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

Before beginning the material on dimensional analysis, it is worth considering a simple
example that demonstrates what we are doing. One that qualifies as simple is the situation of …

The mathematical description of localized solitons in the presence of large‐scale waves is a
fundamental problem in nonlinear science, with applications in fluid dynamics, nonlinear …

Discontinuity structures in solutions of a hyperbolic system of equations are considered. The
system of equations has a rather general form and, in particular, can describe the …

The aim of this work is multifold. Firstly, it intends to present a complete, quantitative and self-
contained description of the periodic traveling wave solutions and Whitham modulation …

Ubiquitous nonlinear waves in dispersive media include localized solitons and extended
hydrodynamic states such as dispersive shock waves. Despite their physical prominence …

The possibility of shocks was first suggested by Stokes in 1848, but no consistent theory
emerged for another almost 30 years. Indeed, severe criticism by Lord Kelvin and Lord …

We study the long-time asymptotic behavior of the solution q(x,t), x∈R, t∈R^+, of the
modified Korteweg--de Vries equation (MKdV) q_t+6q^2q_x+q_xxx=0 with step-like initial …

In this paper, we investigate the combined KdV-mKdV equation which serves as a valuable
tool in the study of water waves, enabling researchers to understand and predict the …

Undular bore (dispersive shock wave) solutions in the (3+ 1) dimensional modified
Kadomtsev-Petviashvili (mKP) equation for step type initial condition along a paraboloid …