On the superposition of solutions of the (3+1) dimensional Charney-Obukhov equation for the ocean

Article Physics, Multidisciplinary

Coupled superposed solutions in nonlinear nonlocal equations

Avinash Khare et al.

Summary: We investigate novel periodic and hyperbolic solutions of an Ablowitz-Musslimani variant of the coupled nonlocal, nonlinear Schrödinger equation and a coupled nonlocal modified Korteweg-de Vries equation, which can be expressed as a linear superposition of two hyperbolic or two periodic kink or pulse solutions. Additionally, we discuss other solutions admitted by these coupled equations. These findings highlight the extension of the notion of superposed solutions to coupled nonlocal nonlinear equations.

ANNALS OF PHYSICS (2023)

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Article Mechanics

Contrasting eddy-driven transport in baroclinically unstable eastward currents and subtropical return flows

G. G. Sutyrin et al.

Summary: This article identifies and explores the fundamental differences in the dynamics of mesoscale vortices in eastward background (EB) parts in mid-latitude ocean gyres and in westward background (WB) return flows. It is found that the systematic meridional drift of eddies in WB flow leads to poleward expulsion of cold-core cyclones and equatorward expulsion of warm-core anticyclones. This lateral transfer mechanism is not captured by local models of homogeneous turbulence. The results indicate the importance of non-local parameterizations of eddy fluxes in subtropical regions with return WB flows.

PHYSICS OF FLUIDS (2022)

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Article Mechanics

New exact spatially localized solutions of the (3+1)-dimensional Charney-Obukhov equation for the ocean

A. G. Kudryavtsev et al.

Summary: New spatially localized solutions are discovered for the Charney-Obukhov equation on the background of a zonal flow. These solutions can describe both irrotational flow and vortex flow with localized vortices, depending on the parameter values.

PHYSICS OF FLUIDS (2022)

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Article Physics, Multidisciplinary

Linear superposition in the general heavenly equation

S. Y. Lou et al.

Summary: This letter discusses the possibility of linear superpositions in nonlinear systems and shows that balancing different nonlinear effects can lead to non-trivial solutions.

PHYSICS LETTERS A (2022)

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Article Physics, Multidisciplinary

On exact solutions of the Charney Obukhov equation for the ocean

A. G. Kudryavtsev et al.

Summary: (English Summary:) In this paper, exact solutions for the (3 + 1)-dimensional nonlinear Charney-Obukhov equation are obtained, and their application in modeling waves and vortices in the ocean is discussed. The solutions for the ocean demonstrate the transition from laminar flow to a flow containing vortices by changing the parameter values.

PHYSICS LETTERS A (2022)

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Article Mathematics, Applied

Research on nonlinear waves of blood flow in arterial vessels

Yuanhong Bi et al.

Summary: This paper investigates the propagation of blood flow in blood vessels by deriving a new higher order nonlinear Schrodinger equation and its traveling wave solution. Analysis shows that the width and velocity of the blood wave increase during propagation. Numerical solutions obtained by the meshless radial basis function method provide more accurate solutions, and influencing factors of stroke volume are discussed for blood diseases.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2021)

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Article Physics, Multidisciplinary