Double-soliton and conservation law structures for a higher-order type of Korteweg‐de Vries equation

The second-order Korteweg‐de Vries (sKdV) equation was introduced as a type of KdV-typed model that describes the wave propagations in a weakly nonlinear and weakly dispersive system. However, the question about the multisoliton solution still remains open. In this article, we discovered numerically that the solitons with different speeds and amplitudes seem to be almost unaffected in shapes by passing through each other (though this could cause a change in their position). Such a double-soliton phenomenon characterizes the most important feature of the equation. In addition, we present the conservation laws, Hamiltonian and Lagrangian density functions for the equation and perform the numerical computation to shed light on the existence of soliton phenomenon.