Soliton solutions to generalized (3 + 1)-dimensional shallow water-like equation using the (ϕ'/ϕ,1/ϕ)-expansion method

Dey, Pinakee; Sadek, Lamiaa H.; Tharwat, M. M.; Sarker, Shuvo; Karim, Rezaul; Akbar, M. Ali; Elazab, Nasser S.; Osman, M. S.

doi:10.1080/25765299.2024.2313245

Cited by 8 publications

(1 citation statement)

References 48 publications

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“…Based on the results, we can establish a fifth-order nonlinear Schrödinger equation of ocean surface gravity waves. Afterward, the corresponding abundant solutions can be obtained through various methods [36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

The Dynamical and Kinetic Equations of Four-Five-Six-Wave Resonance for Ocean Surface Gravity Waves in Water with a Finite Depth

Lin,

Huang

2024

Symmetry

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Based on the Hamilton canonical equations for ocean surface waves with four-five-six-wave resonance conditions , the determinate dynamical equation of four-five-six-wave resonances for ocean surface gravity waves in water with a finite depth is established, thus leading to the elimination of the nonresonant second-, third-, fourth-, and fifth-order nonlinear terms though a suitable canonical transformation. The four kernels of the equation and the 18 coefficients of the transformation are expressed in explicit form in terms of the expansion coefficients of the gravity wave Hamiltonian in integral-power series in normal variables. The possibilities of the existence of integrals of motion for the wave momentum and the wave action are discussed, particularly the special integrals for the latter. For ocean surface capillary–gravity waves on a fluid with a finite depth, the sixth-order expansion coefficients of the Hamiltonian in integral-power series in normal variables are concretely provided, thus naturally including the classical fifth-order kinetic energy expansion coefficients given by Krasitskii.

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Section: Introductionmentioning

confidence: 99%

The Dynamical and Kinetic Equations of Four-Five-Six-Wave Resonance for Ocean Surface Gravity Waves in Water with a Finite Depth

Lin,

Huang

2024

Symmetry

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A Novel Investigation on Propagation of Envelop Optical Soliton Structure Through a Dispersive Medium in the Nonlinear Whitham–Broer–Kaup Dynamical Equation

Iqbal,

Lu,

Faridi

et al. 2024

Int J Theor Phys

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A generalized nonlinear Schrödinger equation with logarithmic nonlinearity and its Gaussian solitary wave

Hosseini,

Alizadeh,

Hinçal

et al. 2024

Opt Quant Electron

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In the current paper, a generalized nonlinear Schrödinger (gNLS) equation with logarithmic nonlinearity is studied as a model for the propagation of optical pulses. More precisely, after applying a specific hypothesis for the solution of the governing equation, its Gaussian solitary wave is retrieved using the ansatz method. Some numerical simulations in two- and three-dimensional postures are presented to investigate the impact of different physical parameters on Gaussian solitary wave’ dynamics. Results confirm that the physical parameters of the gNLS equation have a key role in controlling the dynamics of the Gaussian solitary wave.

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Soliton solutions to generalized (3 + 1)-dimensional shallow water-like equation using the (ϕ'/ϕ,1/ϕ)-expansion method

Cited by 8 publications

References 48 publications

The Dynamical and Kinetic Equations of Four-Five-Six-Wave Resonance for Ocean Surface Gravity Waves in Water with a Finite Depth

The Dynamical and Kinetic Equations of Four-Five-Six-Wave Resonance for Ocean Surface Gravity Waves in Water with a Finite Depth

A Novel Investigation on Propagation of Envelop Optical Soliton Structure Through a Dispersive Medium in the Nonlinear Whitham–Broer–Kaup Dynamical Equation

A generalized nonlinear Schrödinger equation with logarithmic nonlinearity and its Gaussian solitary wave

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