Long-time asymptotics for the Korteweg-de Vries equation with integrable reflectionless initial data by Jonathan Eckhardt

“…We show that solutions of the Korteweg–de Vries equation with reflectionless integrable initial data decompose into a (in general infinite) linear superposition of solitons after long enough time. …”
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Experimental and theoretical study of longitudinal undular bores generated by fracture by Curtis Hooper

“…A Gardner equation is derived as a uni-directional model by looking for a solution in the form of an asymptotic multiple scales expansion.The leading order viscoelastic term is introduced from a suitable spring and dashpot model, and higher order nonlinear and dispersive corrections are introduced based on the extended Korteweg - de Vries equation for a hyperelastic rod, which results in the viscoelastic extended Korteweg – de Vries (veKdV) equation.The veKdV equation is solved using a pseudospectral method, with an initial profile that is numerically fitted to experimental measurements that are taken close to the fracture site. …”
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