On the non-integrability of the spherically-symmetric nonlinear Schrodinger equation in the Langmuir collapse problem
Abbreviated Journal Title
Phys. Lett. A
PAINLEVE PROPERTY; Physics, Multidisciplinary
In the present paper we give some analytic considerations of the spherically-symmetric nonlinear Schrodinger equation arising in the Langmuir collapse problem. We will make a systematic exploration of the various group symmetries of this equation and show that the latter possesses only a three-parameter symmetry group. We will then give a variational formulation of this equation and use the three-parameter symmetry group to show that the equation in question possesses apparently only two polynomial conservation laws. Finally, we will make a study of the singularity structure of the present equation and show that it does not seem to possess the Painleve property. The conclusion is that the spherically-symmetric nonlinear Schrodinger equation in question is apparently not integrable. (C) 1998 Elsevier Science B.V.
Physics Letters A
"On the non-integrability of the spherically-symmetric nonlinear Schrodinger equation in the Langmuir collapse problem" (1998). Faculty Bibliography 1990s. 2456.