Breather Wave Solutions for the (3+1)-D Generalized Shallow Water Wave Equation with Variable Coefficients

• Lafta Abed Dawod ^[1] ; Mehrdad Lakestani ^[1] ; Jalil Manafian ^[1]
  1. [1] University of Tabriz

     University of Tabriz

     Irán

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 4, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • The equation of the shallow water wave in oceanography and atmospheric science is extended to (3+1) dimensions, which is a known equation. To achieve this, an illustrative example of the VC generalized shallow water wave equation is provided to demonstrate the feasibility and reliability of the used procedure in this study. It is shown that Hirota bilinear method is an important scheme. So, it has plenty of classes of rational solutions by selecting the interaction breather and dark soliton solutions and homoclinic breather wave solutions. Here many types of rough and breather solutions are obtained. The mentioned equation is transformed into the Hirota bilinear form with help of the Hirota direct method. In this process, the Hirota bilinear operator plays a significant role. Based on the Hirota bilinear form, the breather wave forms solutions of the equation are obtained. Meanwhile, the figures of the breather wave forms solutions and periodic wave solutions are plotted. The trajectory solutions of the traveling waves are shown explicitly and graphically. The effect of the free parameters on the behavior of the acquired figures to a few of the obtained solutions for two nonlinear rational exact cases was also discussed. In addition to addressing a scientific explanation of the analytical work, the results are graphically presented to make it simple to recognize the dynamical aspects. Many new types of traveling-wave solutions are revealed, including the breather wave, the dark kink singular, the periodic solitary singular and the singular soliton solutions. By comparing the proposed method with the other existing methods, the results show that the execution of this method is concise, simple, and straightforward.

• Referencias bibliográficas
  • 1. Randall, D. A.: The Shallow Water Equations. Technical Report, Atmospheric Science, Colorado State University, Fort Collins (2006)
  • 2. Shinbrot, M.: The shallow water equations. J. Eng. Math. 4(4), 293–304 (1970)
  • 3. Zhou, B., Ding, K., Wang, J., Wang, L., Jin, P., Tang, T.: Experimental study on the interactions between wave groups in double-wave-group...
  • 4. Feng, Q., Feng, Z., Su, X., Bai, Y.D., Ding, B.Y.: Design and simulation of human resource allocation model based on double-cycle neural...
  • 5. Jiang, S., Zhao, C., Zhu, Y., Wang, C., Du, Y., Lei, W., Wang, L.: A practical and economical ultrawideband base station placement approach...
  • 6. Zhang, X., Wang, Y., Yang, M., Geng, G.: Toward concurrent video multicast orchestration for cachingassisted mobile networks. IEEE Trans....
  • 7. Ye, R., Liu, P., Shi, K., Yan, B.: State damping control: a novel simple method of rotor UAV with high performance. IEEE Access 8, 214346–214357...
  • 8. Alsufi, N.A., Fatima, N., Noor, A., Gorji, M.R., Alam, M.M.: Lumps and interactions, fission and fusion phenomena in multi solitons of...
  • 9. Zhang, Q., Yan, T., Gao, G.H.: The energy method for high-order invariants in shallow water wave equations. Appl. Math. Lett. 142, 108626...
  • 10. Yu, S., Huang, L.: Exact solutions of the generalized (2+1)-dimensional shallow water wave equation. Results Phys. 42, 106020 (2022)
  • 11. Li, R., Ilhan, O.A., Manafian, J., Mahmoud, K.H., Abotaleb, M., Kadi, A.: A mathematical study of the (3+1)-D variable coefficients...
  • 12. Gu, Y., Zia, S.M., Isam, M., Manafian, J., Hajar, A., Abotaleb, M.: Bilinear method and semi-inverse variational principle approach to...
  • 13. Ilhan, O.A., Manafian, J., Alizadeh, A., Mohammed, S.A.: M lump and interaction between M lump and N stripe for the third-order evolution...
  • 14. Zhou, B., Hu, J., Jin, P., Sun, K., Li, Y., Ning, D.: Power performance and motion response of a floating wind platform and multiple heaving...
  • 15. Zhou, B., Zheng, Z., Zhang, Q., Jin, P., Wang, L., Ning, D.: Wave attenuation and amplification by an abreast pair of floating parabolic...
  • 16. Hu, Q., Han, E.,Wang,W.,Wang, X., Li, Z.: The Interactive Relationship BetweenWater Environmental Pollution and the Quality of Economic...
  • 17. Li, R., Bu Sinnah, Z.A., Shatouri, Z.M.,Manafian, J., Aghdaei,M.F., Kadi, A.: Different forms of optical soliton solutions to the Kudryashov’s...
  • 18. Nourani, V., Rouzegari, N., Molajou, A., Baghanam, A.H.: An integrated simulation–optimization framework to optimize the reservoir operation...
  • 19. Guo, B., Dong, H., Fang, Y.: Lump solutions and interaction solutions for the dimensionally reduced nonlinear evolution equation. Complexity...
  • 20. Zhen, L.: Research on mathematical teaching innovation strategy and best practices based on deep learning algorithm. J. Commer. Biotech....
  • 21. Chen, N., Li, H., Li, Y.: Evaluation of binary offset carrier signal capture algorithm for development of the digital health literacy...
  • 22. Della Volpe, C., Siboni, S.: From van der Waals equation to acid-base theory of surfaces: chemicalmathematical journey. Math. J. Rev....
  • 23. Rikani, A.S.: Numerical analysis of free heat transfer properties of flat panel solar collectors with different geometries. J. Res. Sci....
  • 24. Cai, W., Mohammaditab, R., Fathi, G., Wakil, K., Ebadi, A.G., Ghadimi, N.: Optimal bidding and offering strategies of compressed air energy...
  • 25. Han, E., Ghadimi, N.: Model identification of proton-exchange membrane fuel cells based on a hybrid convolutional neural network and extreme...
  • 26. Zhang, J., Khayatnezhad, M., Ghadimi, N.: Optimal model evaluation of the proton exchange membrane fuel cells based on deep learning and...
  • 27. Chen, L., Huang, H., Tang, P., Yao, D., Yang, H., Ghadimi, N.: Optimal modeling of combined cooling, heating, and power systems using...
  • 28. Jiang, W., Wang, X., Huang, H., Zhang, D., Ghadimi, N.: Optimal economic scheduling of microgrids considering renewable energy sources...
  • 29. Mehrpooya, M., Ghadimi, N., Marefati, M., Ghorbanian, S.A.: Numerical investigation of a new combined energy system includes parabolic...
  • 30. Erfeng, H., Ghadimi, N.: Model identification of proton-exchange membrane fuel cells based on a hybrid convolutional neural network and...
  • 31. Yu, D., Zhang, T., He, G., Nojavan, S., Jermsittiparsert, K., Ghadimi, N.: Energy management of wind-PV-storage-grid based large electricity...
  • 32. Saeedi, M., Moradi, M., Hosseini, M., Emamifar, A., Ghadimi, N.: Robust optimization based optimal chiller loading under cooling demand...
  • 33. Mir, M., Shafieezadeh, M., Heidari, M.A., Ghadimi, N.: Application of hybrid forecast engine based intelligent algorithm and feature selection...
  • 34. Liu, J.G., Zhu, W.H.: Breather wave solutions for the generalized shallow water wave equation with variable coefficients in the atmosphere,...
  • 35. Liu, J.G., Zhu, W.H., He, Y., Lei, Z.Q.: Characteristics of lump solutions to a (3+1)-dimensional variable-coefficient generalized...
  • 36. Zayeda, E.M.E., Gepreel, K.A.: The (G’/G)-expansion method for finding traveling wave solutions of nonlinear partial differential equations...
  • 37. Darvishi, M.T., Najafi, M.: Some new exact solutions of the (3+1)-dimensional breaking soliton equation by the Exp-function method....
  • 38. Chen, Y., Liu, R.: Some new nonlinear wave solutions for two (3+1)-dimensional equations. Appl. Math. Comput. 260, 397–411 (2015)
  • 39. Huang, Q.M., Gao, Y.T., Jia, S.L., Wang, Y.L., Deng, G.F.: Bilinear backlund transformation, soliton and periodic wave solutions for a...
  • 40. Huang, Q.M., Gao, Y.T.: Bilinear backlund transformation and dynamic features of the soliton solutions for a variable-coefficient (3+1)-dimensional...
  • 41. Duran, S.: An investigation of the physical dynamics of a traveling wave solution called a bright soliton. Phys. Scr. 96, 125251 (2021)
  • 42. Zhang, Z., Guo, Q., Li, B., Chen, J.C.: A new class of nonlinear superposition between lump waves and other waves for Kadomtsev–Petviashvili...
  • 43. Moghadam, R.A., Ebrahimi, S.: Design and analysis of a torsional mode MEMS disk resonator for RF applications. J. Multidiscip. Eng. Sci....
  • 44. Fu, H.H., Guo, Y., Shen, Z., Zhao, J., Xie, Y., Ling, Y., Ouyang, S., Li, S., Zhang, W.: Tuning the shell thickness of core-shell alpha-Fe2O3@SiO2...
  • 45. Bai, J.L., Wang, X., Zhu, Y., Yuan, G., Wu, S., Qin, F., Yu, X., Ren, L.: Polymer types regulation strategy toward the synthesis of carbonized...
  • 46. Ma, W.X.: Generalized bilinear differential equations. Stud. Nonlinear Sci. 2, 140–144 (2011)
  • 47. Zhang, R.F., Bilige, S.: Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations...
  • 48. Zhang, R.F., Li, M.C., Gan, J,Y., Qing, Li., Lan, Z.Z.: Novel trial functions and rogue waves of generalized breaking soliton equation...
  • 49. Zhang, R.F., Li, M.C., Albishari, M., Zheng, F.C., Lan, Z.Z.: Generalized lump solutions, classical lump solutions and rogue waves of...
  • 50. Younas, T., Sulaiman, T.A., Ren, J.: Propagation of M-truncated optical pulses in nonlinear optics. Opt. Quan. Electron. 55, 102 (2023)
  • 51. Younas, T., Sulaiman, T.A., Ren, J.: On the study of optical soliton solutions to the three-component coupled nonlinear Schrödinger equation:...
  • 52. Younas, T., Ren, J., Akinyemi, L., Rezazadeh, H.: On the multiple explicit exact solutions to the double-chain DNA dynamical system. Math....
  • 53. Younas, T., Ren, J.: Construction of optical pulses and other solutions to optical fibers in absence of self-phase modulation. Int. J....
  • 54. Bashar, Md.H., Inc, M., Islam, S.M.R., Mahmoud, K.H., Akbar, M.A.: Soliton solutions and fractional effects to the time-fractional modified...
  • 55. Islam, S.M.R., Bashar, Md.H., Arafat, S.M.Y., Wang, H., Roshid, Md.M.: Effect of the free parameters on the Biswas–Arshed model with a...
  • 56. Duran, S.: Exact solutions for time-fractional Ramani and Jimbo–Miwa equations by direct algebraic method. Adv. Sci. Eng. Med. 12, 982–988...
  • 57. Duran, S., Kaya, D.: Breaking analysis of solitary waves for the shallow water wave system in fluid dynamics. Eur. Phys. J. Plus 136,...
  • 58. Yokus, A., Isah, M.A.: Stability analysis and solutions of (2+1)-Kadomtsev–Petviashvili equation by homoclinic technique based on...
  • 59. Safi Ullah, M., Abdeljabbar, A., Roshid, H.O., Ali, M.Z.: Application of the unified method to solve the Biswas–Arshed model. Results...
  • 60. Safi Ullah, M., Ali, M. Z., Roshid, H. O., Hoque, Md. F.: Collision phenomena among lump, periodic and stripe soliton solutions to a (2+1)-dimensional...
  • 61. Safi Ullah, M., Ahmed, O., Mahbub, Md. A.: Collision phenomena between lump and kink wave solutions to a (3+1)-dimensional Jimbo–Miwa-like...
  • 62. Safi Ullah, M., Roshid, H.O., Ali, M.Z., Noor, N.F.M.: Novel dynamics of wave solutions for Cahn– Allen and diffusive predator–prey models...
  • 63. Safi Ullah, M., Seadawy, A.R., Ali, M.Z., Roshid, H.O.: Optical soliton solutions to the Fokas–Lenells model applying the ϕ6-model expansion...
  • 64. Seadawy, A.R., Iqbal, M., Lu, D.: Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg–de Vries...
  • 65. Seadawy, A.R., Iqbal, M., Lu, D.: Nonlinear wave solutions of the Kudryashov–Sinelshchikov dynamical equation in mixtures liquid-gas bubbles...
  • 66. Iqbal, M., Seadawy, A.R., Lu, D.: Applications of nonlinear longitudinal wave equation in a magnetoelectro-elastic circular rod and new...
  • 67. Seadawy, A.R., Iqbal, M., Lu, D.: Applications of propagation of long-wave with dissipation and dispersion in nonlinear media via solitary...
  • 68. Ma, W.X.: Bilinear equations, Bell polynomials and linear superposition principle. J. Phys. Conf. Ser. 411, 012021 (2013)