{"id":3478,"date":"2026-04-11T16:37:37","date_gmt":"2026-04-11T08:37:37","guid":{"rendered":"https:\/\/iweb20wp-b205b.url.tku.edu.tw\/jase\/?post_type=tkuisotope&p=3478"},"modified":"2026-06-10T14:56:31","modified_gmt":"2026-06-10T06:56:31","slug":"the-new-extended-direct-algebraic-method-for-modified-kdv-zakharov-kuznetsov","status":"publish","type":"tkuisotope","link":"\/jase\/?tkuisotope=the-new-extended-direct-algebraic-method-for-modified-kdv-zakharov-kuznetsov","title":{"rendered":"The new extended direct algebraic method for modified KdV-Zakharov-Kuznetsov"},"content":{"rendered":"\n
\n
\n

<\/i> 2024<\/a><\/p>\n<\/div>\n\n\n\n

\n

<\/i> Volume 27, Issue 10<\/a><\/p>\n<\/div>\n\n\n\n

\n
\n
\n
\n

Bolun Ding1<\/sup><\/i><\/a>, Xiaojun Xie2<\/sup>, and Tingting Ling1<\/sup><\/p>\n\n\n\n

1<\/sup>Department of Basic Sciences,Yangzhou Polytechnic Institute,Yangzhou 225000, Jiangsu, China<\/p>\n\n\n\n

2<\/sup>Department of Fundamental Education,Guangzhou College of Technology and Business, Guangzhou 510000, Guangdong, China<\/p>\n<\/div>\n\n\n\n

\n

Received: June 22, 2023
Accepted: November 12, 2023
Publication Date: April 11, 2026<\/p>\n<\/div>\n<\/div>\n\n\n\n

\"\u4e0a\u50b3\u5716\u7247\"\n\n\n

2D, 3D, and contour plots of |\u03c71<\/sub>| with a = 0.5, b = 1, c = 1.5, \u03ba1<\/sub> = \u22122, \u03ba2<\/sub> = 1, \u03ba3<\/sub> = 1.5, \u03b4 = \u22120.5, \u00b7p = 1.2, q = 1.1 with y = z = 1 and \u0398 = 2.6. (b) 3D<\/p>\n<\/div>\n<\/div>\n\n\n\n

<\/i> Copyright <\/strong>The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0)<\/a>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.<\/p>\n\n\n\n

Download Citation:  BibTeX <\/a>| http:\/\/dx.doi.org\/10.6180\/jase.202410_27(10).0013<\/a>  <\/p>\n\n\n\n

Download PDF<\/a><\/p>\n\n\n\n

<\/div>\n\n\n\n

Finding traveling wave (TW) solutions for nonlinear equations has always been one of the most important concerns of researchers in various mathematics, physics, and engineering fields. In this paper, we employ a new extended direct algebraic (NEDA) technique to study the modified KdV-Zakharov-Kuznetsov (mKdV-ZK) equation. In the framework of this technique, various forms of analysis solutions for the equation are obtained, which have many applications in the field of electric and magnetic fields. The correctness of all the solutions introduced in this paper has been checked after their direct replacement in the equation. Moreover, numerical simulations corresponding to some of these analytical solutions are included in the paper.<\/p>\n\n\n\n

Keywords: Travelling wave solution, The modified KdV-Zakharov-Kuznetsov equation; New extended direct algebraic method; Analytical solutions; Numerical simulations<\/em><\/p>\n\n\n\n

<\/div>\n\n\n\n
\n
    \n
  1. [1] N. Cheemaa, A. R. Seadawy, and S. Chen, (2019) “Some new families of solitary wave solutions of the generalized Schamel equation and their applications in plasma physics” The European Physical Journal Plus 134: 117. DOI: 10.1140\/epjp\/i2019-12467-7. <\/span><\/span><\/li>\n
  2. [2] D. Kumar, A. R. Seadawy, and M. R. Haque, (2018) “Multiple soliton solutions of the nonlinear partial differential equations describing the wave propagation in nonlinear low-pass electrical transmission lines” Chaos, Solitons Fractals 115: 62-76. <\/span>DOI: 10.1016\/j.chaos.2018.08.016. <\/span><\/span><\/li>\n
  3. [3] A. Goswami, J. Singh, D. Kumar, and S. Gupta, (2019) “An efficient analytical technique for fractional partial differential equations occurring in ion acoustic waves in plasma” Journal of Ocean Engineering and Science 4: 85-99. <\/span>DOI: 10.1016\/j.joes.2019.01.003. <\/span><\/span><\/li>\n
  4. [4] A. Ara, N. A. Khan, O. A. Razzaq, T. Hameed, and M. A. Z. Raja, (2018) “Wavelets optimization method for evaluation of fractional partial differential equations: an application to financial modelling” Advances in Difference Equations 2018: 1-13. <\/span>DOI: 10.1186\/s13662-017-1461-2. <\/span><\/span><\/li>\n
  5. [5] J. Berg and K. Nystr\u00f6m, (2018) “A unified deep artificial neural network approach to partial differential equations in complex geometries” Neurocomputing 317: 28-41. <\/span>DOI: 10.1016\/j.neucom.2018.06.056. <\/span><\/span><\/li>\n
  6. [6] H. Dehestani, Y. Ordokhani, and M. Razzaghi, (2018) “Fractional-order Legendre-Laguerre functions and their applications in fractional partial differential equations” Applied Mathematics and Computation 336: 433-453. <\/span>DOI: 10.1016\/j.amc.2018.05.017. <\/span><\/span><\/li>\n
  7. [7] K. M. Owolabi, A. Atangana, and A. Akgul, (2020) “Modelling and analysis of fractal-fractional partial differential equations: application to reaction-diffusion model” Alexandria Engineering Journal 59: 2477-2490. <\/span>DOI: 10.1016\/j.aej.2020.03.022. <\/span><\/span><\/li>\n
  8. [8] Q. Pan, T. Rabczuk, and X. Yang, (2021) “Subdivision-based isogeometric analysis for second order partial differential equations on surfaces” Computational Mechanics 68: 1205-1221. <\/span>DOI: 10.1007\/s00466-021-02065-7. <\/span><\/span><\/li>\n
  9. [9] M. Senol, (2020) “New analytical solutions of fractional symmetric regularized-long-wave equation” Revista mexicana de f\u00edsica 66: 297-307. <\/span>DOI: 10.31349\/revmexfis.66.297. <\/span><\/span><\/li>\n
  10. [10] K. S. Nisar, L. Akinyemi, M. Inc, M. \u015eenol, M. Mirzazadeh, A. Houwe, S. Abbagari, and H. Rezazadeh, (2022) “New perturbed conformable Boussinesq-like equation: Soliton and other solutions” Results in Physics 33: 105200. DOI: 10.1016\/j.rinp.2022.105200. <\/span><\/span><\/li>\n
  11. [11] M. Inc, A. Houwe, and H. Bicer, (2021) “Ellipticity angle effect on exact optical solitons and modulation instability in birefringent fiber” Optical and Quantum Electronics 53: 1-18. <\/span>DOI: 10.1007\/s11082-021-03297-w. <\/span><\/span><\/li>\n
  12. [12] N. M. Rasheed, M. O. Al-Amr, E. A. Az-Zobi, M. A. Tashtoush, and L. Akinyemi, (2021) “Stable optical solitons for the Higher-order Non-Kerr NLSE via the modified simple equation method” Mathematics 9: 1986. DOI: 10.3390\/math9161986. <\/span><\/span><\/li>\n
  13. [13] M. Kaplan, A. Akbulut, and N. Raza, (2022) “Research on sensitivity analysis and traveling wave solutions of the (4+1)-dimensional nonlinear Fokas equation via three different techniques” Physica Scripta 97: 015203. DOI: 10.1088\/1402-4896\/ac42eb. <\/span><\/span><\/li>\n
  14. [14] G. Yel, T. A. Sulaiman, and H. M. Baskonus, (2020) “On the complex solutions to the (3+1)-dimensional conformable fractional modified KdV-Zakharov-Kuznetsov equation” Modern Physics Letters B 34: 2050069. DOI: 10.1142\/S0217984920500694. <\/span><\/span><\/li>\n
  15. [15] B. Ghanbari and M. Inc, (2018) “A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schr\u00f6dinger equation” The European Physical Journal Plus 133: 142. DOI: 10.1140\/epjp\/i2018-11984-1. <\/span><\/span><\/li>\n
  16. [<\/span><\/span>16] B. Ghanbari and D. Baleanu, (2019) “A novel technique to construct exact solutions for nonlinear partial differential equations” The European Physical Journal Plus 134: 506. DOI: 10.1140\/epjp\/i2019-13037-9. <\/span><\/span><\/li>\n
  17. [17] A. Houwe, S. Abbagari, Y. Salathiel, M. Inc, S. Y. Doka, K. T. Crepin, and D. Baleanu, (2020) “Complex traveling-wave and solitons solutions to the Klein-Gordon-Zakharov equations” Results in Physics 17: 103127. DOI: 10.1016\/j.rinp.2020.103127. <\/span><\/span><\/li>\n
  18. [18] M. A. Kayum, S. Ara, M. S. Osman, M. A. Akbar, and K. A. Gepreel, (2021) “Onset of the broad-ranging general stable soliton solutions of nonlinear equations in physics and gas dynamics” Results in Physics 20: 103762. DOI: 10.1016\/j.rinp.2020.103762. <\/span><\/span><\/li>\n
  19. [19] \u0395. \u0397. \u039c. <\/span>Zahran, M. S. M. Shehata, S. M. Mirhosseini-Alizamini, M. N. Alam, and L. Akinyemi, (2021) “Exact propagation of the isolated waves model described by the three coupled nonlinear Maccari’s system with complex structure” International Journal of Modern Physics B 35: 2150193. DOI: 10.1142\/S0217979221501939. <\/span><\/span><\/li>\n
  20. [20] M. Khater, A.-H. <\/span>Abdel-Aty, G. Alnemer, M. Zakarya, and D. Lu, (2020) “New optical explicit plethora of the resonant Schrodinger’s equation via two recent computational schemes” Thermal Science 24: 247-255. <\/span><\/span><\/li>\n
  21. [21] A. Akbulut, M. S. Hashemi, and H. Rezazadeh, (2021) “New conservation laws and exact solutions of coupled Burgers’ equation” Waves in Random and Complex Media: 1-20. <\/span>DOI: 10.1080\/17455030.2021.1979691. <\/span><\/span><\/li>\n
  22. [22] D. Kumar, M. Kaplan, M. R. Haque, M. S. Osman, and D. Baleanu, (2020) “A variety of novel exact solutions for different models with the conformable derivative in shallow water” Frontiers in Physics 8: 177. DOI: 10.3389\/fphy.2020.00177. <\/span><\/span><\/li>\n
  23. [23] H. A. Ghany, A.-A. <\/span>Hyder, and M. Zakarya, (2020) “Exact solutions of stochastic fractional Korteweg de-Vries equation with conformable derivatives” Chinese Physics B 29: 030203. DOI: 10.1088\/1674-1056\/ab75c9. <\/span><\/span><\/li>\n
  24. [24] A. Biswas, M. Mirzazadeh, M. Savescu, D. Milovic, K. R. Khan, M. F. Mahmood, and M. Belic, (2014) “Singular solitons in optical metamaterials by ansatz method and simplest equation approach” Journal of Modern Optics 61: 1550-1555. <\/span>DOI: 10.1080\/09500340.2014.944357. <\/span><\/span><\/li>\n
  25. [25] A. Biswas, H. Rezazadeh, M. Mirzazadeh, M. Eslami, Q. Zhou, S. P. Moshokoa, and M. Belic, (2018) “Optical solitons having weak non-local nonlinearity by two integration schemes” Optik 164: 380-384. <\/span>DOI: 10.1016\/j.ijleo.2018.03.026. <\/span><\/span><\/li>\n
  26. [26] M. Mirzazadeh, M. Ekici, A. Sonmezoglu, S. Ortakaya, M. Eslami, and A. Biswas, (2016) “Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics” The European Physical Journal Plus 131: 1-11. <\/span>DOI: 10.1140\/epjp\/i2016-16166-7. <\/span><\/span><\/li>\n
  27. [27] H. Rezazadeh, H. Tariq, M. Eslami, M. Mirzazadeh, and Q. Zhou, (2018) “New exact solutions of nonlinear conformable time-fractional Phi-4 equation” Chinese Journal of Physics 56: 2805-2816. <\/span>DOI: 10.1016\/j.cjph.2018.08.001. <\/span><\/span><\/li>\n
  28. [28] K. Hosseini, M. Mirzazadeh, D. Baleanu, S. Salahshour, and L. Akinyemi, (2022) “Optical solitons of a high-order nonlinear Schr\u00f6dinger equation involving nonlinear dispersions and Kerr effect” Optical and Quantum Electronics 54: 177. DOI: 10.1007\/s11082-022-03522-0. <\/span><\/span><\/li>\n
  29. [29] L. Akinyemi, M. \u015eenol, and O. S. Iyiola, (2021) “Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method” Mathematics and Computers in Simulation 182: 211-233. <\/span>DOI: 10.1016\/j.matcom.2020.10.017. <\/span><\/span><\/li>\n
  30. [30] M. T. Darvishi, M. Najafi, L. Akinyemi, and H. Rezazadeh, (2023) “Gaussons of some new nonlinear logarithmic equations” Journal of Nonlinear Optical Physics Materials 32: 2350013. DOI: 10.1142\/S0218863523500133. <\/span><\/span><\/li>\n
  31. [31] A. Houwe, S. Abbagari, L. Akinyemi, H. Rezazadeh, and S. Y. Doka, (2023) “Peculiar optical solitons and modulated waves patterns in anti-cubic nonlinear media with cubic-quintic nonlinearity” Optical and Quantum Electronics 55: 719. DOI: 10.1007\/s11082-023-04950-2. <\/span><\/span><\/li>\n
  32. [32] A. R. Adem, B. P. Ntsime, A. Biswas, S. Khan, A. K. Alzahrani, and M. R. Belic, (2021) “Stationary optical solitons with nonlinear chromatic dispersion for Lakshmanan-Porsezian-Daniel model having Kerr law of nonlinear refractive index.” <\/span>Ukrainian Journal of Physical Optics 22: DOI: 10.3116\/16091833\/22\/2\/83\/2021. <\/span><\/span><\/li>\n
  33. [33] E. Zayed, R. Shohib, M. Alngar, A. Biswas, M. Ekici, S. Khan, A. Alzahrani, and M. Belic, (2021) “Optical solitons and conservation laws associated with Kudryashov’s sextic power-law nonlinearity of refractive index” Ukrainian Journal of Physical Optics 22: DOI: 10.3116\/16091833\/22\/1\/38\/2021. <\/span><\/span><\/li>\n
  34. [34] A. Biswas, J. Edoki, P. Guggilla, S. Khan, A. Alzahrani, and M. R. Belic, (2021) “Cubic-quartic optical soliton perturbation with lakshmanan-porsezian-daniel model by semi-inverse variational principle” Ukrainian Journal of Physical Optics 22: 123-127. <\/span>DOI: 10.3116\/16091833\/22\/3\/123\/2021. <\/span><\/span><\/li>\n
  35. [35] Y. Y\u0131ld\u0131r\u0131m, A. Biswas, P. Guggilla, S. Khan, H. M. Alshehri, and M. R. Belic, (2021) “Optical solitons in fibre Bragg gratings with third-and fourth-order dispersive reflectivities” Ukrainian Journal of Physical Optics 22: 239-254. <\/span>DOI: 10.3116\/16091833\/22\/4\/239\/2021. <\/span><\/span><\/li>\n
  36. [36] Y. Yildrim, A. Biswas, A. Dakova, P. Guggilla, S. Khan, H. M. Alshehri, and M. R. Belic, (2021) “Cubic-quartic optical solitons having quadratic-cubic nonlinearity by sine-Gordon equation approach.” <\/span>Ukrainian Journal of Physical Optics 22: DOI: 10.3116\/16091833\/22\/4\/255\/2021. <\/span><\/span><\/li>\n
  37. [37] E. M. E. Zayed, R. Shohib, M. E. M. Alngar, A. Biswas, Y. Y\u0131ld\u0131r\u0131m, A. Dakova, H. M. Alshehri, and M. R. Belic, (2022) “Optical solitons in the Sasa-Satsuma model with multiplicative noise via It\u00f4 calculus.” Ukrainian Journal of Physical Optics 23: 9-14. <\/span>DOI: 10.3116\/16091833\/23\/1\/9\/2022. <\/span><\/span><\/li>\n
  38. [38] Y. Y\u0131ld\u0131r\u0131m, A. Biswas, S. Khan, M. F. Mahmood, and H. M. Alshehri, (2022) “Highly dispersive optical soliton perturbation with Kudryashov’s sextic-power law of nonlinear refractive index.” Ukrainian Journal of Physical Optics 23: 24-29. <\/span>DOI: 10.3116\/16091833\/23\/1\/24\/2022. <\/span><\/span><\/li>\n
  39. [39] O. Gonz\u00e1lez-Gaxiola, A. Biswas, Y. Yildirim, and H. M. Alshehri, (2022) “Highly dispersive optical solitons in birefringent fibres with non) local form of nonlinear refractive index: Laplace-Adomian decomposition.” <\/span>Ukrainian Journal of Physical Optics 23: DOI: 10.3116\/16091833\/23\/2\/68\/2022. <\/span><\/span><\/li>\n
  40. [40] A. Q. AA, B. AM, M. ASHF, A. AA, and B. HO, (2023) “Dark and singular cubic-quartic optical solitons with Lakshmanan-Porsezian-Daniel equation by the improved Adomian decomposition scheme.” <\/span>Ukrainian Journal of Physical Optics 24: DOI: 10.3116\/16091833\/24\/1\/46\/2023. <\/span><\/span><\/li>\n
  41. [41] A. H. Arnous, A. Biswas, Y. Y\u0131ld\u0131r\u0131m, L. Moraru, M. Aphane, S. P. Moshokoa, and H. M. Alshehri, (2023) “Quiescent optical solitons with Kudryashov’s generalized quintuple-power and nonlocal nonlinearity having nonlinear chromatic dispersion: generalized temporal evolution.” Ukrainian Journal of Physical Optics 24: 105-113. <\/span>DOI: 10.3116\/16091833\/24\/2\/105\/2023. <\/span><\/span><\/li>\n
  42. [42] A. Kukkar, S. Kumar, S. Malik, A. Biswas, Y. Y\u0131ld\u0131r\u0131m, S. P. Moshokoa, S. Khan, and A. A. Alghamdi, (2023) “Optical solitons for the concatenation model with Kurdryashov’s approaches.” Ukrainian Journal of Physical Optics 24: 155-160. <\/span>DOI: 10.3116\/16091833\/24\/2\/155\/2023. <\/span><\/span><\/li>\n
  43. [43] A. Biswas, J. M. Vega-Guzm\u00e1n, Y. Yildirim, S. P. Moshokoa, M. Aphane, and A. A. Alghamdi, (2023) “Optical solitons for the concatenation model with power-law nonlinearity: undetermined coefficients.” Ukrainian Journal of Physical Optics 24: 185-192. <\/span>DOI: 10.3116\/16091833\/24\/3\/185\/2023. <\/span><\/span><\/li>\n
  44. [44] O. Gonz\u00e1lez-Gaxiola, A. Biswas, J. R. de Chavez, and A. Asiri, (2023) “Bright and dark optical solitons for the concatenation model by the Laplace-Adomian decomposition scheme.” Ukrainian Journal of Physical Optics 24: 222-234. <\/span>DOI: 10.3116\/16091833\/24\/3\/222\/2023. <\/span><\/span><\/li>\n
  45. [45] R. Kumar, R. Kumar, A. Bansal, A. Biswas, Y. Yildirim, S. Moshokoa, and A. A. Asiri, (2023) “Optical solitons and group invariants for Chen-Lee-Liu equation with time-dependent chromatic dispersion and nonlinearity by Lie symmetry” Ukrainian Journal of Physical Optics 24: 4021-4029. <\/span>DOI: 10.3116\/16091833\/24\/4\/04021\/2023. <\/span><\/span><\/li>\n
  46. [46] Z. Elsayed, R. Shohib, A. Biswas, Y. Yildirim, M. Aphane, S. Moshokoa, S. Khan, and A. Asiri, (2023) “Gap solitons with cubic-quartic dispersive reflectivity and parabolic law of nonlinear refractive index” Ukrainian Journal of Physical Optics 24: 4030-4045. <\/span>DOI: 10.3116\/16091833\/24\/4\/04030\/2023. <\/span><\/span><\/li>\n
  47. [47] F. Demontis, (2011) “Exact solutions of the modified Korteweg-de Vries equation” Theoretical and Mathematical Physics 168: 886-897. <\/span>DOI: 10.1007\/s11232-011-0072-4. <\/span><\/span><\/li>\n
  48. [48] K. P. Das and F. Verheest, (1989) “Ion-acoustic solitons in magnetized multi-component plasmas including negative ions” Journal of plasma physics 41: 139-155. <\/span>DOI: 10.1017\/S0022377800013726. <\/span><\/span><\/li>\n
  49. [49] S. Sahoo, G. Garai, and S. S. Ray, (2017) “Lie symmetry analysis for similarity reduction and exact solutions of modified KdV-Zakharov-Kuznetsov equation” Nonlinear Dynamics 87: 1995-2000. <\/span>DOI: 10.1007\/s11071-016-3169-3. <\/span><\/span><\/li>\n
  50. [50] M. Eslami, H. Rezazadeh, M. Rezazadeh, and S. S. Mosavi, (2017) “Exact solutions to the space-time fractional Schr\u00f6dinger-Hirota equation and the space-time modified KDV-Zakharov-Kuznetsov equation” Optical and Quantum Electronics 49: 1-15. <\/span>DOI: 10.1007\/s11082-017-1112-6. <\/span><\/span><\/li>\n
  51. [51] K. Khan and M. A. Akbar, (2013) “Exact and solitary wave solutions for the Tzitzeica-Dodd-Bullough and the modified KdV-Zakharov-Kuznetsov equations using the modified simple equation method” Ain Shams Engineering Journal 4: 903-909. <\/span>DOI: 10.1016\/j.asej.2013.01.010. <\/span><\/span><\/li>\n
  52. [52] K. S. Al-Ghafri and H. Rezazadeh, (2019) “Solitons and other solutions of (3+1)-dimensional space-time fractional modified KdV-Zakharov-Kuznetsov equation” Applied Mathematics and Nonlinear Sciences 4: 289-304. <\/span>DOI: 10.2478\/AMNS.2019.2.00002. <\/span><\/span><\/li>\n
  53. [53] M. H. Islam, K. Khan, M. A. Akbar, and M. A. Salam, (2014) “Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation” SpringerPlus 3: 1-9. <\/span>DOI: 10.1186\/2193-1801-3-105. <\/span><\/span><\/li>\n
  54. [<\/span>54] D. Lu, A. R. Seadawy, M. Arshad, and J. Wang, (2017) “New solitary wave solutions of (3+1)-dimensional nonlinear extended Zakharov-Kuznetsov and modified KdV-Zakharov-Kuznetsov equations and their applications” Results in physics 7: 899-909. <\/span>DOI: 10.1016\/j.rinp.2017.02.002. <\/span><\/span><\/li>\n
  55. [55] H. Rezazadeh, (2018) “New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity” Optik 167: 218-227. <\/span>DOI: 10.1016\/j.ijleo.2018.04.026.<\/span><\/span><\/li>\n<\/ol>\n<\/div>\n\n\n\n

    <\/p>\n","protected":false},"author":3,"template":"wp-custom-template-detail-4-aricles","meta":{"_uag_custom_page_level_css":""},"categories":[10,6,524],"tags":[674],"acf":[],"uagb_featured_image_src":[],"uagb_author_info":{"display_name":"\u6797\u923a\u6db5","author_link":"\/jase\/?author=3"},"uagb_comment_info":0,"uagb_excerpt":" Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited. Download Citation:  BibTeX | http:\/\/dx.doi.org\/10.6180\/jase.202410_27(10).0013   Download PDF Finding traveling wave (TW) solutions for nonlinear equations has always been…","_links":{"self":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/tkuisotope\/3478"}],"collection":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/tkuisotope"}],"about":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/types\/tkuisotope"}],"author":[{"embeddable":true,"href":"\/jase\/index.php?rest_route=\/wp\/v2\/users\/3"}],"wp:attachment":[{"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3478"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3478"},{"taxonomy":"post_tag","embeddable":true,"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3478"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}