## Exact solutions of a two-dimensional nonlinear Schrödinger equation.(English)Zbl 1241.35191

Summary: We convert the resulting nonlinear equation for the evolution of weakly nonlinear hydrodynamic disturbances on a static cosmological background with self-focusing in a two-dimensional nonlinear Schrödinger (NLS) equation. Applying the function transformation method, the NLS equation is transformed to an ordinary differential equation, which depends only on one function $$\xi$$ and can be solved. The general solution of the latter equation in $$\zeta$$ leads to a general solution of the NLS equation. A new set of exact solutions for the two-dimensional NLS equation is obtained.

### MSC:

 35Q55 NLS equations (nonlinear Schrödinger equations) 35A24 Methods of ordinary differential equations applied to PDEs 35Q85 PDEs in connection with astronomy and astrophysics

### Keywords:

NLS equation; hydrodynamics; exact solutions
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### References:

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