THERMAL SCIENCE
International Scientific Journal
INVERSE SCATTERING TRANSFORM FOR A SUPERSYMMETRIC KORTEWEG-DE VRIES EQUATION
ABSTRACT
In this paper, the inverse scattering transform is extended to a super Korteweg-de Vries equation with an arbitrary variable coefficient by using Kulish and Zeitlin’s approach. As a result, exact solutions of the super Korteweg-de Vries equation are obtained. In the case of reflectionless potentials, the obtained exact solutions are reduced to soliton solutions. More importantly, based on the obtained results, an approach to extending the scattering transform is proposed for the supersymmetric Korteweg-de Vries equation in the 1-D Grassmann algebra. It is shown the the approach can be applied to some other supersymmetric non-linear evolution equations in fluids.
KEYWORDS
PAPER SUBMITTED: 2018-05-12
PAPER REVISED: 2018-11-29
PAPER ACCEPTED: 2018-12-01
PUBLISHED ONLINE: 2019-03-31
THERMAL SCIENCE YEAR
2019, VOLUME
23, ISSUE
Supplement 3, PAGES [S677 - S684]
- Zhang, M. X., Liu, Q. P., A Supersymmetric Second Modified KdV Equation, Journal of Nonlinear Mathematical Physics, 14 (2007), 2, pp. 230-237
- Fan, E. G., New Bilinear Bäcklund Transformation and Lax Pair for the Supersymmetric Two-Boson Equation, Studies in Applied Mathematics, 2011 (2014), 3, pp. 284-301
- Mathieu, P., Supersymmetric Extension of the Korteweg-de Vries Equation, Journal of Mathematical Physics, 29 (1988), 11, pp. 2499-2506
- Zhang, M. X., Construction of the New Supersymmetric Systems and Integrability of the Supersymmetric Integrable Systems (in Chinese), Doctorial Degree Dessertation, Beijing Normal University, Beijing, China, 2008
- Kupershmidt B. A., A Super Korteweg-de Vries Equation: an Integrable System, Physics Letters A, 102 (1984), 5-6, pp. 213-215.
- Ghosh S., Sarma D., Bilinearization of N=1 Supersymmetric Modified KdV Equation, Nonlinearity, 16 (2003), 2, pp. 411-418.
- Xue L. L., et al., Supersymmetric KdV Equation: Darboux Transformation and Discrete System, Journal of Physics A: Mathematical and Theoretical, 46 (2013), 20, ID 502001
- Zhang M. X., et al., A New Supersymmetric classical Boussinesq Equation, Chinese Physics B, 17 (2013), 1, pp. 10-17
- Garder, C. S., et al., Method for Solving the Korteweg-de Vries Equation, Physical Review Letters, 19 (1967), 19, pp. 1095-1097
- Chaichian, M., On the Method of Inverse Scattering Problem and Bäcklund Transformations for Supersymmetirc Equations, Physics Letters B, 78 (1978), 4, pp. 413-416
- Girardello, L., Sciuto, S., Inverse Scattering-Like Pproblem for Supersymmetric Models, Physics Letters B, 78 (1978), 3, pp. 267-269
- Izergin, A. G., Kulish, P. P., On the Inverse Scattering Method for the Classical Massive Thirring Model with Anticommuting Variables, Letters in Mathematical Physics, 2 (1978), 4, pp. 297-302
- Izergin, A. G., Kulish, P. P., Inverse Scattering Problem for Systems with Anticommuting Variables and the Massive Thirring Model, Theoretical and Mathematical Physics, 44 (1980), 2, pp. 189-193
- Mikhailov, A. V., Integrability of Supersymmetrical Generalizations of Classical Chiral Models in Two-Dimensional Space-Time, JETP Letters, 28 (1978), 8, pp. 512-515
- P.P. Kulish, S.A. Tsyplyaev, Supersymmetric cosΦ2 Model and the Inverse Scattering Technique, Theoretical and Mathematical Physics, 46 (1981), 2, pp. 172-186
- Kulish, P. P. Zeitlin, A. M., Group-Theoretical Structure and Inverse Scattering Method for the Super-KdV Equation, Journal of Mathematical Sciences, 125 (2005), 2, pp. 203-214
- Yang, X. J., et al., Local Fractional Integral Transforms and their Applications, Elsevier, London, UK, 2015
- Yang, X. J., et al., On Exact Traveling-Wave Solutions for Local Fractional Korteweg-de Vries Equation, Chaos, 26 (2016), 8, pp.1-8
- Yang, X. J., et al., Exact Travelling Wave Solutions for the Local Fractional Two-Dimensional Burgers-Type Equations, Computers and Mathematics with Applications, 73(2017), 2, pp. 203-210
- Yang, X. J., et al., A New Computational Approach for Solving Nonlinear Local Fractional PDEs, Journal of Computational and Applied Mathematics, 339(2018), pp.285-296
- Yang, X. J., et al., Exact Traveling-wave Solution for Local Fractional Boussinesq Equation in Fractal Domain, Fractals, 25(2017), 4, pp.1-6
- Yang, X. J., et al., On Exact Traveling-wave Solutions for Local Fractional Korteweg-de Vries Equation, Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(2016), 8, pp.1-8