Deformed solitons of a typical set of (2+1)–dimensional complex modified Korteweg–de Vries equations
By: Feng Yuan, Xiaoming Zhu and Yulei Wang
References
- Ablowitz, M.J., Ablowitz, M.A., Clarkson, P.A. and Clarkson, P.A. (1991). Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge.
- Biondini, G. (2007). Line soliton interactions of the Kadomtsev–Petviashvili equation, Physical Review Letters99(6): 064103.
- Dai, C.Q., Zhu, S.Q., Wang, L.L. and Zhang, J.F. (2010). Exact spatial similaritons for the generalized (2+1)-dimensional nonlinear Schrödinger equation with distributed coefficients, EPL (Europhysics Letters)92(2): 24005.
- El-Tantawy, S.A. and Moslem, W.M. (2014). Nonlinear structures of the Korteweg–de Vries and modified Korteweg–de Vries equations in non-Maxwellian electron-positron-ion plasma: Solitons collision and rogue waves, Physics of Plasmas21(5): 052112.
- Erbay, H.A. (1998). Nonlinear transverse waves in a generalized elastic solid and the complex modified Korteweg–de Vries equation, Physica Scripta58(1): 9.
- Erbay, S. and Şuhubi, E.S. (1989). Nonlinear wave propagation in micropolar media. II: Special cases, solitary waves and Painlevé analysis, International Journal of Engineering Science27(8): 915–919.
- Gorbacheva, O.B. and Ostrovsky, L.A. (1983). Nonlinear vector waves in a mechanical model of a molecular chain, Physica D: Nonlinear Phenomena8(1–2): 223–228.
- He, J.S., Tao, Y.S., Porsezian, K. and Fokas, A.S. (2013). Rogue wave management in an inhomogeneous nonlinear fibre with higher order effects, Journal of Nonlinear Mathematical Physics20(3): 407–419.
- He, J.S., Wang, L.H., Li, L.J., Porsezian, K. and Erdélyi, R. (2014). Few-cycle optical rogue waves: Complex modified Korteweg–de Vries equation, Physical Review E89(6): 062917.
- Hirota, R. (1972). Exact solution of the modified Korteweg–de Vries equation for multiple collisions of solitons, Journal of the Physical Society of Japan33(5): 1456–1458.
- Kao, C.Y. and Kodama, Y. (2012). Numerical study of the KP equation for non-periodic waves, Mathematics and Computers in Simulation82(7): 1185–1218.
- Karney, C.F.F., Sen, A. and Chu, F.Y.F. (1979). Nonlinear evolution of lower hybrid waves, The Physics of Fluids22(5): 940–952.
- Khater, A.H., El-Kalaawy, O.H. and Callebaut, D.K. (1998). Bäcklund transformations and exact solutions for Alfvén solitons in a relativistic electron–positron plasma, Physica Scripta58(6): 545.
- Kodama, Y., Oikawa, M. and Tsuji, H. (2009). Soliton solutions of the KP equation with V-shape initial waves, Journal of Physics A: Mathematical and Theoretical42(31): 312001.
- Komatsu, T.S. and Sasa, S.-i. (1995). Kink soliton characterizing traffic congestion, Physical Review E52(5): 5574.
- Korteweg, D.J. and de Vries, G. (1895). XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science39(240): 422.
- Kundu, A. (2008). Exact accelerating solitons in nonholonomic deformation of the KdV equation with a two-fold integrable hierarchy, Journal of Physics A: Mathematical and Theoretical41(49): 495201.
- Li, Z.J., Hai, W.H. and Deng, Y. (2013). Nonautonomous deformed solitons in a Bose–Einstein condensate, Chinese Physics B22(9): 090505.
- Liu, X.T., Yong, X.L., Huang, Y.H., Yu, R. and Gao, J.W. (2015). Deformed soliton, breather and rogue wave solutions of an inhomogeneous nonlinear Hirota equation, Communications in Nonlinear Science and Numerical Simulation29(1–3): 257–266.
- Lonngren, K. E. (1998). Ion acoustic soliton experiments in a plasma, Optical and Quantum Electronics30(7–10): 615–630.
- Lü, X., Zhu, H. W. Meng, X.H.Y.Z.C. and Tian, B. (2007). Soliton solutions and a Bäcklund transformation for a generalized nonlinear Schrödinger equation with variable coefficients from optical fiber communications, Journal of Mathematical Analysis and Applications336(2): 1305–1315.
- Mollenauer, L.F., Stolen, R.H. and Gordon, J.P. (1980). Experimental observation of picosecond pulse narrowing and solitons in optical fibers, Physical Review Letters45(13): 1095.
- Myrzakulov, R., Mamyrbekova, G., Nugmanova, G. and Lakshmanan, M. (2015). Integrable (2+1)-dimensional spin models with self-consistent potentials, Symmetry7(3): 1352–1375.
- Osman, M.S. and Wazwaz, A.M. (2018). An efficient algorithm to construct multi-soliton rational solutions of the (2+1)-dimensional KdV equation with variable coefficients, Applied Mathematics and Computation321: 282–289.
- Pal, R., Kaur, H., Raju, T.S. and Kumar, C. (2017). Periodic and rational solutions of variable-coefficient modified Korteweg–de Vries equation, Nonlinear Dynamics89(1): 617–622.
- Porsezian, K., Seenuvasakumaran, P. and Ganapathy, R. (2006). Optical solitons in some deformed MB and NLS–MB equations, Physics Letters A348(3–6): 233–243.
- Russell, S.J. (1844). Report on waves, 14th Meeting of the British Association for the Advancement of Science, York, UK, pp. 311–390.
- Sun, Z.Y. Gao, Y.T.L.Y. and Yu, X. (2011). Soliton management for a variable-coefficient modified Korteweg–de Vries equation, Physical Review E84(2): 026606.
- Tao, Y.S., He, J.S. and Porsezian, K. (2013). Deformed soliton, breather, and rogue wave solutions of an inhomogeneous nonlinear Schrödinger equation, Chinese Physics B22(7): 074210.
- Wadati, M. (1972). The exact solution of the modified Korteweg–de Vries equation, Journal of the Physical Society of Japan32(6): 1681–1681.
- Wadati, M. (2008). Construction of parity-time symmetric potential through the soliton theory, Journal of the Physical Society of Japan77(7): 074005.
- Wadati, M. and Ohkuma, K. (1982). Multiple-pole solutions of the modified Korteweg–de Vries equation, Journal of the Physical Society of Japan51(6): 2029–2035.
- Wu, H.X., Zeng, Y.B. and Fan, T.Y. (2008). Complexitons of the modified KdV equation by Darboux transformation, Applied Mathematics and Computation196(2): 501–510.
- Xing, Q.X., Wang, L.H., Mihalache, D., Porsezian, K. and He, J.S. (2017a). Construction of rational solutions of the real modified Korteweg–de Vries equation from its periodic solutions, Chaos: An Interdisciplinary Journal of Nonlinear Science27(5): 053102.
- Xing, Q.X., Wu, Z.W., Mihalache, D. and He, J.S. (2017b). Smooth positon solutions of the focusing modified Korteweg–de Vries equation, Nonlinear Dynamics89(4): 2299–2310.
- Xu, T.X., Qiao, Z.J. and Li, Y. (2011). Darboux transformation and shock solitons for complex mKdV equation, Pacific Journal of Applied Mathematics3(1/2): 137.
- Yan, J.L. and Zheng, L.H. (2017). Conservative finite volume element schemes for the complex modified Korteweg–de Vries equation, International Journal of Applied Mathematics and Computer Science27(3): 515–525. DOI:10.1515/amcs-2017-0036.
- Yesmakhanova, K., Shaikhova, G., Bekova, G. and Myrzakulov, R. (2017). Darboux transformation and soliton solution for the (2+1)-dimensional complex modified Korteweg–de Vries equations, Journal of Physics: Conference Series936: 012045.
- Zabusky, N.J. and Kruskal, M.D. (1965). Interaction of solitons in a collisionless plasma and the recurrence of initial states, Physical Review Letters15(6): 240.
- Zha, Q.L. and Li, Z.B. (2008). Darboux transformation and multi-solitons for complex mKdV equation, Chinese Physics Letters25(1): 8.
- Zhang, H.Q. Tian, B.L.L.L. and Xue, Y.S. (2009). Darboux transformation and soliton solutions for the (2+1)-dimensional nonlinear Schrödinger hierarchy with symbolic computation, Physica A: Statistical Mechanics and Its Applications388(1): 9–20.
- Zhang, Y.S., Guo, L.J., Chabchoub, A. and He, J.S. (2017). Higher-order rogue wave dynamics for a derivative nonlinear Schrödinger equation, Romanian Journal of Physics62: 102.
- Zhang, Y.S., Guo, L.J., He, J.S. and Zhou, Z.X. (2015). Darboux transformation of the second-type derivative nonlinear Schrödinger equation, Letters in Mathematical Physics105(6): 853–891.
Language: English
Page range: 337 - 350
Submitted on: Nov 15, 2019
Accepted on: Jan 30, 2020
Published on: Jul 4, 2020
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
Related subjects:
© 2020 Feng Yuan, Xiaoming Zhu, Yulei Wang, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.