Chin. Phys. B, 2022, Vol. 31(12): 120201    DOI: 10.1088/1674-1056/ac673b
 GENERAL Prev   Next

# Reciprocal transformations of the space-time shifted nonlocal short pulse equations

Jing Wang(王静), Hua Wu(吴华), and Da-Jun Zhang(张大军)
Department of Mathematics, Shanghai University, Shanghai 200444, China
Abstract  Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated. Covariance of dependent and independent variables involved in the reciprocal transformations is investigated. Exact solutions of the space-time shifted nonlocal short pulse equations are given in terms of double Wronskians. Realness of independent variables involved in the reciprocal transformations is verified. Dynamics of some obtained solutions are illustrated.
Keywords:  reciprocal transformation      space-time shifted nonlocal short pulse equation      covariance of variable      solution
Received:  19 March 2022      Revised:  08 April 2022      Accepted manuscript online:  14 April 2022
 PACS: 02.30.Ik (Integrable systems) 02.30.Ks (Delay and functional equations) 05.45.Yv (Solitons)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11875040 and 12171308).
Corresponding Authors:  Da-Jun Zhang     E-mail:  djzhang@staff.shu.edu.cn

 [1] Albares P, Estévez P G and Sardón C 2020 in: Nonlinear Systems and Their Remarkable Mathematical Structures Vol. 2, eds. Euler N and Nucci M C (CRC Press, Taylor & Francis: Boca Raton) p. 1[2] Camassa R and Holm D D 1993 Phys. Rev. Lett. 71 1661[3] Vakhnenko V A 1992 J. Phys. A: Math. Gen. 25 4181[4] Schäfer T and Wayne C E 2004 Physica D 196 90[5] Baran H and Marvan M 2009 J. Phys. A: Math. Theor. 42 404007[6] Chung Y, Jones C K R T, Schäfer T and Wayne C E 2005 Nonlinearity 18 1351[7] Rabelo M L 1987 "Caracterizac$\tilde{\mathrm{a}}$o das Equac$\tilde{\mathrm{o}}$es Diferenciais do Tipo $u_{xt}=F(u, \partial u/\partial x, \cdots, \partial^k u/{\partial x}^k)$, Que Descrevem Superficies Pseudo-esfericas" Doctoral Thesis (University de Brasilia)[8] Beals R, Rabelo M and Tenenblat K 1998 Stud. Appl. Math. 81 125[9] Rabelo M L 1989 Stud. Appl. Math. 81 221[10] Wadati M, Konno K and Ichikawa Y H 1979 J. Phys. Soc. Jpn. 47 1698[11] Sakovich A and Sakovich S 2005 J. Phys. Soc. Jpn. 74 239[12] Pedlosky J 1972 J. Atmos. Sci. 29 680[13] Konno K and Oono H 1994 J. Phys. Soc. Jpn. 63 377[14] Kuetche V K, Bouetou T B and Kofane T C 2007 J. Phys. Soc. Jpn. 76 024004[15] Matsuno Y 2007 J. Phys. Soc. Jpn. 76 084003[16] Pietrzyk M, Kanattsikov I and Bandelow U 2008 J. Nonl. Math. Phys. 15 162[17] Dimakis A and Müller-Hoissen F 2010 Symmetry Integrability Geom.: Meth. Appl. (SIGMA) 6 055[18] Matsuno Y 2011 J. Math. Phys. 52 123702[19] Feng B F 2012 J. Phys. A: Math. Theor. 45 085202[20] Feng B F 2015 Physica D 297 62[21] Ablowitz M J and Musslimani Z H 2013 Phys. Rev. Lett. 110 064105[22] Ablowitz M J and Musslimani Z H 2014 Phys. Rev. E 90 032912[23] Ablowitz M J and Musslimani Z H 2016 Nonlinearity 29 915[24] Fokas A S 2016 Nonlinearity 29 319[25] Ablowitz M J and Musslimani Z H 2016 Stud. Appl. Math. 139 7[26] Lou S Y and Huang F 2017 Sci. Rep. 7 869[27] Gerdjikov V S and Saxena A 2017 J. Math. Phys. 58 013502[28] Song C Q, Xiao D M and Zhu Z N 2017 J. Phys. Soc. Jpn. 86 054001[29] Yang B and Yang J K 2018 Stud. Appl. Math. 140 178[30] Zhou Z X 2018 Stud. Appl. Math. 141 186[31] Ablowitz M J, Feng B F, Luo X D and Musslimani Z H 2018 Stud. Appl. Math. 141 267[32] Chen K, Deng X, Lou S Y and Zhang D J 2018 Stud. Appl. Math. 141 113[33] Chen K and Zhang D J 2018 Appl. Math. Lett. 75 82[34] Deng X, Lou S Y and Zhang D J 2018 Appl. Math. Comput. 332 477[35] Gürses M and Pekcan A 2018 J. Math. Phys. 59 051501[36] Yang J 2018 Phys. Rev. E 98 042202[37] Ablowitz M J and Musslimani Z H 2019 J. Phys. A: Math. Theor. 52 15[38] Yang B and Yang J K 2019 Lett. Math. Phys. 109 945[39] Feng W and Zhao S L 2019 Rep. Math. Phys. 84 75[40] Lou S Y 2019 Stud. Appl. Math. 143 123[41] Chen K, Liu S M and Zhang D J 2019 Appl. Math. Lett. 88 360[42] Liu S M, Wu H and Zhang D J 2020 Rep. Math. Phys. 86 271[43] Zhang D D, van der Kamp P H and Zhang D J 2020 Symmetry Integrability Geom.: Meth. Appl. (SIGMA) 16 060[44] Lou S Y 2020 Commun. Theor. Phys. 72 057001[45] Ablowitz M J, Luo X D and Musslimani Z H 2020 Nonlinearity 33 3653[46] Rao J G, Cheng Y, Porsezian K, Mihalache D and He J S 2020 Physica D 401 132180[47] Matveev V B and Smirnov A O 2020 Theor. Math. Phys. 204 1154[48] Zhang G Q and Yan Z Y 2020 Physica D 402 132170[49] Rybalko Y and Shepelsky D 2021 J. Diff. Equ. 270 694[50] Rybalko Y and Shepelsky D 2021 Commun. Math. Phys. 382 87[51] Liu S Z, Wang J and Zhang D J 2022 Stud. Appl. Math. 148 651[52] Liu Y K and Li B 2017 Chin. Phys. Lett. 34 010202[53] Lou S Y 2020 Acta Phys. Sin. 69 010503 (in Chinese)[54] Song C Q and Zhu Z N 2020 Acta Phys. Sin. 69 010204 (in Chinese)[55] Yang X Y, Zhang Z and Li B 2020 Chin. Phys. B 29 100501[56] Ablowitz M J and Musslimani Z H 2021 Phys. Lett. A 409 127516[57] Zhang D J, Ji J and Zhao S L 2009 Physica D 238 2361[58] Zhao S L, Zhang D J and Ji J 2010 Chin. Phys. Lett. 27 020201[59] Hirota R 1974 Prog. Theor. Phys. 52 1498[60] Shi Y, Shen S F and Zhao S L 2019 Nonlinear Dyn. 95 1257[61] Wang J, Wu H and Zhang D J 2020 Commun. Theor. Phys. 72 045002[62] Wang J and Wu H 2022 Commun. Nonlinear Sci. Numer. Simul. 104 106052[63] Liu S M, Wang J and Zhang D J 2022 Rep. Math. Phys. 89 199[64] Gürses M and Pekcan A 2022 Phys. Lett. A 422 127793