We consider two physically and mathematically distinct regularization mechanisms of scalar
hyperbolic conservation laws. When the flux is convex, the combination of diffusion and …

There is growing physical and mathematical interest in the hydrodynamics of
dissipationless/dispersive media. Since GB Whitham's seminal publication fifty years ago …

We present an introduction to the theory of dispersive shock waves in the framework of the
approach proposed by Gurevich and Pitaevskii (Zh. Eksp. Teor. Fiz., Vol. 65, p. 590 …

The complete classification of solutions to the defocusing complex modified KdV equation
with step-like initial condition is studied by the finite-gap integration approach and Whitham …

The Riemann problem of the high‐order Jaulent–Miodek (JM) equation with initial data of
step discontinuity is explored by Whitham modulation theory, which is a modified version of …

We address the most general periodic travelling wave of the modified Korteweg–de Vries
(mKdV) equation written as a rational function of Jacobian elliptic functions. By applying an …

We suggest a method for calculation of parameters of dispersive shock waves in the
framework of Whitham modulation theory applied to nonintegrable wave equations with a …

Several threads of the last 25 years' developments in nonlinear wave theory that stem from
the classical Korteweg–de Vries (KdV) equation are surveyed. The focus is on various …

Traveling wave solution of the Gardner equation is studied analytically by using the two
dependent (G′/G, 1/G)-expansion and (1/G′)-expansion methods and direct integration …

An alternative way for the derivation of the new Korteweg–de Vries (KdV)-type equation is
presented. The equation contains terms depending on the bottom topography (there are six …