Abstract
In this paper, by the direct algebraic method, together with the inheritance solving strategy, new types of interaction solutions among solitons, rational waves and periodic waves are constructed for a (3+1)-dimensional nonlinear evolution equation. Meanwhile, based on the simplified Hirota method, its interaction solutions among solitons, breathers and lumps of any higher orders are established by an N-soliton decomposition algorithm, together with the parameters conjugated assignment and long wave limit techniques. Finally, we demonstrate the dynamical behaviors of new interaction solutions by graphs.
Similar content being viewed by others
References
Xu, G.Q., Wazwaz, A.M.: Integrability aspects and localized wave solutions for a new (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation. Nonlinear Dyn. 98(2), 1379 (2019)
Zha, Q.L.: A symbolic computation approach to constructing rogue waves with a controllable center in the nonlinear systems. Comput. Math. Appl. 75(9), 3331 (2018)
An, H.L., Feng, D.L., Zhu, H.X.: General M-lump, high-order breather and localized interaction solutions to the \(2+1\)-dimensional Sawada-Kotera equation. Nonlinear Dyn. 98(2), 1275 (2019)
Li, Z.Q., Tian, S.F., Wang, H., Yang, J.J., Zhang, T.T.: Characteristics of the lump, lumpoff and rouge wave solutions in a \((3{+}1)\)-dimensional generalized potential Yu–Toda–Sasa–Fukuyama equation. Mod. Phys. Lett. B 33(24), 1950291 (2019)
Ma, W.X.: Lump and interaction solutions to linear (4+1)-dimensional PDEs. Acta Math. Sci. 39(2), 498 (2019)
Xu, H., Ma, Z.Y., Fei, J.X., Zhu, Q.Y.: Novel characteristics of lump and lump-soliton interaction solutions to the generalized variable-coefficient Kadomtsev–Petviashvili equation. Nonlinear Dyn. 98(1), 551 (2019)
Guo, F., Lin, J.: Interaction solutions between lump and stripe soliton to the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation. Nonlinear Dyn. 96(2), 1233 (2019)
Geng, X.G.: Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations. J. Phys. A Math. Gen. 36(9), 2289 (2003)
Zakharov, V.E., Shabat, A.B.: Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34(1), 62 (1972)
Rodriguez, R.F., Reyes, J.A., Espinosa-Ceron, A., Fujioka, J., Malomed, B.A.: Standard and embedded solitons in nematic optical fibers. Phys. Rev. E 68(3), 036606 (2003)
Lakshmanan, M., Porsezian, K., Daniel, M.: Effect of discreteness on the continuum limit of the Heisenberg spin chain. Phys. Lett. A 133(9), 483 (1988)
Agrawal, G.P.: Nonlinear fiber optics. In: Nonlinear Science at the Dawn of the 21st Century (Springer, 2000), pp. 195–211
El-Tantawy, S.A., Wazwaz, A.M.: Anatomy of modified Korteweg-de Vries equation for studying the modulated envelope structures in non-Maxwellian dusty plasmas: freak waves and dark soliton collisions. Phys. Plasmas 25(9), 092105 (2018)
Geng, X.G., Ma, Y.L.: N-soliton solution and its Wronskian form of a (3+1)-dimensional nonlinear evolution equation. Phys. Lett. A 369(4), 285 (2007)
Wang, X., Wei, J., Geng, X.G.: Rational solutions for a (3+1)-dimensional nonlinear evolution equation. Commun. Nonlinear Sci. Numer. Simul. 83, 105116 (2020)
Zha, Q.L.: Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation. Phys. Lett. A 377(42), 3021 (2013)
Xie, J.J., Yang, X.: Rogue waves, breather waves and solitary waves for a (3+1)-dimensional nonlinear evolution equation. Appl. Math. Lett. 97, 6 (2019)
Fang, T., Wang, H., Wang, Y.H., Ma, W.X.: High-order lump-type solutions and their interaction solutions to a (3+1)-dimensional nonlinear evolution equation. Commun. Theor. Phys. 71(8), 927 (2019)
Liu, X.Z., Lou, Z.M., Qian, X.M., Thiam, L.: A study on lump and interaction solutions to a (3+1)-dimensional soliton equation. Complexity 2019, 9857527 (2019)
Tang, Y.N., Tao, S.Q., Zhou, M.L., Guan, Q.: Interaction solutions between lump and other solitons of two classes of nonlinear evolution equations. Nonlinear Dyn. 89(1), 429 (2017)
Zha, Q.L., Li, Z.B.: Darboux transformation and various solutions for a nonlinear evolution equation in (3+1)-dimensions. Mod. Phys. Lett. B 22(30), 2945 (2008)
Liu, Y.Q., Wen, X.Y., Wang, D.S.: Novel interaction phenomena of localized waves in the generalized (3+1)-dimensional KP equation. Comput. Math. Appl. 78(1), 1 (2019)
Hirota, R.: The Direct Method in Soliton Theory, vol. 155. Cambridge University Press, Cambridge (2004)
Satsuma, J., Ablowitz, M.J.: Two-dimensional lumps in nonlinear dispersive systems. J. Math. Phys. 20(7), 1496 (1979)
Acknowledgements
The work was supported by the National Natural Science Foundation of China (No. 11871328), Key project of Shanghai Municipal Science and Technology Commission (No. 18511103105), Shanghai Natural Science Foundation(No. 19ZR1414000), and is supported in part by Science and Technology Commission of Shanghai Municipality (No. 18dz2271000).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Cui, W., Li, W. & Liu, Y. Multiwave interaction solutions for a (3+1)-dimensional nonlinear evolution equation. Nonlinear Dyn 101, 1119–1129 (2020). https://doi.org/10.1007/s11071-020-05809-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-020-05809-x