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Darboux Transformation and General Soliton Molecule Pairs for a Generalized Reverse Space Nonlinear Schrödinger Equation

  • Tao Xu [1] ; Zhijun Qiao [2]
    1. [1] Zhengzhou University of Light Industry

      Zhengzhou University of Light Industry

      China

    2. [2] University of Texas Rio Grande Valley

      University of Texas Rio Grande Valley

      Estados Unidos

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 4, 2026
  • Idioma: inglés
  • Enlaces
  • Resumen

    • The generalized reverse space nonlinear Schrödinger (NLS) equation, which can be derived from the parity-symmetric reduction of the Manakov system, is studied by the Darboux transformation (DT) method. To ensure the target equation’s integrability, we present both Lax pair and infinitely-many conservation laws. Starting from the two-fold DT, we reduce it to fulfill two symmetry conditions for the Lax pair, ultimately yield the N-step DT for the equation in a compact determinant form. As an application, the general L-soliton molecule pair-(N−L)-soliton solutions (2≤L≤N), which include the soliton molecule pairs formed by arbitrary L soliton pairs and the common (N−L) soliton pairs, are successfully obtained through our resulted DT.

      Furthermore, the general soliton molecule pairs can be reduced to N-soliton pairs, pure soliton molecule pairs, and their interactions. Particularly, the one-soliton pair solution is verified to admit the interactions between two head-on solitons. Finally, the generation mechanism and dynamics of the soliton molecule pairs are all discussed in detail.

  • Referencias bibliográficas
    • 1. Bender, C.M.: Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys. 70, 947 (2007)
    • 2. Markum, H., Pullirsch, R., Wettig, T.: Non-Hermitian random matrix theory and lattice QCD with chemical potential. Phys. Rev. Lett. 83,...
    • 3. Dalfovo, F.,Giorgini, S., Pitaevskii, L.P., Stringari, S.: Theory of Bose-Einstein condensation in trapped gases. Rev. Mod. Phys. 71, 463...
    • 4. Ruter, C.E., Makris, K.G., EI-Ganainy, R., Christodoulides, D.N., Segev, M., Kip, D.: Observation of parity-time symmetry in optics. Nat....
    • 5. Lin, Z., Schindler, J., Ellis, F.M., Kottos, T.: Experimental observation of the dual behavior of PTsymmetric scattering. Phys. Rev. A...
    • 6. Ablowitz, A.J., Musslimani, Z.H.: Integrable nonlocal nonlinear Schrödinger equation. Phys. Rev. Lett. 110, 064105 (2013)
    • 7. Ablowitz, A.J., Musslimani, Z.H.: Integrable nonlocal nonlinear equations. Stud. Appl. Math. 139, 7 (2017)
    • 8. Lou, S.Y., Huang, F.: Alice-Bob physics: coherent solutions of nonlocal KdV systems. Sci. Rep. 7, 869 (2017)
    • 9. Lou, S.Y.: Multi-place physics and multi-place nonlocal systems. Commun. Theor. Phys. 72, 057001 (2020)
    • 10. Yan, Z.Y.: Integrable PT-symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model. Appl. Math....
    • 11. Yang, B., Yang, J.K.: Transformations between nonlocal and local integrable equations. Stud. Appl. Math. 140, 178–201 (2017)
    • 12. Lou, S.Y.: Alice-Bob systems, ˆP - ˆ T - ˆC symmetry invariant and symmetry breaking soliton solutions. J. Math. Phys. 59, 083507 (2018)
    • 13. Peng, W.Q., Chen, Y.: PT-symmetric PINN for integrable nonlocal equations: forward and inverse problems. Chaos 34, 043124 (2024)
    • 14. Zhou, Z.X.: Darboux transformations and global explicit solutions for nonlocal Davey-Stewartson I equation. Stud. Appl. Math. 141, 186...
    • 15. Yang, B., Yang, J.K.: Transformations between nonlocal and local integrable equations. Stud. Appl. Math. 140, 178–201 (2017)
    • 16. Wang, X., He, J.S.: Darboux transformation and general soliton solutions for the reverse space-time nonlocal short pulse equation. Physica...
    • 17. Yang, B.,Chen,Y.:Dynamics of roguewaves in the partially PT-symmetric nonlocal Davey-Stewartson systems. Commun. Nonl. Sci. Numer. Simu....
    • 18. Xu, T., An, L.C., Li, M., Xu, C.X.: N-fold Darboux transformation of the discrete PT-symmetric nonlinear Schrödinger equation and new...
    • 19. Song, C.Q., Zhao, H.Q., Zhu, Z.N.: Nonlocal Yajima-Oikawa system: binary Darboux transformation, exact solutions and dynamic properties....
    • 20. An, L., Li, C.Z., Zhang, L.X.: Darboux transformations and solutions of nonlocal Hirota andMaxwell- Bloch equations. Stud. Appl. Math....
    • 21. Wang, X., Wang, L., Du, Z., He, J.M., Zhao, J.: General soliton solutions for the complex reverse space-time nonlocal mKdV equation on...
    • 22. Sun, H.Q., Shen, S.F., Zhu, Z.N.: A nonlocal coupled modified complex integrable dispersionless equation: Darboux transformation, soliton-type...
    • 23. Liu, X.Y., Guo, R.: The Riemann-Hilbert approach for the nonlocal derivative nonlinear Schrödinger equation with nonzero boundary conditions....
    • 24. Shan, J.Q., Li, M.H.: The dynamic of the positons for the reverse space Ctime nonlocal short pulse equation. Physica D 470, 134419 (2024)
    • 25. Rohrmann, P., Hause, A., Mitschke, F.: Solitons beyond binary: possibility of fibre-optic transmission of two bits per clock period. Sci....
    • 26. Lakomy, K., Nath, R., Santos, L.: Soliton molecules in dipolar Bose-Einstein condensates. Phys. Rev. A 86, 013610 (2012)
    • 27. Herink, G., Kurtz, F., Jalali, B., Solli, D.R., Ropers, C.: Real time spectral interferometry probes the internal dynamics of femtosecond...
    • 28. Krupa, K., Nithyanandan, K., Andral, U., Tchofo-Dinda, P., Grelu, P.: Real-time observation of internal motion within ultrafast dissipa-tive...
    • 29. Liu, X.M., Yao, X.K., Cui, Y.D.: Real-time observation of the buildup of soliton molecules. Phys. Rev. Lett. 121, 023905 (2018)
    • 30. Łakomy, K., Nath, R., Santos, L.: Soliton molecules in dipolar Bose-Einstein condensates. Phys. Rev. A 86, 013610 (2012)
    • 31. Lou, S.Y.: Solitonmolecules and asymmetric solitons in three fifth order systems via velocity resonance. J. Phys. Commun. 4, 041002 (2020)
    • 32. Yan, Z.W., Lou, S.Y.: Soliton molecules in Sharma-Tasso-Olver-Burgers equation. Appl. Math. Lett. 104, 106271 (2020)
    • 33. Xu, D.H., Lou, S.Y.: Dark soliton molecules in nonlinear optics. Acta. Phys. Sin-CH ED 69, 014208 (2020)
    • 34. Wang, X., Li, J.N., Wang, L., Kang, J.F.: Dark-dark solitons, soliton molecules and elastic collisions in the mixed three-level coupled...
    • 35. Yang, X.Y., Fan, R., Li, B.: Soliton molecules and some novel interaction solutions to the (2+1)- dimensional B-type Kadomtsev-Petviashvili...
    • 36. Xu, T.,Wang, Y., Shan, Y.N.: The generalized N-coupled nonautonomous Gross-Pitaevskii equations: Darboux transformation and three new...
    • 37. Xu, T., Qiao, Z.J.: The massive Thirring model in Bragg grating: Soliton molecules, breather-positon and semirational solutions. Wave...
    • 38. Stalina, S., Lakshmanan, M.: Vector soliton molecules and their collisions. Phys. Rev. E 111, 044205 (2025)
    • 39. Yang, J.K.: Physically significant nonlocal nonlinear Schrödinger equation and its soliton solutions. Phys. Rev. E 98, 042202 (2018)
    • 40. Manakov, S.V.: On the theory of two-dimensional stationary self-focusing of electromagnetic waves. Zh. Eksp. Teor. Fiz. 65, 505 (1973)
    • 41. Tang, D.Y., Zhang, H., Zhao, L.M., Wu, X.: Observation of high-order polarization-locked vector solitons in a fiber laser. Phys. Rev....
    • 42. Hamner,C., Chang, J.J., Engels, P., Hoefer,M.A.: Generation of dark-bright soliton trains in superfluidsuperfluid counterflow. Phys. Rev....
    • 43. Yan, Z.Y.: Vector financial rogue waves. Phys. Lett. A 375, 4274 (2011)
    • 44. Wu, J.P.: A novel Riemann-Hilbert approach via t-part spectral analysis for a physically significant nonlocal integrable nonlinear Schrödinger...
    • 45. Chen, J.C.,Yan, Q.X., Zhang, H.: Multiple bright soliton solutions of a reverse-space nonlocal nonlinear Schrödinger equation. Appl. Math....
    • 46. Zhao, N., Cheng, L., Chen, J.C., Zhu, S.D.: Bright soliton solutions to the nonlocal Manakov equations of reverse-space type. Appl. Math....
    • 47. Wang, X., He, J.S.: Rogue waves in a reverse space nonlocal nonlinear Schrödinger equation. Physica D 469, 134313 (2024)
    • 48. Xu,C.X., Xu, T., Li,M.: Inverse scattering transform for the defocusing nonlinear Schrödinger equation with local and nonlocal nonlinearities...
    • 49. Miura, R.M., Gardner, C.S., Kruskal, M.D.: KdV equation and generalizations. II. existence of conservation laws and constantsof motion....
    • 50. Terng, C.-L., Uhlenbeck, K.: Bäcklund transformations and loop group actions, Commun. Pur. Appl. Math. 53, 1–75 (2000)
    • 51. Gu, C.H., Hu, H.S., Zhou, Z.X.: Darboux transformations in integrable systems: theory and their applications to geometry. Springer, New...
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