Higher-order Long-wave Short-wave Interaction Equations in a Generalized Elastic Solid

Hacinliyan, Irma

doi:10.1063/1.3636941

Cited by 1 publication

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“…However, for fairly short pulses, the CNLS equation is not a correct model of the wave motion, so higher-order dispersive effects need to be included in the evolution equation. Therefore, in the same study [6], the evolution equation with thirdorder dispersive term valid at the level 4…”

Section: Introductionmentioning

confidence: 95%

“…The function u in Equation ( 5) denotes the envelope of the complex amplitude of the short wave. The CNLS equation was recently re-derived in a study examining the contribution of the high-order dispersive effects on the longitudinal wave modulation emitted in a generalized elastic medium [6]. In [6], under the assumption 1 ( , ) 0 Dk  , the components of the displacement vector were expanded into asymptotic power series of .…”

Section: Introductionmentioning

confidence: 99%

“…The CNLS equation was recently re-derived in a study examining the contribution of the high-order dispersive effects on the longitudinal wave modulation emitted in a generalized elastic medium [6]. In [6], under the assumption 1 ( , ) 0 Dk  , the components of the displacement vector were expanded into asymptotic power series of .  Then 0, v  0, w  and the CNLS equation valid at the level 3  was obtained.…”

Section: Introductionmentioning

confidence: 99%

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Quintic-Septic Nonlinear Schrödinger Equation with a Third-Order Dispersion Term

Hacinliyan

2022

Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi

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In the present study, the quintic-septic nonlinear modulation of a longitudinal wave propagating to contribute the dispersive and higher-order nonlinear effects in a generalized cubically nonlinear elastic medium is considered. In recent work, for the modulation of a longitudinal wave, a cubic nonlinear Schrödinger equation with a third-order dispersive term is obtained by using a multi-scale expansion of quasi-monochromatic wave solutions. The thirdquintic-septic longitudinal wave, by choosing specific values of material constants and wave number for which some coefficients of nonlinear terms are disappeared. In this case, a new perturbation expansion is needed to balance nonlinear effects with dispersive effects. As a result, a quintic-septic nonlinear Schrödinger equation with a third-order dispersion term is obtained as a new model that balances quintic-septic nonlinearity with a third-order dispersion term.

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Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%