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For the purpose of a numerical investigation of the nonlocal impacts on the NLS equation, it has been investigated whether envelope solitary wave solutions exist by utilizing the physical and geometric features of the carbon nanotubes. Amplitude dependent wave frequencies, phase and group velocities have been obtained and they have compared for the linear local, the linear nonlocal, the nonlinear local and the nonlinear nonlocal cases.


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  • Nonlinear Nonlocal Equations in the Theory of Waves.

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Nonlinear Waves in Integrable and Nonintegrable Systems

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Authors: Nakao Hayashi Elena Kaikina. Hardcover ISBN: Imprint: Elsevier Science.

Nonlinear water waves and nonlocal model equations

Published Date: 13th January Page Count: View all volumes in this series: North-Holland Mathematics Studies. For regional delivery times, please check When will I receive my book? Sorry, this product is currently out of stock. Institutional Subscription.

Abstract In this paper we briefly present a general approach to the description of the nonlinear and nonlocal Whitham-Benjamin model, based on the introduction of a system of auxiliary fields that interact locally with the initial nonlinear field. In the case of stationary waves a corresponding dynamical system is defined that admits of a Hamiltonian representation.

Some results are presented of a qualitative and numerical analysis of the stationary solitary waves of the Whitham-Benjamin equation with a rapidly decreasing oscillatory kernel. An investigation is made into a phenomenon related to the loss of smoothness of the solution of the original equation and the noncontinuability of these solutions when the structural parameters of the system are changed this phenomenon is analogous to the formation of limiting Stokes waves.

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