Iryna Yehorchenko
Using contact transformations for construction of exact solutions of the Schrodinger equation with power, logarithm and derivative nonlinearities
We will use a reduction procedure to the Schr/"odinger equation with power, logarithm and derivative nonlinearities. The resulting reduction conditions (overdetermined systems of first- and second-order PDEs) may be solved by means of contact and hodograph transformations. Solutions produce ansatzes leading to exact solutions of the original equations. In some cases we can obtain only solutions that may be obtained also by Lie symmetry algorithm, but there are special cases when it is possible to obtain new families of exact solutions.
