Similarity solutions to nonlinear models of coupled fractional equations

Abstract

Scalar similarity transformation method is extended to nonlinear models of coupled fractional equations, as to 2‐coupled fractional generalized derivative nonlinear schrödinger (GDNLS) equations, whose two similarity solutions corresponding to time‐fractional GDNLS equations and space‐fractional GDNLS equations are obtained, respectively. Furthermore, by using generalized similarity transformation 3‐coupled fractional nonlinear Heisenberg equations are reduced to ordinary differential equations, from which three different similarity solutions are also worked out, including a kind of traveling‐wave similarity solutions.