A generalized integrable hierarchy related to the relativistic Toda lattice: Hamiltonian structure, Darboux transformation, soliton solution and conservation law
Abstract
Starting from a more generalized discrete matrix spectral problem and using the Tu scheme, some integrable lattice hierarchies (ILHs) are presented which include the well-known relativistic Toda lattice hierarchy and some new three-field ILHs. Taking one of the hierarchies as example, the corresponding Hamiltonian structure is constructed and the Liouville integrability is illustrated. For the first nontrivial lattice equation in the hierarchy, the -fold Darboux transformation (DT) of the system is established basing on its Lax pair. By using the obtained DT, we generate the discrete -soliton solutions in determinant form and plot their figures with proper parameters, from which we get some interesting soliton structures such as kink and anti-bell-shaped two-soliton, kink and anti-kink-shaped two-soliton and so on. These soliton solutions are much stable during the propagation, the solitary waves pass through without change of shapes, amplitudes, wave-lengths and directions. Finally, we derive infinitely many conservation laws of the system and give the corresponding conserved density and associated flux formulaically.
References
- 1. , Prog. Theor. Phys. Suppl. 45 (1970) 174. Crossref, ADS, Google Scholar
- 2. , Prog. Theor. Phys. Suppl. 59 (1976) 36. Crossref, ADS, Google Scholar
- 3. , J. Math. Phys. 16 (1975) 598. Crossref, Web of Science, ADS, Google Scholar
- 4. , Math. Comput. Simul. 69 (2005) 322. Crossref, Web of Science, Google Scholar
- 5. , Stud. Appl. Math. 55 (1976) 213. Crossref, Web of Science, Google Scholar
- 6. , Phys. Lett. A 130 (1988) 456. Crossref, Web of Science, ADS, Google Scholar
- 7. , J. Math. Phys. 35 (1994) 4661. Crossref, Web of Science, ADS, Google Scholar
- 8. , J. Phys. A 23 (1990) 3903. Crossref, Google Scholar
- 9. , Inverse Probl. 10 (1994) 1315. Crossref, Web of Science, ADS, Google Scholar
- 10. , J. Phys. A 31 (1998) L677. Crossref, ADS, Google Scholar
- 11. , Phys. Lett. A 349 (2002) 439. Crossref, Web of Science, ADS, Google Scholar
- 12. , J. Geom. Phys. 106 (2016) 26. Crossref, Web of Science, ADS, Google Scholar
- 13. , Mod. Phys. Lett. B 32 (2018) 1850409. Link, Web of Science, Google Scholar
- 14. , Appl. Math. Model. 67 (2019) 201. Crossref, Web of Science, Google Scholar
- 15. , Rep. Math. Phys. 84 (2019) 289. Crossref, Web of Science, ADS, Google Scholar
- 16. , Mod. Phys. Lett. B 32 (2018) 1850085. Link, Web of Science, ADS, Google Scholar
- 17. , Darboux Transformations and Solitons (Springer, Berlin, 1991). Crossref, Google Scholar
- 18. , Darboux Transformations in Integrable Systems: Theory and their Applications to Geometry (Springer, Berlin, 2005). Crossref, Google Scholar
- 19. , Chaos 26 (2016) 123110. Crossref, Web of Science, ADS, Google Scholar
- 20. , Appl. Math. Lett. 63 (2017) 88. Crossref, Web of Science, Google Scholar
- 21. , J. Nonlinear Sci. 30 (2020) 991. Crossref, Web of Science, ADS, Google Scholar
- 22. , Phys. Lett. A 293 (2002) 161. Crossref, Web of Science, ADS, Google Scholar
- 23. , J. Opt. B: Quantum Semiclass. Opt. 7 (2005) R53. Crossref, ADS, Google Scholar
- 24. , Proc. Rom. Acad. A 16 (2015) 62. Web of Science, Google Scholar
- 25. , Optical Solitons: From Fibers to Photonic Crystals (Academic Press, New York, 2003). Google Scholar
- 26. , Nonlinear Fiber Optics (Academic Press, New York, 2013). Google Scholar
- 27. , IEEE Antennas Wirel. Propag. Lett. 8 (2009) 798. Crossref, Web of Science, ADS, Google Scholar
- 28. , J. Phys. A: Math. Theor. 48 (2015) 485101. Crossref, Web of Science, Google Scholar
- 29. , Int. J. Syst. Sci. 47 (2016) 2745. Crossref, Web of Science, Google Scholar
- 30. , Sci. China Technol. Sci. 64 (2021) 1212. Crossref, Web of Science, ADS, Google Scholar
- 31. , Commun. Theor. Phys. 73 (2021) 065003. Crossref, Web of Science, Google Scholar
- 32. , Phys. Lett. A 236 (1997) 30. Crossref, Web of Science, ADS, Google Scholar
- 33. , Physica D 123 (1998) 425. Crossref, Web of Science, ADS, Google Scholar
- 34. , Phys. Lett. A 297 (2002) 387. Crossref, Web of Science, ADS, Google Scholar
- 35. , Chaos Solitons Fractals 14 (2002) 573. Crossref, Web of Science, ADS, Google Scholar
- 36. , Comput. Math. Appl. 78 (2019) 3422. Crossref, Web of Science, Google Scholar
- 37. , J. Math. Phys. 49 (2008) 063505. Crossref, Web of Science, Google Scholar
- 38. , J. Geom. Phys. 59 (2009) 1227. Crossref, Web of Science, ADS, Google Scholar
- 39. , Commun. Nonlinear Sci. Numer. Simul. 91 (2020) 105453. Crossref, Web of Science, Google Scholar
- 40. , J. Phys. A: Math. Theor. 54 (2021) 235204. Crossref, Web of Science, ADS, Google Scholar
- 41. , Stud. Appl. Math. 118 (2007) 281. Crossref, Web of Science, Google Scholar
- 42. , J. Phys. A Math. Gen. 37 (2004) 1323. Crossref, ADS, Google Scholar
- 43. , Rep. Math. Phys. 86 (2020) 325. Crossref, Web of Science, ADS, Google Scholar
- 44. , Commun. Theor. Phys. 41 (2004) 321. Crossref, Web of Science, ADS, Google Scholar
- 45. , J. Nonlinear Anal. 64 (2006) 2604. Crossref, Web of Science, Google Scholar
- 46. , Phys. Lett. A 372 (2008) 4578. Crossref, Web of Science, ADS, Google Scholar
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