516
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Elastic and nonelastic interactional solutions for the (2 + 1)-dimensional Ito equation

&
Pages 137-143 | Received 05 Jul 2018, Accepted 25 Jan 2019, Published online: 04 Apr 2019

References

  • Ablowitz, M. J., & Segur, H. (1981). Solitons and the inverse scattering transform. Philadelphia, PA: SIAM.
  • Baronio, F., Degasperis, A., Conforti, M., & Wabnitz, S. (2012). Solutions of the vector nonlinear Schrödinger equations: Evidence for deterministic rogue waves. Physical Review Letters, 109, 044102(1)–044102(4).
  • Chen, Y., Yan, Z. Y., & Zhang, H. Q. (2003). New explicit solitary wave solutions for (2 + 1)-dimensional Boussinesq equation and (3 + 1)-dimensional KP equation. Physics Letters A, 307(2–3), 107–113. doi: 10.1016/S0375-9601(02)01668-7
  • Fokas, A. S., Pelinovsky, D. E., & Sulem, C. (2001). Interaction of lumps with a line soliton for the DSII equation. Physica D, 152–153, 189–198. doi: 10.1016/S0167-2789(01)00170-1
  • Gu, C. H., Hu, H. S., & Zhou, Z. X. (2005). Darboux transformation in integral system: Theory and their applications to geometry. Mathematics Physics Studies (Vol. 26). New York, NY: Springer-Verlag.
  • Hirota, R. (2004). The direct method in soliton theory. Cambridge: Cambridge University Press.
  • Hu, X. B., & Li, Y. (1991). Nonlinear superposition formulae of the Ito equation and a model equation for shallow water waves. Journal of Physics A: Mathematical and General, 24(9), 1979–1986. doi: 10.1088/0305-4470/24/9/010
  • Huang, L. L., & Chen, Y. (2017). Lump solutions and interaction phenomenon for (2 + 1)-dimensional Sawada-Kotera equation. Communications in Theoretical Physics, 67(5), 473–478. doi: 10.1088/0253-6102/67/5/473
  • Ito, M. (1980). An extension of nonlinear evolution equations of the K-dV (mK-dV) type to higher orders. Journal of the Physical Society of Japan, 49(2), 771–778. doi: 10.1143/JPSJ.49.771
  • Kaup, D. J. (1981). The lump solutions and the Bäcklund transformation for the three-dimensional three-wave resonant interaction. Journal of Mathematical Physics, 22(6), 1176–1181. doi: 10.1063/1.525042
  • Li, C. X., & Zeng, Y. B. (2007). Soliton solutions to a higher order Ito equation: Pfaffian technique. Physics Letters A, 363(1–2), 1–4. doi: 10.1016/j.physleta.2006.10.080
  • Li, D. L., & Zhao, J. X. (2009). Multiple-soliton solutions for the generalized (1 + 1)-dimensional and the generalized (2 + 1)-dimensional Ito equations. Applied Mathematics and Computation, 215(5), 1968–1974. doi: 10.1016/j.amc.2009.07.058
  • Lu, Z. M., Tian, E. M., & Grimshaw, R. (2004). Interaction of two lump solitons described by the Kadomtsev-Petviashvili I equation. Wave Motion, 40(2), 123–135. doi: 10.1016/j.wavemoti.2003.12.017
  • Luo, H. Y., Duan, M. Y., Liu, X., & Liu, J. (2010). Explicit periodic solitary wave solutions for the (2 + 1)-dimensional Boussinesq equation. Applied Mathematics and Computation, 217(2), 826–829. doi: 10.1016/j.amc.2010.06.023
  • Ma, W. X. (2015). Lump solutions to the Kadomtsev-Petviashvili equation. Physics Letters A, 379(36), 1975–1978. doi: 10.1016/j.physleta.2015.06.061
  • Ma, W. X., Yong, X. L., & Zhang, H. Q. (2017). Diversity of interaction solutions to the (2 + 1)-dimensional Ito equation. Computers and Mathematics with Applications. Advance Online Publication, 75, 289–295. doi: 10.1016/j.camwa.2017.09.013
  • Rao, J. G., Cheng, Y., & He, J. S. (2017). Rational and semi-rational solutions of the nonlocal Davey-Stewartson equations. Studies in Applied Mathematics, 139(4), 568–598. doi: 10.1111/sapm.12178
  • Rogers, C., & Schief, M. J. (2002). Bäcklund and Darboux transformations geometry and modern application in soliton theory. Cambridge: Cambridge University Press.
  • Tang, Y. N., Tao, S. Q., & Guan, Q. (2016). Lump solitons and the interaction phenomena of them for two classes of Nonlinear Evolution equations. Computers and Mathematics with Applications, 72(9), 2334–2342. doi: 10.1016/j.camwa.2016.08.027
  • Wang, X. B., Tian, S. F., Qin, C. Y., & Zhang, T. T. (2017). Dynamics of the breathers, rogue waves and solitary waves in the (2 + 1)-dimensional Ito equation. Applied Mathematics Letters, 68, 40–47. doi: 10.1016/j.aml.2016.12.009
  • Wang, Y. H., Wang, H., Zhang, H. S., & Temuer, C. L. (2017). Exact interaction solutions of an extended (2 + 1)-dimensional Shallow Water Wave equation. Communications in Theoretical Physics, 68(2), 165–169. doi: 10.1088/0253-6102/68/2/165
  • Wazwaz, A. M. (2008). Multiple-soliton solutions for the generalized (1 + 1)-dimensional and the generalized (2 + 1)-dimensional Ito equations. Applied Mathematics and Computation, 202(2), 840–849. doi: 10.1016/j.amc.2008.03.029
  • Wazwaz, A. M. (2016). Kadomtsev-Petviashvili hierarchy: N-soliton solutions and distinct dispersion relations. Applied Mathematics Letters, 52, 74–79. doi: 10.1016/j.aml.2015.08.018
  • Yang, J. Y., Ma, W. X., & Qin, Z. Y. (2017). Lump and lump-soliton solutions to the (2 + 1)-dimensional Ito equation. Analysis and Mathematical Physics, 1, 1–10.
  • Zhang, C. C., & Chen, A. H. (2016). Bilinear form and new multi-soliton solutions of the classical Boussinesq-Burgers system. Applied Mathematics Letters, 58, 133–139. doi: 10.1016/j.aml.2016.02.015
  • Zhang, Y., & Chen, D. Y. (1991). N-soliton-like solution of Ito equation. Communication in Theoretical Physics, 42, 641–644.
  • Zhang, Y., Dong, H. H., Zhang, X. E., & Yang, H. W. (2017). Rational solutions and lump solutions to the generalized (3 + 1)-dimensional shallow water-like equation. Computers and Mathematics with Applications, 73(2), 246–252. doi: 10.1016/j.camwa.2016.11.009
  • Zhang, W. G., Liu, G., & Ren, Y. C. (2008). Solitary wave solutions and periodic cosine wave solutions of nonlinear wave equations. Journal of University of Shanghai for Science and Technology, 30, 15–21.
  • Zhao, Z. H., Dai, Z. D., & Wang, C. J. (2010). Extend three-wave method for the (1 + 2)-dimensional Ito equation. Applied Mathematics and Computation, 217(5), 2295–2300. doi: 10.1016/j.amc.2010.06.059
  • Zou, L., Yu, Z. B., Tian, S. F., Feng, L. L., & Li, J. (2018). Lump solutions with interaction phenomena in the (2 + 1)-dimensional Ito equation. Modern Physics Letters B, 32(07), 1850104. doi: 10.1142/S021798491850104X