Extraction of Lumps, Solitons, and Multi-Peakons for an Integrable Shallow Water Wave Equation

• Autores: Nauman Raza, Asifa Zahid, M. Higazy, Ahmet Bekir, Y.S. Hamed
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 3, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This article presents the unique analysis of an integrable (3+1)-dimensional shallow water wave equation with potential implications in ocean engineering, marine environments, atmospheric research, and other fields. The paper explored the derivation of lump, multi-peakons, and soliton solutions using a recently developed technique:

    the generalized exponential differential rational function method that relies on a trial solution of an ordinary differential equation, involving the exponential rational function’s ith derivative. To examine the physical characteristics of the obtained solutions, the results are presented visually through 3D surface plots and density plots, offering a clear understanding of the wave dynamics. The findings provide crucial insights into complex wave behavior, particularly in the context of shallow water and nonlinear wave interactions.

• Referencias bibliográficas
  • 1. Duran, S.: Breaking theory of solitary waves for the Riemann wave equation in fluid dynamics. Int. J. Mod. Phys. B 35(09), 2150130 (2021)
  • 2. Khater, M.: On the dynamics of strong Langmuir turbulence through the five recent numerical schemes in the plasma physics. Num. Methods...
  • 3. Shakeel, M., Iqbal, M.A., Mohyud-Din, S.T.: Closed form solutions for nonlinear biological population model. J. Biol. Syst. 26(01), 207–223...
  • 4. Hussain, A., Ibrahim, T.F., Birkea, F.M., Al-Sinan, B.R., Alotaibi, A.M.: Optical solitons for the Kudryashov—Sinelshchikov equation by...
  • 5. Raza, N., Ur Rahman, R., Seadawy, A., Jhangeer, A.: Computational and bright soliton solutions and sensitivity behavior of Camassa-Holm...
  • 6. He, Y., Kai, Y.: Wave structures, modulation instability analysis and chaotic behaviors to Kudryashov’s equation with third-order dispersion....
  • 7. Marchant, T.R., Smyth, N.F.: Soliton interaction for the extended Korteweg-de Vries equation. IMA J. Appl. Math. 56(2), 157–176 (1996)
  • 8. Raza, N., Salman, F., Butt, A.R., Gandarias, M.L.: Lie symmetry analysis, soliton solutions and qualitative analysis concerning to the...
  • 9. Clarkson, P.A., Kruskal, M.D.: New similarity reductions of the Boussinesq equation. J. Math. Phys. 30(10), 2201–2213 (1989)
  • 10. Plastino, A.R., Plastino, A.: Non-extensive statistical mechanics and generalized Fokker-Planck equation. Physica A 222(1–4), 347–354...
  • 11. Bonkile, M.P., Awasthi, A., Lakshmi, C., Mukundan, V., Aswin, V.S.: A systematic literature review of Burgers’ equation with recent advances....
  • 12. Berestycki, H., Nadin, G., Perthame, B., Ryzhik, L.: The non-local Fisher—KPP equation: travelling waves and steady states. Nonlinearity...
  • 13. Mann, N., Kumar, S.: In-depth analysis and exploration of rogue wave, lump wave, and different solitonic patterns to the Painlevé-integrable...
  • 14. Wang, K.L.: New analysis methods for the coupled fractional nonlinear Hirota equation. Fractals 31(09), 2350119 (2023)
  • 15. Wang, K.L.: New solitary wave solutions of the fractional modified Kdv—Kadomtsev—Petviashvili equation. Fractals 31(03), 2350025 (2023)
  • 16. Wang, K.: New computational approaches to the fractional coupled nonlinear Helmholtz equation. Eng. Comput. 41(5), 1285–1300 (2024)
  • 17. Kumar, S., Mann, N.: Dynamic study of qualitative analysis, traveling waves, solitons, bifurcation, quasiperiodic, and chaotic behavior...
  • 18. Hussain, A., Ibrahim, T.F., Birkea, F., Al-Sinan, B.R.: Dynamical behavior of analytical soliton solutions to the Kuralay equations via...
  • 19. Hussain, A., Ibrahim, T.F., Bashier, M.M., Osman, W.M., Dawood, A.A.: The profile of soliton molecules for integrable complex coupled...
  • 20. Shingareva, I., Lizárraga-Celaya, C.: Solving nonlinear partial differential equations with maple and mathematica. Springer Science and...
  • 21. Arshed, S., Raza, N., Alansari, M.: Soliton solutions of the generalized Davey-Stewartson equation with full nonlinearities via three...
  • 22. Wang, K.J.: The generalized (3+ 1)-dimensional B-type Kadomtsev-Petviashvili equation: resonant multiple soliton, N-soliton, soliton...
  • 23. Ma, W.X., Osman, M.S., Arshed, S., Raza, N., Srivastava, H.M.: Practical analytical approaches for finding novel optical solitons in the...
  • 24. Khater, A.H., Hassan, M.M., Callebaut, D.K.: Travelling wave solutions to some important equations of mathematical physics. Rep. Math....
  • 25. Abdel-Gawad, H.I., Sulaiman, T.A., Ismael, H.F.: Bright–dark envelope-optical solitons in spacetime reverse generalized Fokas—Lenells...
  • 26. Lundmark, H., Szmigielski, J.: Multi-peakon solutions of the Degasperis—Procesi equation. Inverse Prob. 19(6), 1241 (2003)
  • 27. Raza, N., Arshed, S., Basendwah, G.A., Gómez-Aguilar, J.F.: A class of new breather, lump, twowave and three-wave solutions for an extended...
  • 28. Dawod, L.A., Lakestani, M., Manafian, J.: Breather wave solutions for the (3+ 1)-D generalized shallow water wave equation with variable...
  • 29. Fischer, B., Modersitzki, J.: A unified approach to fast image registration and a new curvature based registration technique. Linear Algebra...
  • 30. Hussain, A., Ali, H., Zaman, F., Abbas, N.: New closed form solutions of some nonlinear pseudoparabolic models via a new extended direct...
  • 31. Ibrahim, S., Ashir, A.M., Sabawi, Y.A., Baleanu, D.: Realization of optical solitons from nonlinear Schrödinger equation using modified...
  • 32. Faridi, W.A., Iqbal, M., Mahmoud, H.A.: An Invariant Optical Soliton Wave Study on Integrable Model: A Riccati-Bernoulli Sub-Optimal Differential...
  • 33. Shahzad, T., Baber, M.Z., Sulaiman, T.A., Ahmad, M.O., Ahmed, N.: Extraction of optical solitons for nonlinear Biswas—Milovic equation...
  • 34. Broadbridge, P., Arrigo, D.J.: All solutions of standard symmetric linear partial differential equations have classical Lie symmetry....
  • 35. Kumar, S., Dhiman, S.K.: Exploring cone-shaped solitons, breather, and lump-forms solutions using the lie symmetry method and unified...
  • 36. Rao, X., Manafian, J., Gavahi, M., Eslami, B., Abdulameer, M.K., Alwaily, E.R., Qizi, Q.: PaulPainlevè analysis, soliton and periodic...
  • 37. Younas, U., Sulaiman, T.A., Ali, Q., Majeed, A.H., Kedzia, K., Jan, A.Z.: Dynamics Of Optical Wave Profiles To The Fractional Three-Component...
  • 38. Jhangeer, A., Zahid, A., Amjad, Z., Raza, N., Muhammad, T.: Lax pairs and Bäcklund transformations for a new (3+ 1)-dimensional integrable...
  • 39. Ali, K.K., Yokus, A., Seadawy, A.R., Yilmazer, R.: The ion sound and Langmuir waves dynamical system via computational modified generalized...
  • 40. Wang, X., Yang, Y., Kou, W., Wang, R., Chen, X.: Analytical solution of Balitsky-Kovchegov equation with homogeneous balance method. Phys....
  • 41. Yin, T., Xing, Z., Pang, J.: Modified Hirota bilinear method to (3+1)-D variable coefficients generalized shallow water wave equation....
  • 42. Rafiq, M.H., Jhangeer, A., Raza, N.: The analysis of solitonic, supernonlinear, periodic, quasiperiodic, bifurcation and chaotic patterns...
  • 43. Wang, K.J., Liu, X.L., Shi, F., Li, G.: Bifurcation and sensitivity analysis, chaotic behaviors, variational principle, Hamiltonian and...
  • 44. Liang, Y.H., Wang, K.J.: Bifurcation analysis, chaotic phenomena, variational principle, hamiltonian, solitary and periodic wave solutions...
  • 45. Ghanbari, B., Inc, M.: A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear...
  • 46. Wazwaz, A.M., Xu, G.Q.: Variety of optical solitons for perturbed Fokas—Lenells equation through modified exponential rational function...
  • 47. Islam, R., Kawser, M.A., Rana, M.S., Islam, M.N.: Mathematical analysis of soliton solutions in space-time fractional Klein-Gordon model...
  • 48. Aksoy, E., Kaplan, M., Bekir, A.: Exponential rational function method for space–time fractional differential equations. Waves in random...
  • 49. Kumar, S., Dhiman, S.K.: Exploring cone-shaped solitons, breather, and lump-forms solutions using the lie symmetry method and unified...
  • 50. Wang, K.J.: The generalized (3+ 1)-dimensional B-type Kadomtsev-Petviashvili equation: resonant multiple soliton, N-soliton, soliton...
  • 51. Raza, N., Salman, F., Butt, A.R., Gandarias, M.L.: Lie symmetry analysis, soliton solutions and qualitative analysis concerning to the...
  • 52. Wazwaz, A.M., Alhejaili, W., El-Tantawy, S.A.: Analytical study on two new (3+1)–dimensional Painlevè integrable equations: Kink,...
  • 53. Dhiman, S.K., Kumar, S.: Analyzing specific waves and various dynamics of multi-peakons in (3+ 1)-dimensional p-type equation using...