TRANSFORMATIONS OF SOME NONLINEAR EQUATIONS WITH VARIABLE COEFFICIENTS
https://doi.org/10.26583/vestnik.2023.245
Abstract
Transformations for non-linear partial differential equations with a variable coefficient are presented. It is shown that the integrability properties for some equations with variable coefficients are satisfied in a natural way, since these equations are transformed to well-known integrable partial differential equations.
Keywords
soliton transformations,
differential equations with variable coefficients,
integrable differential equations
Supporting agencies: This research was supported by Russian Science Foundation Grant No. 22-11-00141, https://rscf.ru/en/project/22-11-00141/.
About the Authors
P. A. Gribov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
N. A. Kudryashov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
A. A. Kutukov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
References
1. Chan W. L., & Kam‐Shun L. Nonpropagating solitons of the variable coefficient and nonisospectral Korteweg–de Vries equation. Journal of Mathematical Physics, 1989, vol. 30(11), pp. 2521-2526.
2. Lou S. Y. Pseudopotentials, Lax pairs and Backlund transformations for some variable coefficient nonlinear equations. Journal of Physics A: Mathematical and General, 1991, vol. 24(10), L513.
3. Porsezian K. Backlund transformations and explicit solutions of certain inhomogeneous nonlinear Schrodinger-type equations. Journal of Physics A: Mathematical and General, 1991, vol. 24(7), L337.
4. Porsezian K., Daniel, M., Bharathikannan R. Generalized χ-dependent Hirota equation: singularity structure, Bäcklund transformation and soliton solutions. Physics Letters A, 1991, vol. 156(5), pp. 206-210.
5. Winternitz P., Gazeau J. P. Allowed transformations and symmetry classes of variable coefficient Korteweg-de Vries equations. Physics Letters A, 1992, vol. 167(3), pp. 246-250.
6. Gagnon L., Winternitz P. Symmetry classes of variable coefficient nonlinear Schrodinger equations. Journal of Physics A: Mathematical and General, 1993, vol. 26(23), pp. 7061.
7. Kudryashov N. A., Nikitin V. A. Painleve analysis, rational and special solutions of variable coefficient Korteweg-de Vries equations. Journal of Physics A: Mathematical and General, 1994, vol. 27(4), L101.
8. Hirota, R. Exact solution of the Korteweg—de Vries equation for multiple collisions of solitons. Physical Review Letters, 1971, vol. 27(18), pp. 1192.
9. Caudrey P. J., Gibbon J. D., Eilbeck J. C., Bullough R. K. Exact multisoliton solutions of the self-induced transparency and sine-Gordon equations. Physical Review Letters, 1973, vol. 30(6), pp. 237.
10. Kudryashov N.A. Governed optical solitons of the generalized Schrödinger equation with dual-power law of refractive index. Optik, 2022, vol. 266, art. no. 169619.
11. Zhao J., Luan Z., Zhang P., Dai C., Biswas A., Liu W., Kudryashov N. A. Dark three-soliton for a nonlinear Schrödinger equation in inhomogeneous optical fiber. Optik, 2020, vol. 220, art. no. 165189.
12. Popov S. P. Neavtonomnye solitonnye reshenija modificirovannogo uravnenija Kortevega–de Vriza–sinus-Gordona [Nonautonomous soliton solutions of the modified Korteweg–de Vries–sine-Gordon equation]. Computational Mathematics and Mathematical Physics, 2016, vol. 56, № 11, pp. 1960-1969. (in Russian)
13. Liu X., Luan Z., Zhou Q., Liu W., Biswas A. Dark two-soliton solutions for nonlinear Schrödinger equations in inhomogeneous optical fibers. Chinese Journal of Physics, 2019, vol. 61, p. 310-315.
14. Clarkson P. A. Painleve analysis and the complete integrability of a generalized variable-coefficient Kadomtsev-Petviashvili equation. IMA journal of applied mathematics, 1990, vol. 44(1), p. 27-53.
Review
For citations:
Gribov P.A., Kudryashov N.A., Kutukov A.A. TRANSFORMATIONS OF SOME NONLINEAR EQUATIONS WITH VARIABLE COEFFICIENTS. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2023;12(2):90-94. (In Russ.) https://doi.org/10.26583/vestnik.2023.245
Views:
184
Email this article 