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Journals / Turkish Journal of Mathematics / 1998 / Cilt: 22 - Sayı: 3

Derivation of Separable Amplitude Equations by Multiple Scales Method

Mehmet Naci ÖZER, Dursun ESER

Pages
309–317
DOI
—

Abstract

The method of multiple scales is used to derive separable nonlinear Schrödinger equations as amplitude equation from three component 2D nonlinear Klein-Gordon Equation. We further discuss the integrability of the derived separable amplitude equations and reduce them into finite dimensional Hamiltonian systems. Finally we give first integrals for the reduced systems.

Özet

The method of multiple scales is used to derive separable nonlinear Schrödinger equations as amplitude equation from three component 2D nonlinear Klein-Gordon Equation. We further discuss the integrability of the derived separable amplitude equations and reduce them into finite dimensional Hamiltonian systems. Finally we give first integrals for the reduced systems.

Keywords: Multiple Scales Method, Three Component 2D Nonlinear Klein-Gordon Equation, Separable Amplitude NLS Equation, Spectral Problem, Separable Integrable Hamiltonian system. 1991 Mathematics Subject Classification: 35B20, 35Q53, 35Q55, 58G18.