Geodesic
Superfield Bäcklund and Darboux transformations of an $\mathcal N=1$ supersymmetric coupled dispersionless integrable system
Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 1, pp. 114-123
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We use a superfield Darboux matrix to study Darboux transformations of an $\mathcal N=1$ supersymmetric coupled dispersionless integrable system. The notion of quasideterminants is used to obtain superfield $N$-soliton solutions of that system. A superfield Lax representation is used to obtain a superfield Bäcklund transformation via a set of superfield Riccati equations. The Bäcklund and Darboux transformations are further used to compute explicit expressions for superfield soliton solutions of the supersymmetric coupled dispersionless integrable system.
Keywords: integrable system, supersymmetry, Bäcklund transformation, supersymmetric coupled dispersionless system.
Mots-clés : Darboux transformation 
@article{TMF_2024_219_1_a7,
     author = {A. Mirza and M. ul Hassan},
     title = {Superfield {B\"acklund} and {Darboux} transformations of an~$\mathcal N=1$ supersymmetric coupled dispersionless integrable system},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {114--123},
     year = {2024},
     volume = {219},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a7/}
}
TY  - JOUR
AU  - A. Mirza
AU  - M. ul Hassan
TI  - Superfield Bäcklund and Darboux transformations of an $\mathcal N=1$ supersymmetric coupled dispersionless integrable system
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2024
SP  - 114
EP  - 123
VL  - 219
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a7/
LA  - ru
ID  - TMF_2024_219_1_a7
ER  - 
%0 Journal Article
%A A. Mirza
%A M. ul Hassan
%T Superfield Bäcklund and Darboux transformations of an $\mathcal N=1$ supersymmetric coupled dispersionless integrable system
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2024
%P 114-123
%V 219
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a7/
%G ru
%F TMF_2024_219_1_a7
A. Mirza; M. ul Hassan. Superfield Bäcklund and Darboux transformations of an $\mathcal N=1$ supersymmetric coupled dispersionless integrable system. Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 1, pp. 114-123. http://geodesic.mathdoc.fr/item/TMF_2024_219_1_a7/

[1] J. Wess, B. Zumino, “Supergauge transformations in four dimensions”, Nucl. Phys. B, 70:1 (1974), 39–50 | DOI | MR

[2] A. Salam, J. Strathdee, “Super-gauge transformations”, Nucl. Phys. B, 76:3 (1974), 477–482 | DOI | MR

[3] H. Aratyn, T. D. Imbo, W.-Y. Keung, U. Sukhatme (eds.), Supersymmetry and Integrable Models (Chicago, IL, USA, 12–14 June, 1997), Lecture Notes in Physics, 502, Springer, Berlin, 1998 | DOI

[4] Q. P. Liu, M. Mañas, “Pfaffian solutions for the Manin–Radul–Mathieu SUSY KdV and SUSY sine-Gordon equations”, Phys. Lett. B, 436:3–4 (1998), 306–310 | DOI | MR

[5] Q. P. Liu, “Darboux transformations for supersymmetric Korteweg–de Vries equations”, Lett. Math. Phys., 35:2 (1995), 115–122 | DOI | MR

[6] Q. P. Liu, M. Mañas, “Darboux transformation for the Manin–Radul supersymmetric KdV equation”, Phys. Lett. B, 394:3–4 (1997), 337–342 | DOI | MR

[7] A. Mirza, B. Haider, “The rational solution of supersymmetric KdV equation”, AIP Conf. Proc., 1862:1 (2017), 030008, 8 pp. | DOI

[8] A. Mirza, M. ul Hassan, “Bilinearization and soliton solutions of the $N=1$ supersymmetric coupled dispersionless integrable system”, J. Nonlinear Math. Phys., 24:1 (2017), 107–115 | DOI | MR

[9] A. Mirza, M. Khassan, “O svoistvakh integriruemosti supersimmetrichnoi bezdispersionnoi integriruemoi sistemy so vzaimodeistviem”, TMF, 195:3 (2018), 381–390 | DOI | DOI | MR

[10] A. Mirza, M. Khassan, “Bilinearizatsiya i solitonnye resheniya supersimmetrichnoi mnogokomponentnoi bezdispersionnoi integriruemoi sistemy svyazannykh uravnenii”, TMF, 201:3 (2019), 361–370 | DOI | DOI | MR

[11] A. Mirza, M. Khassan, “Bilinearizatsiya i solitonnye resheniya supersimmetrichnogo svyazannogo uravneniya Kortevega–de Friza”, TMF, 202:1 (2020), 14–19 ; “Суперсимметричная иерархия Пенлеве II и билинеаризация”, 216:1 (2023), 36–42 | DOI | DOI | MR | DOI | DOI | MR

[12] K. Konno, H. Oono, “New coupled integrable dispersionless equations”, J. Phys. Soc. Japan, 63:2 (1994), 377–378 | DOI | MR

[13] R. Hirota, S. Tsujimoto, “Note on ‘New coupled integrable dispersionless equations’ ”, J. Phys. Soc. Japan, 63:9 (1994), 3533 | DOI

[14] H. Kakuhata, K. Konno, “A generalization of coupled integrable, dispersionless system”, J. Phys. Soc. Japan, 65:2 (1996), 340–341 ; “Lagrangian, Hamiltonian and conserved quantities for coupled integrable dispersionless equations”, 65:1 (1995), 1–2 ; “Canonical formulation of generalized coupled dispersionless system”, J. Phys. A: Math. Gen., 30:12 (1997), L401–L407 | DOI | MR | DOI | MR | DOI | MR

[15] T. Alagesan, Y. Chung, K. Nakkeeran, “Bäcklund transformation and soliton solutions for the coupled dispersionless equations”, Chaos Solitons Fractals, 21:1 (2004), 63–67 | DOI | MR | Zbl

[16] C. Gu, H. Hu, Z. Zhou, Darboux Transformations in Integrable Systems. Theory and their Applications to Geometry, Mathematical Physics Studies, 26, Springer, Dordrecht, 2005 | DOI | MR

[17] M. Siddiq, M. Hassan, U. Saleem, “On Darboux transformation of the supersymmetric sine-Gordon equation”, J. Phys. A: Math. Gen., 39:23 (2006), 7313–7318 | DOI | MR

[18] M. Hassan, “Darboux transformation of the generalized coupled dispersionless integrable system”, J. Phys. A: Math. Theor., 42:6 (2009), 065203, 11 pp., arXiv: 0912.1671 | DOI | MR

[19] N. Mushahid, M. ul Hassan, “A noncommutative coupled dispersionless system. Darboux transformation and explicit solutions”, Mod. Phys. Lett. A, 29:39 (2014), 1450206, 20 pp. | DOI | MR

[20] Kh. Vadzhakhat A. Riaz, M. Khassan, “Preobrazovanie Darbu dlya poludiskretnogo uravneniya korotkikh impulsov”, TMF, 194:3 (2018), 418–435 | DOI | DOI | MR

[21] H. Wajahat A. Riaz, “Noncommutative coupled complex modified Korteweg–de Vries equation: Darboux and binary Darboux transformations”, Modern Phys. Lett. A, 34:7–8 (2019), 1950054, 15 pp. | MR

[22] Z. Amjad, B. Haider, “Binary Darboux transformation of time-discrete generalized lattice Heisenberg magnet model”, Chaos Solitons Fractals, 130 (2020), 109404, 10 pp. ; “Darboux transformations of supersymmetric Heisenberg magnet model”, J. Phys. Commun., 2:3 (2018), 035019, 8 pp. | DOI | MR | DOI

[23] Z. Amdzhad, D. Khan, “Binarnoe preobrazovanie Darbu dlya uravneniya Ablovitsa–Kaupa–Nyuella–Sigura otritsatelnogo poryadka”, TMF, 206:2 (2021), 149–163 | DOI | DOI | MR

[24] H. Sarfraz, U. Saleem, “Darboux transformation and multi-soliton solutions of local/nonlocal $N$-wave interactions”, Modern Phys. Lett. A, 32:36 (2017), 1750196, 18 pp. ; “Integrable discretizations of AB system and multi-soliton solutions”, Commun. Nonlinear Sci. Numer. Simul., 79 (2019), 104921, 12 pp. | DOI | MR | DOI | MR

[25] U. Salim, Kh. Sarfraz, Ya. Khanif, “Dinamika kink-solitonnykh reshenii $(2+1)$-mernogo uravneniya sinus-Gordon”, TMF, 210:1 (2022), 80–98 | DOI | DOI | MR

[26] I. M. Gelfand, D. Krob, A. Lascoux, B. Leclerc, V. S. Retakh, J.-Y. Thibon, “Noncommutative symmetric functions”, Adv. Math., 112:2 (1995), 218–348 | DOI | MR

[27] I. M. Gelfand, V. S. Retakh, “Teoriya nekommutativnykh determinantov i kharakteristicheskie funktsii grafov”, Funkts. analiz i ego pril., 26:4 (1992), 1–20 ; “Детерминанты матриц над некоммутативными кольцами”, 25:2 (1991), 13–25 | DOI | MR | Zbl | DOI | MR | Zbl

[28] I. Gelfand, S. Gelfand, V. Retakh, R. L. Wilson, “Quasideterminants”, Adv. Math., 193:1 (2005), 56–141 | DOI | MR