Abstract
In this paper, we construct new exact solutions of some (2+1)-dimensional Burgers-type systems by using corresponding Cole–Hopf-type transformations. The obtained linear equations show that abundant (2+1)-dimensional soliton structures can be constructed for the physical quantity \(W=\lambda (\mathrm{ln} f)_{xy}\) by selecting appropriate parameters. In particular, new meshy soliton structures and interactions are revealed for the first time.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Data availability
This paper has no associated data.
References
Infeld, E., Senatorski, A., Skorupski, A.A.: Decay of Kadomtsev–Petviashvili solitons. Phys. Rew. Lett. 72, 1345–1347 (1994)
Serkin, V.N., Hasegawa, A.: Novel soliton solutions of the nonlinear Schrödinger equation model. Phys. Rew. Lett. 85, 4502–4505 (2000)
Lu, F., Lin, Q., Knox, W.H., Govind, P.: Agrawal: Vector soliton fission. Phys. Rew. Lett. 93, 183901 (2004)
Zhang, J.F., Han, P.: New multisoliton solutions of the(2+1)-dimensional dispersive long wave equations. Commun. Nonl. Sci. Nume. Simu. 6, 178–182 (2001)
Maccari, A.: Non-resonant interacting water waves in 2+1 dimensions. Chaos Solitons Fractal 14, 105–116 (2002)
Wang, S., Tang, X.Y., Lou, S.Y.: Soliton fission and fusion: Burgers equation and Sharma–Tasso–Olver equation. Chaos Solitons Fractal 21, 231–239 (2004)
Lin, J., Wu, F.M.: Fission and fusion of localized coherent structures for a (2+1)-dimensional KdV equation. Chaos Solitons Fractal 19, 189–193 (2004)
Radha, B., Duraisamy, C.: The homogeneous balance method and its applications for finding the exact solutions for nonlinear equations. J. Ambient. Intell. Humaniz. Comput. 12, 6591–6597 (2021)
Tang, X.Y., Lou, S.Y., Zhang, Y.: Localized excitations in (2+1)-dimensional systems. Phys. Rev. E 66, 046601 (2002)
Tang, X.Y., Lou, S.Y.: Extended multilinear variable separation approach and multi-valued localized excitations for some (2+1)-dimensional integrable systems. J. Math. Phys. 44, 4000–4025 (2003)
Shen, S.F., Jin, Y.Y., Zhang, J.: Bäcklund Transformations and solutions of some generalized nonlinear evolution equations. Rep. Math. Phys. 73, 225–279 (2014)
Wang, M.M., Chen, Y.: Dynamic behaviors of general N-solitons for the nonlocal generalized nonlinear Schrödinger equation. Nonlinear Dyn. 104, 2621–2638 (2021)
Pu, J.C., Li, J., Chen, Y.: Solving localized wave solutions of the derivative nonlinear Schr?dinger equation using an improved PINN method. Nonlinear Dyn. 105, 1723–1739 (2021)
Zhou, H.J., Chen, Y.: Breathers and rogue waves on the double-periodic background for the reverse-space-time derivative nonlinear Schrödinger equation. Nonlinear Dyn. 106, 3437–3451 (2021)
Gai, L.T., Ma, W.X., Bilige, S.: Abundant multilayer network model solutions and bright-dark solitons for a (3+1)-dimensional p-gBLMP equation. Nonlinear Dyn. 106, 867–877 (2021)
Qu, G.Z., Hu, X.R., Miao, Z.W., Shen, S.F., Wang, M.M.: Soliton molecules and abundant interaction solutions of a general high-order Burgers equation. Results Phys. 23, 104052 (2021)
Bai, C.L., Zhao, H.: Interactions among periodic waves and solitary waves for a higher dimensional system. J. Phys. A: Math. Gen. 39, 3283–3293 (2006)
Wang, J.Y., Liang, Z.F., Tang, X.Y.: Infinitely many generalized symmetries and Painlevé analysis of a (2+1)-dimensional Burgers system. Phys. Scr. 89, 025201 (2014)
Wazwaz, A.M.: Multiple kink solutions for two coupled integrable (2 + 1)-dimensional systems. Appl. Math. Let. 58, 1–6 (2016)
Bruzon, M.S., Gandarias, M.L., Senthilvelan, M.: Nonlocal symmetries of Riccati and Abel chains and their similarity reductions. J. Math. Phys. 53, 023512 (2012)
Tanwar, D.V., Kumar, M.: Lie symmetries, exact solutions and conservation laws of the Date–Jimbo–Kashiwara–Miwa equation. Nonlinear Dyn. 106, 3453–3468 (2021)
Xu, Y.S., Mihalache, D., He, J.S.: Resonant collisions among two-dimensional localized waves in the Mel’nikov equation. Nonlinear Dyn. 106, 2431–2448 (2021)
Acknowledgements
The authors thank Prof. Yong Chen of East China Normal University for helpful discussions. The work was supported by the National Natural Science Foundation of China (11771395).
Funding
Funding was provided by the National Natural Science Foundation of China (Grant No. 11771395).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of interest
The authors declare that they have no conflicts 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
Zhou, K., Peng, JD., Wang, GF. et al. New exact solutions of some (2+1)-dimensional Burgers-type systems and interactions. Nonlinear Dyn 108, 4115–4122 (2022). https://doi.org/10.1007/s11071-022-07426-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-022-07426-2