Some new solutions for the Derrida–Lebowitz–Speer–Spohn equation

The well-known Derrida–Lebowitz–Speer–Spohn equation is investigated. By using specific ansätze and the classical symmetries of the equation, several families of new exact solutions have been found. In particular, there appear traveling waves that include compactons and soliton–compactons. Some other solutions conserve the mass and exhibit diffusion and convection processes from an instantaneous source and localized peakons.

► New exact solutions of the Derrida–Lebowitz–Speer–Spohn equation are found.
► Specific ansätze are used to find several families of new exact solutions from the symmetries of the equation.
► Some interesting structures (sources, compactons, soliton–compactons, etc.) for the solutions are shown.