Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws
We consider two physically and mathematically distinct regularization mechanisms of scalar
hyperbolic conservation laws. When the flux is convex, the combination of diffusion and …
hyperbolic conservation laws. When the flux is convex, the combination of diffusion and …
A rapid numerical method for solving Serre–Green–Naghdi equations describing long free surface gravity waves
A new numerical method for solving the Serre–Green–Naghdi (SGN) equations describing
dispersive waves on shallow water is proposed. From the mathematical point of view, the …
dispersive waves on shallow water is proposed. From the mathematical point of view, the …
Modulational instability in equations of KdV type
It is a matter of experience that nonlinear waves in a dispersive medium, propagating
primarily in one direction, may appear periodic in small space and time scales, but their …
primarily in one direction, may appear periodic in small space and time scales, but their …
Perfectly matched layers methods for mixed hyperbolic–dispersive equations
Absorbing boundary conditions are important when one simulates the propagation of waves
on a bounded numerical domain without creating artificial reflections. In this paper, we …
on a bounded numerical domain without creating artificial reflections. In this paper, we …
Modulation theory solution for nonlinearly resonant, fifth‐order Korteweg–de Vries, nonclassical, traveling dispersive shock waves
A new class of resonant dispersive shock waves was recently identified as solutions of the
Kawahara equation—a Korteweg–de Vries (KdV) type nonlinear wave equation with third …
Kawahara equation—a Korteweg–de Vries (KdV) type nonlinear wave equation with third …
Discontinuous shock solutions of the Whitham modulation equations as zero dispersion limits of traveling waves
Whitham modulation theory describes the zero dispersion limit of nonlinear disperesive
partial differential equations (PDEs) by a system of conservation laws for the parameters of …
partial differential equations (PDEs) by a system of conservation laws for the parameters of …
Spectral stability of inviscid roll waves
We carry out a systematic analytical and numerical study of spectral stability of
discontinuous roll wave solutions of the inviscid Saint-Venant equations, based on a …
discontinuous roll wave solutions of the inviscid Saint-Venant equations, based on a …
[PDF][PDF] Small-amplitude finite-depth Stokes waves are transversally unstable
arxiv:2409.01663v1 [math.AP] 3 Sep 2024 Page 1 arxiv:2409.01663v1 [math.AP] 3 Sep 2024
SMALL-AMPLITUDE FINITE-DEPTH STOKES WAVES ARE TRANSVERSALLY UNSTABLE …
SMALL-AMPLITUDE FINITE-DEPTH STOKES WAVES ARE TRANSVERSALLY UNSTABLE …
Stability of traveling wave solutions of nonlinear dispersive equations of NLS type
We present a rigorous modulational stability theory for periodic traveling wave solutions to
equations of nonlinear Schrödinger type. For Hamiltonian dispersive equations with a non …
equations of nonlinear Schrödinger type. For Hamiltonian dispersive equations with a non …
Stability of viscous St. Venant roll waves: from onset to infinite Froude number limit
We study the spectral stability of roll wave solutions of the viscous St. Venant equations
modeling inclined shallow water flow, both at onset in the small Froude number or “weakly …
modeling inclined shallow water flow, both at onset in the small Froude number or “weakly …