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# Communications in Mathematical Sciences

## Volume 5 (2007)

### Number 2

### New exact solutions for the cubic-quintic nonlinear Schrödinger equation

Pages: 243 – 252

DOI: http://dx.doi.org/10.4310/CMS.2007.v5.n2.a1

#### Authors

#### Abstract

The algebraic method is developed to obtain new exact solutions, including stationary wave solutions and traveling wave solutions, for the cubic-quintic nonlinear Schrödinger (NLS) equation. Specifically, we present two general solution formulae, which degenerate to the corresponding solution of the cubic NLS equation, when the quintic nonlinear term is absent. It is expected that they are useful in correlative physics fields.

#### Keywords

The cubic-quintic nonlinear SchrÄodinger equation; the stationary wave solution; traveling wave solution

#### 2010 Mathematics Subject Classification

35B20, 35Q35, 37K45