- R. Hirota, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys, Rev. Lett. 27 (1971) 1192–1194. [CrossRef] [Google Scholar]
- R. Hirota, Direct method in soliton theory, in Solitons, edited by R.K. Bullough, P.J. Caudrey. Springer, Berlin, (1980). [Google Scholar]
- C.-C. Hu, B. Tian, H.-M. Yin, C.-R. Zhang and Z. Zhang, Dark breather waves, dark lump waves and lump wave-soliton interactions for a (3+1)- dimensional generalized Kadomtsev-Petviashvili equation in a fluid. Comput. Math. Appl. 78 (2019) 166–177. [CrossRef] [Google Scholar]
- L. Huangand Y. Chen, Lump solutions and interaction phenomenon for (2 + 1)-dimensional Sawada-Kotera equation. Theor. Phys. 67 (2017) 473–478. [Google Scholar]
- K. Imai, Dromion and lump solutions of the Ishimori-I equation. Progr. Theor. Phys. 98 (1997) 1013–1023. [CrossRef] [Google Scholar]
- B.-Q. Li and Y.-L. Ma, Multiple-lump waves for a (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation arising from incompressible fluid. Comput. Math. Appl. 76 (2018) 204–214. [CrossRef] [Google Scholar]
- B.-Q. Li and Y.-L. Ma, Solitons resonant behavior for a waveguide directional coupler system in optical fbers. Opt. Quantum Electron. 50 (2018) 270. [CrossRef] [Google Scholar]
- B.-Q. Li, Y.-L. Ma, L.-P. Mo and Y.-Y. Fu, The N-loop soliton solutions for (2 + 1)-dimensional Vakhnenko equation. Comput. Math. Appl. 74 (2017) 504–512. [CrossRef] [Google Scholar]
- Z. Lu and Y. Chen, Construction of rogue wave and lump solutions for nonlinear evolution equations. Eur. Phys. J. B 88 (2015) 1–5. [EDP Sciences] [Google Scholar]
- Z. Lu, E.M. Tian and R. Grimshaw, Interaction of two lump solitons described by the Kadomtsev-Petviashvili I equation. Wave Motion 40 (2004) 123–35. [CrossRef] [Google Scholar]
- Y.-L. Ma, Interaction and energy transition between the breather and rogue wave for a generalized nonlinear Schrödinger system with two higher-order dispersion operators in optical fibers. Nonlinear Dyn. 97 (2019) 95–105. [CrossRef] [Google Scholar]
- Y.-L. Ma and B.-Q. Li, Interactions between soliton and rogue wave for a (2+1)-dimensional generalized breaking soliton system: Hidden rogue wave and hidden soliton. Comput. Math. Appl. 78 (2019) 827–839. [CrossRef] [Google Scholar]
- Y.-L. Ma and B.-Q. Li, Mixed lump and soliton solutions for a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation. AIMS Math. 5 (2020) 1162–1176. [CrossRef] [Google Scholar]
- Y.-L. Ma and B.-Q., Rogue wave solutions, soliton and rogue wave mixed solution for a generalized (3 + 1)-dimensional Kadomtsev-Petviashvili equation in fluids. Mod. Phys. Lett. B 32 (2018) 1850358. [Google Scholar]
- S.V. Manakov and V.E. Zakharov, Two-dimensional solitons of the Kadomtsev-Petviashvili equation and their interaction. Phys. Lett. A 63 (1977) 205–6. [CrossRef] [Google Scholar]
- S. Manukure, Y. Zhou and W.X. Ma, Lump solutions to a (2 + 1)-dimensional extended KP equation. Comput. Math. Appl. 75 (2018) 2414–2419. [CrossRef] [Google Scholar]
- H.E. Nistazakis, D.J. Frantzeskakis and B.A. Malomed, Collisions between spatiotemporal solitons of different dimensionality in a planar waveguide. Phys. Rev. E 64 (2001) 026604. [CrossRef] [Google Scholar]
- H.-L. Si and B.-Q. Li, Two types of soliton twining behaviors for the Kraenkel-Manna-Merle system in saturated ferromagnetic materials. Optik 166 (2018) 49–55. [CrossRef] [Google Scholar]
- H.-Q. Sun and A.-H. Chen, Interactional solutions of a lump and a solitary wave for two higher-dimensional equations. Nonlinear Dyn. 94 (2018) 1753–1762. [CrossRef] [Google Scholar]
- Y. Tang, S. Tao and Q. Guan, Lumpsolitons and the interaction phenomena of them for two classes of nonlinear evolution equations. Comput. Math. Appl. 72 (2016) 2334–2342. [CrossRef] [Google Scholar]
- X. Wang, Y.Q. Li, F. Huang and Y. Chen, Rogue wave solitons of AB system. Commun. Nonlinear Sci. Numer. Simul. 20 (2015) 434–442. [CrossRef] [Google Scholar]
- C. Wang, Z. Dai and C. Liu, Interaction between kink solitary wave and rogue wave for (2 + 1)-dimensional Burgers equation. Mediterr. J. Math. 13 (2016) 1087–1098. [CrossRef] [Google Scholar]
- M. Wang, B. Tian, Y. Sun and Z. Zhang, Lump, mixed lump-stripe and rogue wave-stripe solutions of a (3+1)-dimensional nonlinear. Comput. Math. Appl. 79 (2020) 576–587. [CrossRef] [Google Scholar]
- A.M. Wazwaz, Partial Differential Equations and Solitary Waves Theorem. Springer and HEP, Berlin (2009) [CrossRef] [Google Scholar]
- A.-M. Wazwaz and S.A. El-Tantawy, New (3+1)-dimensional equations of Burgers type and Sharma-Tasso-Olver type: multiple-soliton solutions. Nonlinear Dyn. 87 (2017) 2457–2461. [CrossRef] [Google Scholar]
- H.W. Yang, X. Chen, M. Guo and Y.D. Chen, A new ZK-BO equation for three-dimensional algebraic Rossby solitary waves and its solution as well as fission property. Nonlinear Dyn. 91 (2018) 2019–2032. [Google Scholar]
- H.-M. Yin, B. Tian and X.-C. Zhao, Chaotic breathers and breather fission/fusion for a vector nonlinear Schrödinger equation in a birefringent optical fiber or wavelength division multiplexed system. Appl. Math. Comput. 368 (2020) 124768. [Google Scholar]
- C.-R. Zhang, B. Tian, Q.-X. Qu, L. Liu and H.-Y. Tian, Vector bright solitons and their interactions of the couple Fokas-Lenells system in a birefringent optical fiber. Z. Angew. Math. Phys. 71 (2020) 18. [CrossRef] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.