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 
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/
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     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},
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     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a9/}
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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.

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