Geodesic
Symmetry analysis and exact explicit solutions for Kadomtsev–Petviashvili–Burgers equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 8, pp. 1467-1475

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

We apply the group theory to Kadomtsev–Petviashvili–Burgers (KPBII) equation which is a natural model for the propagation of the two-dimensional damped waves. In correspondence with the generators of the symmetry group allowed by the equation, new types of symmetry reductions are performed. Some new exact solutions are obtained, which can be in the form of solitary waves and periodic waves. Specially, our solutions indicate that the equation may have time-dependent nonlinear shears. Such exact explicit solutions and symmetry reductions are important in both applications and the theory of nonlinear science. 
@article{ZVMMF_2011_51_8_a9,
     author = {Long Wei},
     title = {Symmetry analysis and exact explicit solutions for {Kadomtsev{\textendash}Petviashvili{\textendash}Burgers} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1467--1475},
     publisher = {mathdoc},
     volume = {51},
     number = {8},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a9/}
}
TY  - JOUR
AU  - Long Wei
TI  - Symmetry analysis and exact explicit solutions for Kadomtsev–Petviashvili–Burgers equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 1467
EP  - 1475
VL  - 51
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a9/
LA  - en
ID  - ZVMMF_2011_51_8_a9
ER  - 
%0 Journal Article
%A Long Wei
%T Symmetry analysis and exact explicit solutions for Kadomtsev–Petviashvili–Burgers equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 1467-1475
%V 51
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a9/
%G en
%F ZVMMF_2011_51_8_a9
Long Wei. Symmetry analysis and exact explicit solutions for Kadomtsev–Petviashvili–Burgers equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 8, pp. 1467-1475. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a9/