Geodesic
Riccati pseudopotential of AKNS two-family NLPDEs by Painlev\'e analysis
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 478-486

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

Finding the Bäcklund transformation from the singularity structure only is impossible with the method of Weiss if the PDE has two families of singularities with opposite principal parts, such as the modified KdV and sine-Gordon equations. For such PDEs, we first consider the truncation with one manifold, derive the Darboux transformation (DT) and show that it involves the two entire functions associated to each family. Their ratio is then assumed to satisfy the most general Riccati system. This hypothesis combined with the DT generates a very small number of determining equations, admitting a unique solution, equivalent to the matricial Lax pair by the usual linearization of the Riccati system. 
@article{TMF_1994_99_3_a16,
     author = {M. Musette and R. Conte},
     title = {Riccati pseudopotential of {AKNS} two-family {NLPDEs} by {Painlev\'e} analysis},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {478--486},
     publisher = {mathdoc},
     volume = {99},
     number = {3},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a16/}
}
TY  - JOUR
AU  - M. Musette
AU  - R. Conte
TI  - Riccati pseudopotential of AKNS two-family NLPDEs by Painlev\'e analysis
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1994
SP  - 478
EP  - 486
VL  - 99
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a16/
LA  - ru
ID  - TMF_1994_99_3_a16
ER  - 
%0 Journal Article
%A M. Musette
%A R. Conte
%T Riccati pseudopotential of AKNS two-family NLPDEs by Painlev\'e analysis
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1994
%P 478-486
%V 99
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a16/
%G ru
%F TMF_1994_99_3_a16
M. Musette; R. Conte. Riccati pseudopotential of AKNS two-family NLPDEs by Painlev\'e analysis. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 478-486. http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a16/