Motivated by the ongoing study of dispersive shock waves in non integrable systems, we propose and analyze a set wave parameters for periodic large class Hamiltonian partial differential systems—including generalised Korteweg–de Vries equations Euler–Korteweg systems—that are well-behaved both small amplitude wavelength limits. We use this parametrisation to determine fine asymptotic properties...

The behavior of linear and nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma including inertialess electrons and positrons, ions, and mobile positive/negative dust grains are studied. Reductive perturbation method is employed for small and finite amplitude DAWs. To investigate the solitary waves, the Korteweg–de Vries (KdV) equation is derived and the solution is presented. B...

Recent advances in the numerical solution of Riemann–Hilbert problems allow for the implementation of a Cauchy initial value problem solver for the Korteweg–de Vries equation (KdV) and the defocusing modified Korteweg–de Vries equation (mKdV), without any boundary approximation. Borrowing ideas from the method of nonlinear steepest descent, this method is demonstrated to be asymptotically accur...

We derive rational solutions in Casoratian form for the Nijhoff-Quispel-Capel (NQC) equation by using lattice potential Korteweg-de Vries (lpKdV) and two Miura transformations between ...