[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.10.1017/CBO9780511623998]Search in Google Scholar
[Biondini, G. (2007). Line soliton interactions of the Kadomtsev–Petviashvili equation, Physical Review Letters99(6): 064103.10.1103/PhysRevLett.99.064103]Search in Google Scholar
[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): 24005.10.1209/0295-5075/92/24005]Search in Google Scholar
[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): 052112.10.1063/1.4879815]Search in Google Scholar
[Erbay, H.A. (1998). Nonlinear transverse waves in a generalized elastic solid and the complex modified Korteweg–de Vries equation, Physica Scripta58(1): 9.10.1088/0031-8949/58/1/001]Search in Google Scholar
[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.]Search in Google Scholar
[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): 223–228.10.1016/0167-2789(83)90319-6]Search in Google Scholar
[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): 407–419.10.1080/14029251.2013.855045]Search in Google Scholar
[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): 062917.10.1103/PhysRevE.89.06291725019861]Search in Google Scholar
[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): 1456–1458.10.1143/JPSJ.33.1456]Search in Google Scholar
[Kao, C.Y. and Kodama, Y. (2012). Numerical study of the KP equation for non-periodic waves, Mathematics and Computers in Simulation82(7): 1185–1218.10.1016/j.matcom.2010.05.025]Search in Google Scholar
[Karney, C.F.F., Sen, A. and Chu, F.Y.F. (1979). Nonlinear evolution of lower hybrid waves, The Physics of Fluids22(5): 940–952.10.1063/1.862688]Search in Google Scholar
[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): 545.10.1088/0031-8949/58/6/001]Search in Google Scholar
[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): 312001.10.1088/1751-8113/42/31/312001]Search in Google Scholar
[Komatsu, T.S. and Sasa, S.-i. (1995). Kink soliton characterizing traffic congestion, Physical Review E52(5): 5574.10.1103/PhysRevE.52.55749964055]Search in Google Scholar
[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.]Search in Google Scholar
[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): 495201.10.1088/1751-8113/41/49/495201]Search in Google Scholar
[Li, Z.J., Hai, W.H. and Deng, Y. (2013). Nonautonomous deformed solitons in a Bose–Einstein condensate, Chinese Physics B22(9): 090505.10.1088/1674-1056/22/9/090505]Search in Google Scholar
[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): 257–266.10.1016/j.cnsns.2015.05.016]Search in Google Scholar
[Lonngren, K. E. (1998). Ion acoustic soliton experiments in a plasma, Optical and Quantum Electronics30(7–10): 615–630.10.1023/A:1006910004292]Search in Google Scholar
[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): 1305–1315.10.1016/j.jmaa.2007.03.017]Search in Google Scholar
[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): 1095.10.1103/PhysRevLett.45.1095]Search in Google Scholar
[Myrzakulov, R., Mamyrbekova, G., Nugmanova, G. and Lakshmanan, M. (2015). Integrable (2+1)-dimensional spin models with self-consistent potentials, Symmetry7(3): 1352–1375.10.3390/sym7031352]Search in Google Scholar
[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: 282–289.10.1016/j.amc.2017.10.042]Search in Google Scholar
[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): 617–622.10.1007/s11071-017-3475-4]Search in Google Scholar
[Porsezian, K., Seenuvasakumaran, P. and Ganapathy, R. (2006). Optical solitons in some deformed MB and NLS–MB equations, Physics Letters A348(3–6): 233–243.10.1016/j.physleta.2005.08.065]Search in Google Scholar
[Russell, S.J. (1844). Report on waves, 14th Meeting of the British Association for the Advancement of Science, York, UK, pp. 311–390.]Search in Google Scholar
[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): 026606.10.1103/PhysRevE.84.02660621929127]Search in Google Scholar
[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): 074210.10.1088/1674-1056/22/7/074210]Search in Google Scholar
[Wadati, M. (1972). The exact solution of the modified Korteweg–de Vries equation, Journal of the Physical Society of Japan32(6): 1681–1681.10.1143/JPSJ.32.1681]Search in Google Scholar
[Wadati, M. (2008). Construction of parity-time symmetric potential through the soliton theory, Journal of the Physical Society of Japan77(7): 074005.10.1143/JPSJ.77.074005]Search in Google Scholar
[Wadati, M. and Ohkuma, K. (1982). Multiple-pole solutions of the modified Korteweg–de Vries equation, Journal of the Physical Society of Japan51(6): 2029–2035.10.1143/JPSJ.51.2029]Search in Google Scholar
[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): 501–510.10.1016/j.amc.2007.06.011]Search in Google Scholar
[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): 053102.10.1063/1.498272128576109]Search in Google Scholar
[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): 2299–2310.10.1007/s11071-017-3579-x]Search in Google Scholar
[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.]Search in Google Scholar
[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-2017-0036.10.1515/amcs-2017-0036]Search in Google Scholar
[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: 012045.10.1088/1742-6596/936/1/012045]Search in Google Scholar
[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): 240.10.1103/PhysRevLett.15.240]Search in Google Scholar
[Zha, Q.L. and Li, Z.B. (2008). Darboux transformation and multi-solitons for complex mKdV equation, Chinese Physics Letters25(1): 8.10.1088/0256-307X/25/1/003]Search in Google Scholar
[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): 9–20.10.1016/j.physa.2008.09.032]Search in Google Scholar
[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.]Search in Google Scholar
[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): 853–891.10.1007/s11005-015-0758-x]Search in Google Scholar