The Commutative Property of Reciprocal Transformations and Dimensional Deformations

• Wen-Xiu Ma ^[1]
  1. [1] University of South Florida

     University of South Florida

     Estados Unidos

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • The paper aims to analyze the commutative property of reciprocal transformations and dimensional deformations using conservation laws. First, a geometric proof of the commutative property of reciprocal transformations is presented, based on the coordinate-free property of the exponential map. Second, it is shown that the deformation algorithm does not always keep the commutative property. Illuminating examples are provided.

• Referencias bibliográficas
  • 1. Ablowitz, M.J., Kaup, D.J., Newell, A.C., Segur, H.: The inverse scattering transform-Fourier analysis for nonlinear problems. Stud. Appl....
  • 2. Ma,W.X.: The algebraic structures of isospectral Lax operators and applications to integrable equations. J. Phys. A Math. Gen. 25, 5329–5343...
  • 3. Ma, W.X., Strampp, W.: An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems. Phys. Lett. A 185,...
  • 4. Manukure, S.: Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy...
  • 5. Novikov, S.P., Manakov, S.V., Pitaevskii, L.P., Zakharov, V.E.: Theory of Solitons: The Inverse Scattering Method. Consultants Bureau,...
  • 6. Kingston, J.G., Rogers, C.: Reciprocal Bäcklund transformations of conservation laws. Phys. Lett. A 92, 261–264 (1982)
  • 7. Błaszak, M., Sergyeyev, A.: A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable...
  • 8. Konopelchenko, B.G., Rogers,C.: Bäcklund and reciprocal transformations: gauge connections. In: Ames, W.F., Rogers, C. (eds.) Nonlinear...
  • 9. Lou, S.Y., Hao, Z.Z., Jia, M.: Deformation conjecture: deforming lower dimensional integrable systems to higher dimensional ones by using...
  • 10. Olver, P.J.: Applications of Lie Groups to Differential Equations. Springer-Verlag, New York (1986)
  • 11. Ma, W.X.: Reduced non-local integrable NLS hierarchies by pairs of local and non-local constraints. Int. J. Appl. Comput. Math. 8, 206...
  • 12. Ma, W.X.: Integrable non-local nonlinear Schrödinger hierarchies of type (-λ∗, λ) and soliton solutions. Rep. Math. Phys. 92, 19–36 (2023)
  • 13. Ma, W.X.: Soliton hierarchies and soliton solutions of type (-λ∗,-λ) reduced nonlocal integrable nonlinear Schröodinger equations of arbitrary...
  • 14. Ma, W.X.: Soliton solutions to reduced nonlocal integrable nonlinear Schrödinger hierarchies of type (-λ,λ). Int. J. Geom. Methods Mod....
  • 15. Ma, W.X., Zhou, Y.: Lump solutions to nonlinear partial differential equations via Hirota bilinear forms. J. Differ. Equ. 264, 2633–2659...
  • 16. Sulaiman, T.A., Yusuf, A., Abdeljabbar, A., Alquran, M.: Dynamics of lump collision phenomena to the (3+1)-dimensional nonlinear evolution...
  • 17. Manukure, S., Chowdhury, A., Zhou, Y.: Complexiton solutions to the asymmetric Nizhnik–Novikov– Veselov equation. Int. J. Mod. Phys. B...
  • 18. Zhou, Y., Manukure, S., McAnally, M.: Lump and rogue wave solutions to a (2+1)-dimensional Boussinesq type equation. J. Geom. Phys....
  • 19. Manukure, S., Zhou, Y.: A study of lump and line rogue wave solutions to a (2+1)-dimensional nonlinear equation. J. Geom. Phys. 167,...