Inclusion of dispersive terms in the averaged Lagrangian method: turning to the complex amplitude of envelope View Full Text


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Article Info

DATE

2015-07

AUTHORS

Yu. V. Sedletsky

ABSTRACT

Whitham’s method of averaged Lagrangian is extended to include dispersive terms on the example of Stokes waves on the surface of a layer of ideal fluid. We derive a Lagrangian with explicit AxA¯x and AxA¯ terms partially present in Whitham’s Lagrangian in implicit form in the term with nonlinear frequency, A being the complex-valued amplitude of the wave envelope. The AxA¯x term generates the ax2 term in the dispersive part of the Lagrangian, in addition to Whitham’s terms with a2 and a4 (a being the real wave amplitude). The use of complex amplitude of envelope in the averaged Lagrangian allowed us to avoid the introduction of the nonlinear dispersion relation in the Whitham’s method. The variation of the generalized Lagrangian gives the correct evolution equations for the wave envelope and velocity potential. More... »

PAGES

383-393

References to SciGraph publications

Journal

TITLE

Nonlinear Dynamics

ISSUE

1-2

VOLUME

81

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11071-015-1998-0

DOI

http://dx.doi.org/10.1007/s11071-015-1998-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1006197758


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