A variable coefficient nonlinear Schrödinger equation with a four-dimensional symmetry group and blow-up of its solutions

Abstract

A canonical variable coefficient nonlinear Schrödinger equation with a four dimensional symmetry group containing $\SL(2,\mathbb{R})$ group as a subgroup is considered. This typical invariance is then used to transform by a symmetry transformation a known solution that can be derived by truncating its Painlevé expansion and study blow-ups of these solutions in the $L_p$-norm for $p>2$, $L_{\infty }$-norm and in the sense of distributions.

10 pages

References in corpus (1)

• The generalized Davey-Stewartson equations, its Kac-Moody-Virasoro symmetry algebra and relation to DS equations

Cited by in corpus (1)

• Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations