Coupled superposed solutions in nonlinear nonlocal equations

Khare, Avinash; Saxena, Avadh

doi:10.1016/j.aop.2023.169217

Cited by 3 publications

(1 citation statement)

References 26 publications

(19 reference statements)

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“…Can one extend this notion to nonlocal theories? Recently, we have made an attempt in this direction [21,22] and partially extended it in the case of nonlocal NLS [23,24],…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Superposed periodic kink and pulse solutions of coupled nonlinear equations

Khare¹,

Banerjee²,

Saxena³

2023

Preprint

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We obtain novel periodic solutions in terms of Jacobi elliptic functions of a coupled φ 4 model as well as a coupled nonlinear Schrödinger equation (NLS) model which can be re-expressed as a linear superposition of a periodic kink and antikink, or two periodic kinks or two periodic pulse solutions. These results demonstrate that the notion of the superposed solutions extends to the coupled nonlinear equations as well.

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“…Can one extend this notion to nonlocal theories? Recently, we have made an attempt in this direction [21,22] and partially extended it in the case of nonlocal NLS [23,24],…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Superposed periodic kink and pulse solutions of coupled nonlinear equations

Khare¹,

Banerjee²,

Saxena³

2023

Preprint

View full text Add to dashboard Cite

show abstract

Superposed periodic kink and pulse solutions of coupled nonlinear equations

2023

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

Kudryavtsev

Myagkov

2023

Physics of Fluids

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New exact solutions describing Rossby waves and vortices in ocean propagating along the zonal direction at a constant velocity are found for the (3 + 1)-dimensional nonlinear Charney–Obukhov equation. These solutions are a partial superposition of previously discovered exact solutions of the Charney–Obukhov equation. Partial superposition is found for that part of the solution of the Charney–Obukhov equation, which complements the zonal stream. The presence of such a superposition in the solutions of a nonlinear equation with two nonlinear boundary conditions is a remarkable property of the Charney–Obukhov equation for the ocean and allows one to simulate a wide class of fluid flows based on exact solutions. As an example, we discuss solutions that include superposition of trigonometric functions and the functions of Bessel in a horizontal plane, and superposition of spherically symmetrical solutions in the vertical coordinate. Visualization of the solutions found shows that, depending on the values of the parameters included in the solutions, they can describe both a flow with a large number of vortices and a periodic structure with alternating high and low pressure fronts.

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Coupled superposed solutions in nonlinear nonlocal equations

Cited by 3 publications

References 26 publications

Superposed periodic kink and pulse solutions of coupled nonlinear equations

Superposed periodic kink and pulse solutions of coupled nonlinear equations

Superposed periodic kink and pulse solutions of coupled nonlinear equations

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

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