Adaptive method of lines solutions for the extended fifth-order Korteweg–de Vries equation

In this paper, we investigate the dynamics and interaction properties of recently discovered “embedded solitons” in an extended fifth-order KdV model inspired by water waves in the presence of surface tension. The dynamical behaviour of the solitons can be efficiently followed by using a moving or an adaptive finite difference mesh in combination with a suitable time-integrator. We will demonstrate this numerically for different types of wave solutions, such as solitary waves, multihumped waves, and interacting waves.