Nonautonomous soliton solutions of the modified Korteweg–de Vries-sine-Gordon equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 11, pp. 1960-1969 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Multisoliton solutions of the modified Korteweg–de Vries-sine-Gordon (mKdV-SG) equation with time-dependent coefficients are considered. Cases describing changes in the shape of soliton solutions (kinks and breathers) observed in gradual transitions between the mKdV, SG, and mKdV-SG equations are numerically studied.
@article{ZVMMF_2016_56_11_a8,
     author = {S. P. Popov},
     title = {Nonautonomous soliton solutions of the modified {Korteweg{\textendash}de} {Vries-sine-Gordon} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1960--1969},
     year = {2016},
     volume = {56},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_11_a8/}
}
TY  - JOUR
AU  - S. P. Popov
TI  - Nonautonomous soliton solutions of the modified Korteweg–de Vries-sine-Gordon equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2016
SP  - 1960
EP  - 1969
VL  - 56
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_11_a8/
LA  - ru
ID  - ZVMMF_2016_56_11_a8
ER  - 
%0 Journal Article
%A S. P. Popov
%T Nonautonomous soliton solutions of the modified Korteweg–de Vries-sine-Gordon equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2016
%P 1960-1969
%V 56
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_11_a8/
%G ru
%F ZVMMF_2016_56_11_a8
S. P. Popov. Nonautonomous soliton solutions of the modified Korteweg–de Vries-sine-Gordon equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 11, pp. 1960-1969. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_11_a8/

[1] Konno K., Kameyama W., Sanuki H., “Effect of weak dislocation potential on nonlinear wave propagation in anharmonic cristal”, J. Phys. Soc. Japan, 37 (1974), 171–176 | DOI

[2] Hirota R., “Exect solution of the Sine-Gordon equation for multiple collisions of solitons”, J. Phys. Soc. Japan, 33 (1972), 1459–1463 | DOI

[3] Sayed S. M., “The Backhand transformation, exact solutions, and conservation laws for the compound Modified Korteveg-de Vries-Sine-Gordon equations which describe pseudospherical surfaces”, J. Appl. Mat., 2013 (2013), 613065 | MR | Zbl

[4] Khater A. H., Callebaut D. K., Sayed S. M., “Conservation laws for some nonlinear evolution equation which describe pseudo-spherical surfaces”, J. Geometry and Physics, 51:2 (2004), 332–352 | DOI | MR | Zbl

[5] Chen D., Zhang D., Deng S., “The novel multi-soliton solutions of the MKdV-sine Gordon equations”, J. Phys. Soc. of Japan, 71:2 (2002), 658–659 | DOI | MR | Zbl

[6] Alejo M. A., Munos C., “On the nonlinear stability of mKdV breathers”, J. Phys. A.: Math. Theor., 45:43 (2012), 432001 | DOI | MR | Zbl

[7] Leblond H., Mihalache D., “Few-optical-cycle solitons: Modified Korteveg-de Vries sine-Gordon equation versus other non-slowly-varying-envelope - approximation models”, Phys. Rev. A, 79 (2009), 063835 | DOI

[8] Leblond H., Mihalache D., “Optical solitons in the few-cycle regime: recent theoretical results”, Romanian Reports in Physic, 63 (2011), 1254–1266

[9] Leblond H., Mihalache D., “Few-optical-cycle dissipative solitons”, J. Phys. A.: Math. Theor., 43:37 (2010), 375205–375222 | DOI | MR

[10] Gomes J. F., de Melo G. R., Ymai L. H., Zimerman A. H., “Nonautonomus mixed nKdV-sinh-Gordon hierarchy”, J. Phys. A.: Math. Theor., 43:39 (2010), 395203–395212 | DOI | MR

[11] Popov S. P., “O primenenii kvazispektralnogo metoda Fure k solitonosoderzhaschim uravneniyam”, Zh. vychisl. matem. i matem. fiz., 50:12 (2010), 2176–2183 | MR | Zbl

[12] Popov S. P., “Vozmuschennye solitonnye resheniya uravneniya sin-Gordona”, Zh. vychisl. matem. i matem. fiz., 49:12 (2009), 2182–2188 | MR

[13] Goatham S. W., Mannering L. E., Hann R., Krusch S., “Dynamics of multi-kinks in the presence of wells and barriers”, Acta Physica Polonica B, 42:10 (2011), 2087–2106 | DOI

[14] Ekomasov E. G., Gumerov A. M., “Kollektivnoe vliyanie primesei na dinamiku kinkov modifitsirovannogo uravneniya sinus-Gordona”, Kompyuternye issledovaniya i modelirovanie, 5:3 (2013), 403–412

[15] Gumerov A. M., Ekomasov E. G., Kudryavtsev R. V., Zakiryanov F. K., “Struktura i svoistva chetyrekhkinkovykh multisolitonov uravneniya sinus-Gordona”, Zh. vychisl. matem. i matem. fiz., 54:3 (2014), 481–495 | DOI | Zbl

[16] Popov S. P., “Vliyanie dislokatsii na kinkovye resheniya dvoinogo sinus-Gordona uravneniya”, Zh. vychisl. matem. i matem. fiz., 53:12 (2013), 2072–2081 | DOI | Zbl

[17] Gumerov A. M., Ekomasov E. G., “Issledovanie vliyaniya tochechnykh defektov na nelineinuyu dinamiku magnitnykh neodnorodnostei”, Pisma o materialakh, 3:2 (2013), 103–105

[18] Ekomasov E. G., Murtazin R. R., Bogomazova O. B., Gumerov A. M., “One-dimensional dynamics of domain walls in two-layer ferromagnet structure with different parameters of magnetic anisotropy and exchange”, J. Magn. Magn. Mater., 339 (2013), 133–137 | DOI

[19] Shamsutdinov M. A., Shamsutdinov D. M., Ekomasov E. G., “Dinamika domennykh stenok v ortorombicheskikh antiferromagnetikakh vblizi predelnoi skorosti”, Fizika metallov i metallovedenie, 96:4 (2003), 16–22

[20] Shamsutdinov M. A., Nazarov V. N., Lomakina I. Yu. i dr., Ferro- i antiferromagnitodinamika. Nelineinye kolebaniya, volny i solitony, Nauka, M., 2009