Geodesic
Kink for modificated regularized long-wave equation
Problemy fiziki, matematiki i tehniki, no. 4 (2021), pp. 7-10.

Voir la notice de l'article provenant de la source Math-Net.Ru

A new version of the modified regularized long-wave equation is considered. The equations of such a type are used as an alternative to the Korteweg-de Vries equation. A modification of the equation consists in an accounting the term which describes an interaction of dispersion and dissipation. Using the direct Hirota method for nonlinear equations in partial derivatives a kink-type (antikink-type) solution for modified equation is constructed. A possibility to construct a coupled solution of kink and antikink is analysed.
Keywords: regularized long-wave equation, kink, anti-kink, Hirota direct method. 
@article{PFMT_2021_4_a0,
     author = {M. A. Knyazev},
     title = {Kink for modificated regularized long-wave equation},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {7--10},
     publisher = {mathdoc},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2021_4_a0/}
}
TY  - JOUR
AU  - M. A. Knyazev
TI  - Kink for modificated regularized long-wave equation
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2021
SP  - 7
EP  - 10
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2021_4_a0/
LA  - ru
ID  - PFMT_2021_4_a0
ER  - 
%0 Journal Article
%A M. A. Knyazev
%T Kink for modificated regularized long-wave equation
%J Problemy fiziki, matematiki i tehniki
%D 2021
%P 7-10
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2021_4_a0/
%G ru
%F PFMT_2021_4_a0
M. A. Knyazev. Kink for modificated regularized long-wave equation. Problemy fiziki, matematiki i tehniki, no. 4 (2021), pp. 7-10. http://geodesic.mathdoc.fr/item/PFMT_2021_4_a0/

[1] D.H. Peregrine, “Calculation of the development of an undular bore”, J. Fluid Mech., 25 (1966), 321–330 | DOI

[2] D.H. Peregrine, “Long waves on a beach”, J. Fluid Mech., 25 (1967), 815–827 | DOI

[3] T.B. Benjamin, J.L. Bona, J.J. Mahony, “Model equation for long waves in nonlinear dispersive systems”, Phil. Trans. Royal Soc. London, A, 272 (1972), 47–78 | Zbl

[4] J.L. Bona, P.J. Bryant, “A mathematical model for long waves generated by wavemakers in non-linear dispersive systems”, Proc. Camb. Phil. Soc., 73 (1973), 391–405 | DOI | Zbl

[5] R. Dodd, Dzh. Eilbek, Dzh. Gibbon, Kh. Morris, Solitony i nelineinye volnovye uravneniya, Mir, M., 1984, 694 pp.

[6] J.C. Eilbeck, G.R. McGuire, “Numerical study of the regularized long-wave equation I: Numerical methods”, J. Computational Physics, 19 (1975), 43–57 | DOI | MR | Zbl

[7] J.D. Gibbon, J.C. Eilbeck, R.K. Dodd, “A modified regularized longwave equation with an exact two-soliton solution”, J. Phys. A: Math. and General, 9 (1976), L127–L130 | DOI

[8] J.L. Bona, A. Soyeur, “On the stability of solitary-wave solutions of model equations for long waves”, J. Nonlinear Sci., 4 (1994), 449–470 | DOI | MR | Zbl

[9] Seydi Battal Gazi Karakoc, Samir Kumar Bhowmik, Numerical approximation of the generalized regularized long wave equation using Petrov–Galerkin finite element method, 28 pp., arXiv: 1904.03354 [math.NA]

[10] F. ter Braak, W.J. Zakrewski, Aspects of the modified regularized long-wave equation, 10 pp., arXiv: 1707.00669 [nlin.PS]

[11] M. Ablovits, Kh. Sigur, Solitony i metod obratnoi zadachi, Mir, M., 1982, 479 pp.

[12] R. Radzharaman, Solitony i instantony v kvantovoi teorii polya, Mir, M., 1985, 416 pp.