Localized characteristics of lump and interaction solutions to two extended Jimbo–Miwa equations*

Abstract

We focus on the localized characteristics of lump and interaction solutions to two extended Jimbo–Miwa equations. Based on the Hirota bilinear method and the test function method, we construct the exact solutions to the extended equations including lump solutions, lump–kink solutions, and two other types of interaction solutions, by solving the under-determined nonlinear system of algebraic equations for associated parameters. Finally, analysis and graphical simulation are presented to show the dynamical characteristics of our solutions and the interaction behaviors are revealed.