Bäcklund transformations, Lax pair and solutions of a Sharma-Tasso-Olver-Burgers equation for the nonlinear dispersive waves
Abstract
Burgers-type equations are considered as the models of certain phenomena in plasma astrophysics, ocean dynamics, atmospheric science and so on. In this paper, a Sharma-Tasso-Olver-Burgers equation for the nonlinear dispersive waves is studied. Based on the Painlevé-Bäcklund equations, one auto-Bäcklund transformation and two hetero-Bäcklund transformations are derived. Motivated by the Burgers hierarchy, a Lax pair is given. Via two hetero-Bäcklund transformations with different constant seed solutions, we find some multiple-kink solutions, complex periodic solutions, hybrid solutions composed of the lump, periodic and multiple kink waves. Then we discuss the influence of the coefficients of the above equation on such solutions. Via the auto-Bäcklund transformation with the nontrivial seed solutions, we obtain certain lump-type solutions, kink-type solutions and recurrence relation of the above equation.
References
- 1. , Phys. Lett. A 383 (2019) 2176. Crossref, ISI, ADS, Google Scholar
- 2. , Commun. Theor. Phys. 72 (2020) 095002. Crossref, ISI, Google Scholar
- 3. , Chin. J. Phys. 63 (2020) 122. Crossref, ISI, Google Scholar
- 4. , Chaos Solitons Fract. 147 (2021) 110875. Crossref, ISI, Google Scholar
- 5. , Appl. Math. Lett. 104 (2020) 106271. Crossref, ISI, Google Scholar
- 6. , Appl. Math. Lett. 112 (2021) 106722. Crossref, ISI, Google Scholar
- 7. , Adv. Appl. Mech. 1 (1948) 171. Crossref, Google Scholar
- 8. , J. Appl. Math. Comput. 65 (2021) 541. Crossref, ISI, Google Scholar
- 9. , Nonlinear Dyn. 87 (2017) 2457. Crossref, ISI, Google Scholar
- 10. , Quart. Appl. Math. 8 (1951) 225. Crossref, ISI, Google Scholar
- 11. , Phys. Rep. 447 (2007) 1. Crossref, ISI, ADS, Google Scholar
- 12. , Commun. Nonlinear Sci. Numer. Simul. 19 (2014) 2131. Crossref, ISI, ADS, Google Scholar
- 13. , J. Math. Phys. 18 (1977) 1212. Crossref, ISI, ADS, Google Scholar
- 14. , Phys. Rev. Lett. 27 (1971) 1192. Crossref, ISI, ADS, Google Scholar
- 15. , Phys. Lett. A 384 (2020) 126310. Crossref, ISI, Google Scholar
- 16. , Appl. Math. Comput. 217 (2011) 7172. Crossref, ISI, Google Scholar
- 17. , Phys. Plasmas 13 (2006) 102305. Crossref, ISI, ADS, Google Scholar
- 18. , J. Franklin Inst. 348 (2011) 1751. Crossref, ISI, Google Scholar
- 19. , J. Math. Anal. Appl. 288 (2003) 326. Crossref, ISI, Google Scholar
- 20. , Chaos Solitons Fract. 144 (2021) 110559. Crossref, ISI, Google Scholar
- 21. , Eur. Phys. J. Plus 136 (2021) 656. Crossref, ISI, Google Scholar
- 22. , Nonlinear Dyn. 100 (2020) 2729. Crossref, ISI, Google Scholar
- 23. , Appl. Math. Lett. 114 (2021) 106702. Crossref, ISI, Google Scholar
- 24. , Nonlinear Dyn. 98 (2019) 269. Crossref, ISI, Google Scholar
- 25. , Mod. Phys. Lett. B 35 (2021) 2150261. Link, ISI, ADS, Google Scholar
- 26. , Eur. Phys. J. Plus 136 (2021) 572. Crossref, ISI, Google Scholar
- 27. , Phys. Lett. A 405 (2021) 127429. Crossref, ISI, Google Scholar
- 28. , Chaos Solitons Fract. 152 (2021) 111355. Crossref, ISI, Google Scholar
- 29. , Commun. Theor. Phys. 72 (2020) 115004. Crossref, ISI, ADS, Google Scholar
- 30. , Mod. Phys. Lett. B 34 (2020) 2050336. Link, ISI, ADS, Google Scholar
- 31. , Nonlinear Dyn. 104 (2021) 1519. Crossref, ISI, Google Scholar
- 32. , Chaos Solitons Fract. 150 (2021) 110487. Crossref, ISI, Google Scholar
- 33. , Mod. Phys. Lett. B 33 (2019) 1950376. Link, ISI, ADS, Google Scholar
- 34. , Mod. Phys. Lett. B 34 (2020) 2150013. Link, ISI, ADS, Google Scholar
- 35. , Optik 247 (2021) 166815. Crossref, ISI, ADS, Google Scholar
- 36. , Wave Random Complex 28 (2018) 343. Crossref, ISI, ADS, Google Scholar
- 37. , Comput. Math. Appl. 74 (2017) 1399. Crossref, ISI, Google Scholar
- 38. , Chaos Solitons Fract. 133 (2020) 109580. Crossref, ISI, Google Scholar
- 39. , Nonlinear Dyn. 97 (2019) 2023. Crossref, ISI, Google Scholar
- 40. , Chaos Solitons Fract. 140 (2020) 110085. Crossref, ISI, Google Scholar
- 41. , Nonlinear Dyn. 99 (2020) 1039. Crossref, ISI, Google Scholar
- 42. , Phys. Rev. E 100 (2019) 042210. Crossref, ISI, ADS, Google Scholar
- 43. , Appl. Math. Lett. 88 (2019) 201. Crossref, ISI, Google Scholar
- 44. , Eur. Phys. J. Plus 135 (2020) 272. Crossref, ISI, Google Scholar
- 45. , Mod. Phys. Lett. B 33(29) (2019) 1950354. Link, ISI, ADS, Google Scholar
- 46. , Comput. Math. Appl. 79 (2020) 576. Crossref, ISI, Google Scholar
- 47. , Appl. Math. Lett. 119 (2021) 106936. Crossref, ISI, Google Scholar
- 48. , Mod. Phys. Lett. B 35 (2021) 2150020. Link, ISI, ADS, Google Scholar
- 49. , Int. J. Comput. Math. 97 (2020) 2474. Crossref, ISI, Google Scholar
- 50. , Eur. Phys. J. Plus 136 (2021) 635. Crossref, ISI, Google Scholar
- 51. , Eur. Phys. J. Plus 136 (2021) 1002. Crossref, ISI, Google Scholar
- 52. , J. Franklin Inst. 347 (2010) 618. Crossref, ISI, Google Scholar
- 53. , Phys. Lett. A 379 (2015) 2903. Crossref, ISI, ADS, Google Scholar
- 54. , Phys. Lett. A 384 (2020) 126788. Crossref, ISI, Google Scholar
- 55. , Qual. Theory Dyn. Syst. 20 (2021) 87. Crossref, ISI, Google Scholar
- 56. , Appl. Math. Lett. 120 (2021) 107161. Crossref, ISI, Google Scholar
- 57. X. Y. Gao, Y. J. Guo and W. R. Shan, Wave. Random Complex (2021) in press. https://doi.org/10.1080/17455030.2021.1942308 Google Scholar
- 58. , Rom. Rep. Phys. 73 (2021) 111. Google Scholar
- 59. , Regul. Chaotic Dyn. 20 (2015) 74. Crossref, ISI, ADS, Google Scholar
- 60. , Chaos Solitons Fract. 151 (2021) 111222. Crossref, ISI, Google Scholar
- 61. , Appl. Math. Lett. 122 (2021) 107301. Crossref, ISI, Google Scholar
- 62. , Z. Angew. Math. Phys. 72 (2021) 75. Crossref, ISI, Google Scholar
- 63. , Pramana-J. Phys. 95 (2021) 137. Crossref, ISI, ADS, Google Scholar
- 64. , Chin. J. Phys. 73 (2021) 600. Crossref, ISI, Google Scholar
- 65. , Int. J. Mod. Phys. B 35 (2021) 2150108. Link, ISI, ADS, Google Scholar
- 66. , Mod. Phys. Lett. B 35 (2021) 2150315. Link, ISI, ADS, Google Scholar
- 67. , J. Phys. A 29 (1996) 7779. Crossref, ADS, Google Scholar
- 68. , J. Math. Phys. 31 (1990) 1374. Crossref, ISI, ADS, Google Scholar
- 69. , Phys. Lett. A 374 (2010) 2340. Crossref, ISI, ADS, Google Scholar
- 70. , Commun. Theor. Phys. 58 (2012) 317. Crossref, ISI, ADS, Google Scholar
- 71. , J. Phys. A: Math. Gen. 36 (2003) 11981. Crossref, ADS, Google Scholar
- 72. H. Y. Tian, B. Tian, C. R. Zhang and S. S. Chen, Int. J. Comput. Math. (2021) in press. https://doi.org/10.1080/00207160.2021.1900568 Google Scholar
- 73. H. Y. Tian, B. Tian, Y. Sun and C. R. Zhang, Commun. Nonlinear Sci. Numer. Simul. (2021) in press. https://doi.org/10.1016/j.cnsns.2021.106097 Google Scholar
- 74. L. Q. Li, Y. T. Gao, X. Yu, T. T. Jia, L. Hu and C. Y. Zhang, Chin. J. Phys. (2021) in press. https://doi.org/10.1016/j.cjph.2021.09.004 Google Scholar
- 75. , Chaos Solitons Fract. 152 (2021) 111411. Crossref, ISI, Google Scholar
- 76. M. Wang and B. Tian, Wave. Random Complex (2021) in press. https://doi.org/10.1080/17455030.2021.1986649 Google Scholar
- 77. , Chaos Solitons Fract. 142 (2021) 110363. Crossref, ISI, Google Scholar
Remember to check out the Most Cited Articles! |
---|
Boost your collection with these New Books in Condensed Matter Physics today! |