Geodesic
New exact solutions for the sine-Gordon equation in $2+1$ dimensions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 1, pp. 105-111 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper gives three new solutions to solve the 2D sine-Gordon equation. Of particular interest is the Domain wall collision to 2D sine-Gordon equation which to the authors knowledge have not been presented in the literature. 
@article{ZVMMF_2012_52_1_a9,
     author = {S. Johnson and P. Suarez and A. Biswas},
     title = {New exact solutions for the {sine-Gordon} equation in $2+1$ dimensions},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {105--111},
     year = {2012},
     volume = {52},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_1_a9/}
}
TY  - JOUR
AU  - S. Johnson
AU  - P. Suarez
AU  - A. Biswas
TI  - New exact solutions for the sine-Gordon equation in $2+1$ dimensions
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2012
SP  - 105
EP  - 111
VL  - 52
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_1_a9/
LA  - en
ID  - ZVMMF_2012_52_1_a9
ER  - 
%0 Journal Article
%A S. Johnson
%A P. Suarez
%A A. Biswas
%T New exact solutions for the sine-Gordon equation in $2+1$ dimensions
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2012
%P 105-111
%V 52
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_1_a9/
%G en
%F ZVMMF_2012_52_1_a9
S. Johnson; P. Suarez; A. Biswas. New exact solutions for the sine-Gordon equation in $2+1$ dimensions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 1, pp. 105-111. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_1_a9/

[1] Argyris J., Haase M., Heinrich J.C., “Finite element approximation to two-dimensional sine-Gordon solitons”, Comput. Methods. Appl. Mech. and Engng., 86 (1991), 1–26 | DOI | MR | Zbl

[2] Bratsos A.G., “A third order numerical scheme for the two-dimensional sine-Gordon equation”, Math. Comput. Simulat., 76:4 (2007), 271–278 | DOI | MR

[3] Bratsos A.G., “An explicit numerical scheme for the sine-Gordon equation in 2 + 1 dimensions”, Appl. Numer. Analys. Comput. Math., 2:2 (2005), 189–211 | DOI | MR | Zbl

[4] Christiansen P.L., Lomdahl P.S., “Numerical solutions of 2 + 1 dimensional sine-Gordon solitons”, Physica D: Nonlinear Phenomena, 2:3 (1981), 482–494 | DOI | MR | Zbl

[5] Estivez P.G., Prada J., “A generalization of the sine-Gordon equation to 2 + 1 dimensions”, J. Nonlinear Math. Phys., 11:2 (2004), 164–179 | DOI | MR | Zbl

[6] Grella G., Marinaro M., “Special solutions of the sine-Gordon equation in 2 + 1 dimensions”, Letts. Nuovo Cimento, 23:12 (1978), 459–464 | DOI | MR

[7] Hirota R., “Exact three-soliton solution of the two-dimensional sine-Gordon equation”, J. Phys. Soc. Japan., 35:5 (1973), 1566 | DOI

[8] Leibbrandt G., McKeon G., “Some special solutions of the elliptichyperbolic sine equation in 2 + 1 dimensions”, Phys. Letts. A, 61:2 (1977), 83–85 | DOI | MR

[9] Leibbrandt G., “New exact solutions of the classical sine-Gordon equation in 2 + 1 and 3 + 1 dimensions”, Phys. Rev. Letts., 41:7 (1978), 435–438 | DOI

[10] Majumdar K., Roychoudhury R., “Sine-Gordon equation in curved space-time”, Internat. J. Theor. Phys., 33:11 (1994), 2281–2284 | DOI | MR | Zbl

[11] Mirzaei D., Dehghan M., “Boundary elements solution of the two-dimensional sine-Gordon equation using continuous linear elements”, Engng. Analys. with Boundary Elements, 33:1 (2009), 12–24 | DOI | MR | Zbl

[12] Zagrodzinsky J., “Particular solutions of the sine-Gordon equation in 2 + 1 dimensions”, Phys. Lett. A, 72:2 (1979), 284–286 | DOI | MR