Jaulent–Miodek evolution equation: Analytical methods and various solutions

Abstract

In this study, the m+1G′-expansion technique and the extended rational sine–cosine approach are applied to investigate the (2+1)-dimensional integrodifferential equation, namely the Jaulent–Miodek evolution equation (JMEE). Via these powerful approaches, some wave solutions to the JMEE evolution equation are successfully constructed. Using suitable values of the parameters, we plot the 2- and 3-dimensional graphs of the reported solutions. The two utilized approaches are powerful and efficient mathematical tools that secure important wave solutions. The reported solutions in this study may be used in explaining the physical features of various nonlinear physical models.

Keywords

• Integro-differential Jaulent–Miodek evolution equation
• (m＋1/G′)-expansion method
• Extended rational sine–cosine method