New rogon waves for the nonautonomous variable coefficients Schrö dinger equation.

In this study, the nonautonomous variable coefficients Schrödinger equation describes rogon waves in ocean dynamics and optics, is reduced to the nonlinear ordinary differential equation by using the direct similarity technique. The reduced equation is a Riccati equation of Jacobi elliptic wave type solutions. Therefore, many new Jacobi elliptic wave, periodic and hyperbolic wave solutions are obtained for the nonautonomous variable coefficients Schrödinger equation with some constraints between the variable coefficients. Moreover, a rational solution is given. Finally, many plots for the new rogon wave solutions are investigated. [ABSTRACT FROM AUTHOR]