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

Abstract

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 third- quintic-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.

Keywords

• : Nonlinear Schrödinger Equations
• Nonlinear Wave Propagation
• Generalized Elastic Medium

Üçüncü Mertebe Dispersiyon Terimli Beşli-Yedili Doğrusal Olmayan Schrödinger Denklemi

Abstract

Bu çalışmada, genelleştirilmiş, kübik doğrusal olmayan elastik bir ortamda yayılan boyuna bir dalgada, yüksek mertebeden dağılım ve doğrusal olmayan etkilerin katkılarını incelemek için beşli-yedili doğrusal olmayan modülasyonu düşünülmektedir. Son zamandaki çalışmalarda, hemen hemen tek dalga sayılı dalga çözümlerinin çok ölçekli açılımı kullanılarak boyuna bir dalganın modülasyonu için üçüncü mertebeden dispersiyon terimli kübik, doğrusal olmayan Schrödinger denklemi elde edildi. Elde edilen denklemde bazı doğrusal olmayan terimlerin katsayılarının yer almadığı belirli bir malzeme sabiti ve dalga sayısı değerleri seçilirse, boyuna bir dalganın davranışını tanımlamak için, doğrusal olmayan etkileri dağılım etkilerle dengelendiği yeni bir pertürbasyon açılımına ihtiyaç vardır. Sonuç olarak, üçüncü dereceden dağılım terimli beşli-yedili doğrusal olmayan Schrödinger denklemi, beşli-yedili doğrusal olmayan etkinin üçüncü mertebeden dağılım terimiyle dengelendiği yeni bir model olarak elde edilir.

Keywords

• Doğrusal Olmayan Schrödinger Denklemleri
• Doğrusal Olmayan Dalga Yayılımı
• Genelleştirilmiş Elastik Ortam

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