New solutions for the unstable nonlinear Schrödinger equation arising in natural science

Abstract

In this work, three mathematical methods are applied, namely, the exp(-φ(ξ))-expansion method, the sine-cosine technique and the Riccati-Bernoulli sub-ODE method for constructing many new exact solutions of the unstable nonlinear Schrödinger equation. The exact solutions are obtained in the form of rational, exponential, trigonometric, hyperbolic functions. These solutions may be so important significance for the explanation of some practical physical problems. The computational work and obtained results show that the presented methods are simple, efficient, straightforward and powerful. Moreover, the presented methods can be employed to many other types of nonlinear partial differential equations arising in mathematics, mathematical physics and other areas of natural sciences. Some solutions are simulated for some particular choices of parameters.

Keywords

• schrödinger equation
• exp(-φ(ξ))-expansion method
• sine-cosine method
• riccati-bernoulli sub-ode method
• new exact solutions