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We consider a density-stratified fluid composed of two immiscible layers separated by a sharp interface. We study the regime of long internal waves interacting with modulated surface wave packets and describe their resonant interaction by a…

Analysis of PDEs · Mathematics 2024-08-22 Adilbek Kairzhan , Christopher Kennedy , Catherine Sulem

Energy transmission over long distances by waves is a key mechanism for many natural processes. This possibility arises when an inhomogeneous medium is arranged in such a manner that it enables a certain type of wave to propagate with…

Fluid Dynamics · Physics 2026-05-05 Semyon Churilov

We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…

Fluid Dynamics · Physics 2017-11-22 Konstantin Ilin

Surface and interfacial weakly-nonlinear ring waves in a two-layer fluid are modelled numerically, within the framework of the recently derived 2+1-dimensional cKdV-type equation. In a case study, we consider concentric waves from a…

Pattern Formation and Solitons · Physics 2016-08-24 K. R. Khusnutdinova , X. Zhang

The minimalist approach in the study of perturbations in fluid dynamics and magnetohydrodynamics involves describing their evolution in the linear regime using a single first-order ordinary differential equation, dubbed principal equation.…

Fluid Dynamics · Physics 2025-02-18 Nektarios Vlahakis

In geophysical environments, wave motions that are shaped by the action of gravity and global rotation bear the name of gravito-inertial waves. We present a geometrical description of gravito-inertial surface waves, which are low-frequency…

Analysis of PDEs · Mathematics 2026-04-21 Yves Colin de Verdière , Jérémie Vidal

A wave equation, that governs finite amplitude acoustic disturbances in a thermoviscous Newtonian fluid, and includes nonlinear terms up to second order, is proposed. In contrast to the model known as the Kuznetsov equation, the proposed…

A computational strategy based on large deviation theory (LDT) is used to study the anomalous statistical features of turbulent surface waves propagating past an abrupt depth change created via a step in the bottom topography. The dynamics…

Fluid Dynamics · Physics 2024-06-12 Di Qi , Eric Vanden-Eijnden

Motivated by applications to underwater explosions and volcanic eruptions, this paper considers the evolution of an initial pressure disturbance in the ocean, including effects due to the dynamic and static compression of water and the free…

Fluid Dynamics · Physics 2026-03-04 R. Pethiyagoda , S. Das , B. Wilks , M. H. Meylan

For the KdV equation with box type initial data, the interaction between a trial soliton and large-scale dispersive mean flow is studied theoretically and numerically. The pure box initial value can cause rarefaction wave and dispersive…

Pattern Formation and Solitons · Physics 2024-09-24 Ruizhi Gong , Deng-Shan Wang

In this paper we address a particular fluid-solid interaction problem in which the solid object is lying at the bottom of a layer of fluid and moves under the forces created by waves travelling on the surface of this layer. More precisely,…

Analysis of PDEs · Mathematics 2018-05-03 Krisztian Benyo

A well-known optimal velocity (OV) model describes vehicle motion along a single lane road, which reduces to a perturbed modified Korteweg-de Vries (mKdV) equation within the unstable regime. Steady travelling wave solutions to this…

Dynamical Systems · Mathematics 2016-08-12 Laura Hattam

Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics,…

Computational Physics · Physics 2014-08-12 David Chappell , Gregor Tanner , Niels Sondergaard , Dominik Loechel

We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical…

Analysis of PDEs · Mathematics 2025-02-06 David I. Ketcheson , Lajos Lóczi , Giovanni Russo

The KdV equation models the propagation of long waves in dispersive media, while the NLS equation models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves. A system that couples the two equations to model…

Pattern Formation and Solitons · Physics 2016-10-12 Bernard Deconinck , Nghiem V. Nguyen , Benjamin L. Segal

This report concerns the inverse problem of estimating a spacially dependent coefficient of a partial differential equation from observations of the solution at the boundary. Such a problem can be formulated as an optimal control problem…

Optimization and Control · Mathematics 2008-09-23 Jesper Carlsson

The algebraic-geometric approach is extended to study solutions of N-component systems associated with the energy dependent Schrodinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows…

Exactly Solvable and Integrable Systems · Physics 2009-10-31 M. S. Alber , Y. N. Fedorov

This paper studies the nonlinear stability of capillary-gravity waves propagating along the interface dividing two immiscible fluid layers of finite depth. The motion in both regions is governed by the incompressible and irrotational Euler…

Analysis of PDEs · Mathematics 2022-03-09 Robin Ming Chen , Samuel Walsh

The static and dynamical properties of a one-dimensional quantum system described by a non-Hermitian Hamiltonian of the so-called Hatano-Nelson type; a tight-binding model with asymmetric (or non-reciprocal) hopping, are studied. The static…

Quantum Physics · Physics 2023-06-21 Takahiro Orito , Ken-Ichiro Imura

The Hamiltonian coupled-mode theory (HCMT), recently derived by Athanassoulis and Papoutsellis [1], provides an efficient new approach for solving fully nonlinear water-wave problems over arbitrary bathymetry. In HCMT, heavy use is made of…

Computational Physics · Physics 2018-02-23 Theodosios K. Papathanasiou , Christos E. Papoutsellis , Gerassimos A. Athanassoulis