22 citations · 27 across the 19 of their papers we have counts for
21 papers
Nonclassical symmetries of polynomial equations and test problems with parameters for computer algebra systems
Inna K. Shingareva, Andrei D. Polyanin
Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" sy…
Two-dimensional nonlinear Schrödinger equations with potential and dispersion given by arbitrary functions: Reductions and exact solutions
Andrei D. Polyanin
For the first time, a nonlinear Schrödinger equation of the general form is considered, depending on time and two spatial variables, the potential and dispersion of which are speci…
Closed-form solutions of the nonlinear Schrödinger equation with arbitrary dispersion and potential
Andrei D. Polyanin, Nikolay A. Kudryashov
For the first time, the general nonlinear Schrödinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equati…
Exact solutions and reductions of nonlinear Schrödinger equations with delay
Andrei D. Polyanin, Nikolay A. Kudryashov
For the first time, Schrödinger equations with cubic and more complex nonlinearities containing the unknown function with constant delay are analyzed. The physical considerations t…
Notes on symmetries and reductions of algebraic equations
Inna K. Shingareva, Andrei D. Polyanin
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce…
Principle of structural analogy of solutions and its application to nonlinear PDEs and delay PDEs
Andrei D. Polyanin
Using the principle of structural analogy of solutions, approaches have been developed for constructing exact solutions of complex nonlinear PDEs, including PDEs with delay, based…